In this paper, the prediction of crack propagation with two cracks using machine learning is described. The analysis results of crack propagation by s-version FEM (s-FEM), which combines the automatic mesh generation technique, are used for generation of training and validation datasets. Plural crack propagation with the different vertical distance between the two cracks as a variable are analyzed. The analysis cases are divided into training and validation datasets. In training process, the input parameters are the coordinates of 4 crack tip, the output data are crack propagation vectors, the number of cycles for crack propagation of 0.25 mm. Initial crack configurations should be specified. After the specification, the predictor iteratively predicts crack propagation direction and the number of loading cycles. A prediction accuracy depends on the training datasets, which contains 0.25 mm length of each crack propagation in this study. To improve prediction accuracy, the data augmentation is effectively applied. In case of plural crack interaction, when the crack tips close each other, the accuracy gets worse and worse. Reducing datasets which satisfy the crack coalescence condition, it is shown that the prediction accuracy is improved. Even if training datasets are not enough number for accurate prediction, it is shown that the prediction accuracy is improved by the data augmentation.

This paper presents a method for predicting the crack growth shape and the number of cycles of a two-dimensional fatigue crack under cyclic loading using a convolutional neural network. All of data sets for train are generated by s-version FEM for fatigue crack propagation analysis. The crack propagation simulations were simulated with different slant angles. Crack tip coordinates, crack growth vectors, and numbers of cycles are prepared as a set of train data for one prediction step, which is determined by the minimum mesh size of the crack tip in the s-FEM simulation. Data augmentation technique, which adds a slight noise to input data, is introduced as regularization in this work. We'd like to evaluate the effectiveness of the data augmentation. Additionally, the interpolation ability and extrapolation ability of the prediction model are evaluated. The crack growth shapes and the number of cycles in the prediction step can be predicted within 6%, 11.1% difference with the reference.

Abstract To predict fracture behavior for ductile materials, some ductile fracture simulation methods different from classical approaches have been investigated based on appropriate models of ductile fracture. For the future use of the methods to overcome restrictions of classical approaches, the applicability to the actual components is of concern. In this study, two benchmark problems on the fracture tests supposing actual components were provided to investigate the prediction ability of simulation methods containing parameter decisions. One was the circumferentially through-wall and surface cracked pipes subjected to monotonic bending, and the other was the circumferentially through-wall cracked pipes subjected to cyclic bending. Participants predicted the ductile crack propagation behavior by their own approaches, including finite element method (FEM) employed Gurson–Tvergaard–Needleman (GTN) yielding function with void ratio criterion, are FEM employed GTN yielding function, FEM with fracture strain or energy criterion modified by stress triaxiality, extended FEM with J or ΔJ criterion, FEM with stress triaxiality and plastic strain based ductile crack propagation using FEM, and elastic-plastic peridynamics. Both the deformation and the crack propagation behaviors for monotonic bending were well reproduced, while few participants reproduced those for cyclic bending. To reproduce pipe deformation and fracture behaviors, most of the groups needed parameters that were determined to reproduce pipe deformation and fracture behaviors in benchmark problems themselves and it is still difficult to reproduce them by using parameters only from basic materials tests.

We have been developing an open-source computer-aided engineering (CAE) software, ADVENTURE, which is a general-purpose parallel finite element analysis system and can simulate a large-scale analysis model with supercomputer. For supercomputer architecture such as an exa-scale system, to obtain high computational efficiency for software that requires large-scale numerical calculation data processing, a programming model that considers the hierarchical structure of hardware, such as a microprocessor and memory, is necessary. From this point of view, ADVENTURE system was developed using the hierarchical domain decomposition method (HDDM) as the basic technology for a large-scale data system. HDDM is technology developed by ourselves mainly for numerical analysis method. In particular, we have developed application-specific system software that can obtain high performance by focusing on simulation of continuum mechanics by finite element method (FEM) and particle method which are highly demanded by academic research and industry. We have developed four research items "DDM I/O (input/output) library," "DDM solver library," "DSL for continuum mechanics," and "continuous mechanics simulator." The software, which is the result of our research, is released as open-source software on the sub-project page in the ADVENTURE project homepage. In this chapter, some of those libraries are described in detail.

In order to achieve reliable fatigue crack growth simulations of shafts under cyclic rotary bending by means of the finite element method, the Stress Intensity Factors (SIFs) along a flaw front have to be evaluated for an arbitrary rotational position. However, the evaluation of such SIFs takes much a great computation effort due to geometry modeling necessary to simulate the flaw propagation. In the present study, a fully automated finite element simulation for fatigue growth of flaw, by combining S-FEM, automatic mesh generation technique, and an effective evaluation method of the SIFs, is developed to analyze multi-surface flaw under rotary bending. Fatigue growth simulations of coplanar and non coplanar parallel surface flaws in shafts under rotary bending are carried out to compare the crack growth behaviors between coplanar and non-coplanar surface flaws. (C) 2016 Elsevier Ltd. All rights reserved.

In the S-version finite element method (S-FEM), a local detailed finite element mesh (local mesh) is superimposed on a coarse finite element model (global mesh) representing the global structure. In the S-FEM developed by Tokyo University of Science, the virtual crack closure integral method is employed to evaluate the stress intensity factor, and a local mesh is re-meshed automatically, which enables easy simulations of crack growth by users. Using S-FEM, crack growth can be simulated in both two-and three-dimensional stress fields, under thermal stress field, under welding residual stress field, and in multiple materials. This paper reports the latest results of the simulations of crack growth in the presence of complicated stress fields.

In this study, some benchmark problems on fracture tests for circumferentially through-wall/surface cracked pipes were provided. The participants predicted the ductile crack propagation behavior by their own approaches, including nucleation, growth, and coalescence of voids simulated by Gurson model, ductile crack propagation using stress modified fracture strain (SMFS) model, J-integral based ductile crack propagation using XFEM, CTOA based ductile crack propagation using FEM, stress triaxiality and plastic strain (STPS) based ductile crack propagation using FEM, and ductile crack propagation using peridynamics. Among them, GTN, CTOA and STPS models were not applied to surface crack problems. Discrepancies between the experimental maximum loads and calculated maximum loads were within 10% in most cases and 25% in the maximum case. Element size dependency of analysis parameters were considered in SMFS and GTN models while those were determined from independent material tests. Gurson model can predict slanting crack propagation directions. XFEM which did not need analysis fitting parameters cannot analyze beyond the peaks of load-LPD curves. Crack propagation directions were given and fixed in both CTOA and STPS models. Parameters in Gurson model and peridynamics were optimized to reproduce load-LPD curve in one of the benchmark problems.

A fully automatic fatigue crack growth simulation system is developed using S-version FEM. This system is extended to fractures in heterogeneous materials. In a heterogeneous material, the crack tip stress field becomes mixed-mode (the crack growth path is affected by inhomogeneous materials and mixed-mode conditions). The stress intensity factors in a mixed-mode condition are evaluated using the virtual crack closure method. The criteria for the crack growth amount and crack growth path are based on these stress intensity factors, and the crack growth configurations are obtained. Three crack growth problems are simulated. One is crack growth in a bi-material made of CFRP plate and aluminum alloy. The crack growth paths are compared with the experimental results. The second problem is crack growth in a bi-material made of PMMA and aluminum alloy. By changing the loading condition, several cases are simulated and compared with the experimental results. In the experiment, the crack grows into and along the phase boundary. The effect of the phase boundary is discussed. The last case is crack growth along interface of CFRP plate. (C) 2016 Elsevier Ltd. All rights reserved.

With the growth of computing technologies including both hardware and simulation algorithms, simulation models have become extremely large in scale. Nowadays the visualization of the huge result data obtained by the large scale simulation is one of the main bottlenecks through all the simulation procedures because the large scale simulation is conducted on the computing servers such as supercomputers and the visualization of the result data is done usually on the local client environment. To avoid time consuming transfer of the result data from the computing server to the local client side, we propose a technique for the server-side screening of the result data in advance of the transfer in this paper. Here, the representative quantities of interest are extracted in each component of the assembled structure and illustrated in simple graphs and heat maps. We demonstrate our proposal with a numerical benchmark of one hundred heterogeneous pillars under seismic excitation and concluded that our server-side screening technique helps the users to find the region of interest in whole the result data.

With the growth of computing technologies including both hardware and simulation algorithms, simulation models have become extremely large in scale. Nowadays the visualization of the huge result data obtained by the large scale simulation is one of the main bottlenecks through all the simulation procedures because such large scale simulation is generally conducted on computing servers such as supercomputers, while the visualization is done on local client environments. To avoid time consuming transfer of the result data from the computing server to the local client, we propose techniques for the server-side screening and network visualization of them in advance to their transfer. We demonstrate that our approach contributes to find out the region of interests in whole the result data by a numerical example.

Fully automatic fatigue crack growth simulation system is developed using S-version FEM (SFEM). This system is extended to fracture in heterogeneous material. In the heterogeneous material, crack tip stress field becomes mixed mode condition, and crack growth path is affected by inhomogeneous materials and mixed mode conditions. Stress Intensity Factors (SIF) in mixed mode condition are evaluated using Virtual Crack Closure Method (VCCM). Criteria for crack growth amount and crack growth path are used based on these SIFs, and growing crack configurations are obtained. Three crack growth problems are simulated. One is crack growth in bi-materila made of CFRP plate and Aluminum alloy. Initial crack is located in CFRP plate, and grows toward Aluminum alloy. Crack growing direction changes and results are compared with experimental one. Second problem is crack growth in bimaterial made of PMMA and Aluminum alloy. Initial crack is located in PMMA plate and parallel to phase boundary. By cahnging loading conditions, several cases are simulated and compared with experimental ones. In the experiment, crack grows into pahse boundary and grow along it. This case is simulated precisely, and the effect of pahse boundary is discussed. Last case is Stress Corrosion Cracking (SCC) at Hot-Leg Safe-End of Pressurized Water Rreactor. This location is made of many kinds of steels by welding. In some steel, SCC does not occur and in other steel, SCC is accelerated. As a result, small surface crack grows in complicated manner.

The objective of this study is to evaluate crack growth behavior under cyclic tensile loading considering crack closure effect. Crack growth behavior under cyclic tensile loading on a plate with surface crack is tested. Material is 2017 aluminum alloy. Crack growth process is studied by experiment and simulation. Crack growth behavior is analyzed by S-version FEM. In order to predict crack growth behavior in detail, crack closure effect is taken into account. Crack closure effect along surface crack tip under cyclic tensile loading is analyzed by ANSYS. In order to consider crack closure effect, an effective stress range ratio is introduced. An effective stress range ratio is defined by load range during crack opening over load amplitude. It is found that an effective stress range ratio is small near the surface of the specimen. This means crack growth rate is small near the surface of the specimen. Effective stress intensity factor range is calculated by effective stress range ratio. Using this effective stress intensity factor range, crack growth simulation with crack closure effect is performed by S-FEM. Crack shape and number of cycles of the simulation which considering crack closure effect comes close to experiment. And even if the thickness of the specimen is different, the influence of crack closure effect hardly varies.

In the in-core monitor (ICM) housing of a reactor pressure vessel (RPV), residual stress has been widely reported to cause stress corrosion cracking (SCC) damage in the weld heat-affected zone. For this reason, it is important to evaluate the crack growth conservatively, and with high confidence to demonstrate fitness for service. This paper presents crack growth simulations in an ICM housing, which is welded at two different angles to the RPV. One weld angle is at the bottom of the RPV, and the welding area of the ICM housing is axisymmetric. The other angle is at the curved position of the RPV, and the weld area of the ICM housing is asymmetric. In these weld areas, crack growth behavior is estimated by superposed-finite element method (S-FEM), which allows generation of a global finite model and a detailed local mesh representing the crack independently. In the axisymmetric weld area, axial, slant and circumferential surface cracks are assumed at two locations where the residual stress fields are different from each other: one is isotropic and the other is circumferential. It is shown that crack growth behaviors are different under different residual stress fields. The results of S-FEM are compared with those of the influence function method (IFM), which assumes that an elliptical crack shape exists in a plate. It is shown that the IFM result is conservative compared to that of S-FEM. Next, an axial surface crack is assumed at the uphill, downhill, and midhill asymmetric weld areas. The midhill crack growth behavior is different from the uphill and downhill behaviors. Finally, two surface cracks are simulated in the asymmetric weld area and two initial crack arrangements are assumed. These results show the differences of the crack interaction and the crack growth process.

The heterogeneous material properties affect on crack growth. For this reason, it is important to develop a simulation system to evaluate the crack growth in heterogeneous materials. This paper develops a fully automatic crack growth simulation system in heterogeneous materials based on Superposed FEM (S-FEM). The simulation should be treats mixed-mode loading condition. The virtual crack closure method (VCCM) is used for evaluation of the stress intensity factors (SIFs). The direction of crack growth is calculated by the maximum tangential stress (MTS) criterion, and the growth rate is calculated through Paris law. First, in order to demonstrate the effectiveness, the SIFs evaluated by the developed system are compared with those of reference solution, the boundary element method (BEM) and body force method (BFM). Then, two-dimensional crack growth problems are simulated using the developed system. The first example is crack growth in a plate with an interface between hard and soft materials. The crack tends to grow into soft material through the interface. The crack path and the change of SIFs are studied. The second example is crack growth in a plate with a slant phase interface. Simulated crack paths are compared with that of experimental paths. The well agreement of these crack paths shows the usefulness of the developed system for crack growth simulation in heterogeneous materials.

In the maintenance code for nuclear power plants, initial defects are modeled as elliptical cracks in a plane normal to the tension loading direction. However, in the S-FEM simulation the defect shape, which is subjected to multi-axial loading, is realistically modeled, and the crack growth due to fatigue can be simulated. The conservativeness of the maintenance code is discussed. Parametric studies are conducted by S-FEM for examination of this problem. A simple new proximity rule was proposed, and the results of this new rule are found to be reasonable and conservative. (C) 2014 Elsevier Ltd. All rights reserved.

This paper describes a surface crack growth simulation using a new mesh generation technique. The generated mesh is constituted of all hexahedral elements. Hexahedral elements are suitable for an analysis of fracture mechanics parameters, i.e. stress intensity factor. The advantage of a hexahedral mesh is good accuracy of an analysis and less number of degrees of freedoms than a tetrahedral mesh. In this study, a plural crack growth simulation is computed using the hexahedral mesh and its distribution of stress intensity factor is investigated.

A fully automatic fatigue crack growth simulation system is developed using the s-version Finite Element Method (s-FEM). This system is extended to fractures in heterogeneous materials. In a heterogeneous material, the crack tip stress field has a mixed-mode condition, and the crack growth path is affected by inhomogeneous materials and mixed-mode conditions. Stress intensity factors (SIFs) in the mixed-mode condition are evaluated using the virtual crack closure method (VCCM). The criteria for the crack growth amount and crack growth path are based on these SIFs, and the growing crack configurations are obtained. At first, the basic problem is solved, and the results are compared with some results available in the literature. It is shown that this system gives an adequate accurate estimation of the SIFs. Then, two-dimensional fatigue crack growth problems are simulated using this system. The first example is a plate with an interface between hard and soft materials. The cracks tend to grow in soft materials through the interface. A second example is a plate with distributed hard inclusions. The crack takes a zig-zag path by propagating around the hard inclusions. In each case, the crack growth path changes in a complicated manner. Changes of the SIFs values are also shown and discussed. (C) 2013 Elsevier Ltd. All rights reserved.

It has been reported that stress corrosion cracking damaged in-core monitor housing, which occurred in weld heat-affected zone because of the existence of residual stress. So it is important to evaluate crack growth behavior with high accuracy. In this study, crack growth behavior in ICM Housing is estimated using S-version FEM (S-FEM), which allows generation of core finite model and the detailed mesh representing the crack independently. At First, axial, slant and circumferential surface crack are assumed at two locations where residual stress fields are different from each other. One is isotropic residual stress field, and another is circumferential residual stress field. It is shown that crack growth behaviors are different under different residual stress fields. Next, effect of the slit, which exists between ICM Housing and Pressure Vessel is evaluated. It is shown that the existences of slit increases stress intensity factors of growing surface crack. Finally S-FEM results are compared with those of Influence Function Method (IFM), which assumes that an elliptical crack shape exists in a plate. It is shown that IFM result is conservative than that of S-FEM. © 2013 The Japan Society of Mechanical Engineers.

In this study, mixed-mode fatigue tests are conducted using surface-cracked specimens. Slant surface-cracked specimens are prepared with crack angles of 15 deg, 30 deg, 45 deg, and 60 deg. It is shown that a "factory roof" fracture is formed at the deepest point of the surface crack due to Delta KIII and causes the crack growth rate to decrease. Additionally, fatigue crack growth is simulated using the superposition finite element method (FEM) with crack growth criteria. It is shown that conventional crack growth criteria are not applicable to factory roof fractures. Finally, a modified criterion for the prediction of crack growth rate is proposed, fatigue crack growth simulation is conducted using this criterion, and the results are compared with experimental results.

The objective of this study is the prediction of crack propagation under thermal, residual stress fields using S-Version FEM (S-FEM). By using the S-FEM technique, only the local mesh should be re-meshed and it becomes easy to simulate crack growth. By combining with an auto-meshing technique, the local mesh is re-meshed automatically, and a curved crack path is modeled easily. Virtual crack closure integral method (VCCM) is used to evaluate energy release rate at the crack tip. For crack growth analyses, crack growth rate and growth direction are determined using criteria for mixed mode loading condition. In order to confirm the validity of this analysis, some comparisons with previously reported analyses were done, and good agreement obtained. In this study, residual stress data were provided by JAEA, Japan Atomic Energy Agency, based on their numerical simulation. Stress corrosion crack (SCC) growth analyses in a pipe are conducted in two-dimensional and three-dimensional fields. Two cases, for an axi-symmetric distribution of residual stress in the pipe wall and a non-axisymmetric one are assumed. Effects of residual stress distribution patterns on SCC cracking are evaluated and discussed. (C) 2011 Elsevier Ltd. All rights reserved.

It has been reported that stress corrosion cracking damaged in-core monitor housing (ICM Housing), which occurred in a weld heat-affected zone because of the existence of residual stress. So it is important to evaluate crack growth behavior with high accuracy. In this study, crack growth behavior in ICM Housing is estimated using S-version FEM (S-FEM), which allows generation of the core finite model and the detailed mesh representing the crack independently. At first, axial, slant and circumferential surface cracks are assumed at two locations where residual stress fields are different from each other. One is isotropic residual stress field, and the other is circumferential residual stress field. It is shown that crack growth behaviors are different under different residual stress fields. Next, the effect of the slit, which exists between the ICM Housing and the Pressure Vessel is evaluated. It is shown that the existences of the slit increases stress intensity factors of growing surface crack. Finally S-FEM results are compared with those of the Influence Function Method (IPM), which assumes that an elliptical crack shape exists in a plate. It is shown that IFM result is conservative comparing to that of S-FEM.

This paper presents formulations that enable the vision-based measurement of displacement and strain fields extensively in a probabilistic manner. The proposed formulations are built on the dot centroid tracking (DCT) method by digital cameras, which measures the darkness of each pixel in gray scale, identify dots marked on a specimen, derives dot centroids using pixel darkness information and derives displacement and strain fields by tracking the centroids and interpolating the nodal displacements and strains. Under the Gaussian assumption, the proposed formulations analytically propagate the standard deviation of uncertainty in darkness measurement and estimate that in the displacement and strain field measurement. As the first step, the formulations were completed for continuous field measurement with triangular elements. Most advantageously, the proposed formulations allow discussion on measurement error bounds, which also enables the quantitative comparison of the DCT method to the other measurement techniques. For numerical validation, standard deviations of nodal displacements and strains estimated from the known darkness uncertainty were compared to those derived from large samples created with the same darkness uncertainty. The results show the validity of the proposed formulations and their potential in measurement with reliability.

In recent years several techniques of full-field measurement have been studied by digital image correlation method, moire interference method and holographic interferometry method and so on. Image based method can be easily applied to large deformation problem and moving specimen at slow speed. Because digital camera capabilities, which are high resolution, low noise and faster data transfer speed, have been improved, very small strain measurement can be achieved by those improvements. The improvement will widen those applications, for example, moving object at high speed and less 0.1% strain measurement which is almost the same accuracy with a precise strain gauge. In order to apply the advanced application, noise reduction for a digital image and lens distortion correction for an optical system should be developed. In this paper we propose noise reduction technique using statistical camera model to be applied to any kinds of digital cameras.

This paper presents a multi-linear modeling technique to characterize the nonlinear behavior of anisotropic materials. The nonlinear behavior of anisotropic materials is represented with a multi-linear stress-strain model under the assumption that the material is path-, rate- and temperature- independent. The multilinear model is constructed by adopting. the energy-based characterization, which equates the applied external work to the induced strain energy and inversely solves for the multi-linear model. A numerical technique based on Kalman filter stochastically identifies multi-linear coefficients and constructs the multilinear model by modeling prior knowledge and empirical knowledge probabilistically. Since the coefficients are estimated with their associated variance, differential entropy can measure the certainty of all estimated coefficients as a single quantity. The validity of the proposed technique in estimating the multi-linear coefficients has been first demonstrated using pseudo-experimental data created by the finite element analysis. Further investigation of the effectiveness of the proposed technique under different measurement noises show its stable ability for nonlinear characterization of anisotropic materials.

This paper presents a new method for the correction of the lens distortion for full-field measurement using dot centroid method. Displacement and strain can be obtained from full-field digital images, which include centroids represented by many dots on the specimen. The captured images are distorted by an optical system. Several ideas to remove such a distortion are developed, however the image is corrected by an interpolation for brightness intensity level. In short it is hard to achieve high accuracy for strain measurement by the interpolation, because high accuracy needs sub-pixel effect for computing a centroid. In this paper, the dot centroid-method is employed and the centroids are directly corrected by the proposed method, which directly compute the only positions of centroids. Due to the correction, 0.1% strain accuracy is accomplished and total computation time is reduced Effectiveness of the idea is shown through numerical examples and the result of strain field measurement is presented and discussed

Surface crack growth process by fatigue is simulated using S-version FEM. Complicated crack growth process in 3-dimensional field under mixed mode loading condition can be modelled easily by this method. Simulation results are compared with experimental ones, and it is pointed out that several factors should be taken into account for the accurate prediction of surface crack growth under mixed mode cyclic loading condition. One of them is plasticity induced crack closure effect, which becomes significant near free surface of the specimen and delays crack growth rate. Another factor is the effect of K-III at the deepest point of surface crack, which results factory roof on the fracture surface and affects crack growth rate, too. Effects of these 2 factors are studied by numerical simulation and they are considered in the crack growth analysis. It is shown that accurate and conservative predictions of surface crack growth processes are conducted well. (C) 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of ICM11

Recent development of crack propagation analysis is rapidly advanced and its applications are being extended. Usually finite element method is utilized for the analysis. One of the most important tasks is mesh generation which requires fully automated system and no failures. It is very difficult to meet all geometrical and mechanical requirements for a surface mesh generation. Recent studies show a factory roof is easily generated under mixed mode loading. How to generate surface crack tetrahedral mesh without failures and surface crack analysis with factory roof are presented.

Fracture in heat affected zone (HAZ) in welding has been a serious problem for the integrity of machines. Prediction of fracture behavior due to the residual stress field in HAZ is important. In this paper, S-Version FEM(S-FEM) is applied to simulate the crack growth under thermal and residual stress fields. For evaluation of stress intensity factor, virtual crack closure integral method (VCCM) is employed. In order to confirm the validity of this analysis, numerical results are compared with previously-reported analytical and experimental results. Then, crack growth analysis in piping structure with welding joint was conducted. The residual stress data was provided by JAEA, Japan Atomic Energy Agency, based on their numerical simulation. Using S-FEM, two- and three-dimensional analyses are conducted, and crack growth behavior under thermal stress field is studied and discussed.

From a view point of engineering application, solid-liquid flow is one of the most practical phenomena, however MPS and other particle methods usually premises a constant size of all particles in the model. In a realistic phenomenon, the size of those particles is different. Koshizuka et al. has proposed new algorithm for solid-liquid flow simulation which is multi-scale DEM-MPS method. The method can calculate solid-liquid flow with a large difference of the particle scale. However, its program code requires a DEM part and a MPS part, and actual phenomenon includes various scales of particles. In order to analyze solid-liquid flow with different particles, modified Laplacian model and variable cut-off radius MPS method is proposed. This modification can directly deals with small particles and large particles. Calculation cost is kept and visualization of the results has more reality by these modifications.

Fracture in heat affected zone (HAZ) in welding has been a serious problem for the integrity of machines. Prediction of fracture behavior due to the residual stress field in HAZ is important. In this paper, S-Version FEM(S-FEM) is applied to simulate the crack growth under thermal and residual stress fields. For evaluation of stress intensity factor, virtual crack closure integral method (VCCM) is employed. The residual stress data was provided by JAEA, Japan Atomic Energy Agency, based on their numerical simulation. SCC crack growth of a surface crack at inner suface of a pipe under thermal residual stress is simulated in three-dimensional filed. Distributions of residual stress is not axi-symmetric along pipe wall, and it affects the crack growth behavior. Ttwo cases, for axi-symmetric and non-symmetric thermal stress distributions, are assumed and crack growth behaviors are obtaiend and discussed.

Study on the interaction of multiple cracks during fatigue crack growth processes is important for the integrity evaluation of nuclear structure. By using S-version FEM, this problem has been simulated by authors. In this study, coalescence behavior of 2 surface cracks is simulated using the method. It is assumed that 2 surface cracks exist on the same plane, and grow towards each other by fatigue. As the inner crack tips overlap, coalescence of 2 cracks occurs, and shape of cracks change significantly over very short cycles. This process is simulated in detail, and changes of stress intensity factor distributions along crack front are studied precisely. Three cases of changing crack sizes are simulated and coalescence behaviors are studied. Experimental studies are also conducted and results are compared with those of numerical simulations. Results are compared with conventional evaluation code and discussed. © 2011 by ASME.

Mixed mode fatigue tests are conducted using through cracked specimen. Slant through cracked specimens are made where crack angle is 15°, 30° and 45°. It is shown that factory roof is made in all crack tips due to ΔK_III, and crack growth rate decreases by the factory roof. Fatigue crack growth is simulated using S-version FEM( Finite Element Method) using crack growth criteria. It is shown that conventional crack growth criteria are not available to predict fatigue crack growth with factory roof. In authors' previous study, modified new criterion for the prediction of crack growth rate is proposed. In this study, by using new criterion, fatigue crack growth simulation is conducted, and results are compared with those of experiments and discussed.

Fatigue crack growth under mixed mode loading conditions is simulated using S-version FEM. By using S-FEM technique, only local mesh should be re-meshed for new crack configuration, and it becomes easy to simulate crack growth. By combining with auto-meshing technique, local mesh easily re-meshed and curved crack path is modeled easily. Fully automatic crack growth simulation system in 3-dimensional problem is developed. Using this system, several kinds of plural surface cracks problems are simulated. It is shown that intereaction effect between two surface cracks appear in complicated manner depending on intial distances between two cracks. © 2010 American Institute of Physics.

Crack closure effect on interaction of two surface crack growth processes by fatigue is studied. At first, change of C value in Paris' law along crack front of single surface crack is measured experimentally. It is shown that C value decreases near specimen surface. Crack closure effect is studied numerically for a surface crack by elastic-plastic cyclic analyses. It is found that closure effect appears more strongly near specimen surface than the maximum-depth point. By determining effective stress intensity factor including closure effect, it is shown that change of C value is equal to the change of closure effect along crack front. Using new C value considering closure effect, fatigue crack growth is predicted using S-FEM. It is shown that fatigue life and crack configuration agree well with experimental ones. Finally, interaction of two surface cracks is evaluated numerically, and it is shown that crack closure plays important role on the interaction of two cracks.

Fracture in the heat affected zone (HAZ) in welding has been a serious problem for the integrity of machines. Prediction of fracture behavior due to the residual stress field in HAZ is important. In this paper, the S-Version FEM(S-FEM) is applied to simulate the crack growth under thermal and residual stress fields. For evaluation of the stress intensity factor, the virtual crack closure integral method (VCCM) is employed. In order to confirm the validity of this analysis, numerical results are compared with previously reported analytical and experimental results. Then, a crack growth analysis in a piping structure with a welding joint was conducted. The residual stress data was provided by JAEA, Japan. Atomic Energy Agency, based on their numerical simulation. Using S-FEM, two- and three-dimensional analyses are conducted, and crack growth behavior under thermal stress field is studied and discussed..

Fracture in heat affected zone (HAZ) in welding has been a serious problem for the integrity of machines. Prediction of fracture behavior due to the residual stress field in HAZ is important. In this paper, S-Version FEM(S-FEM) is applied to simulate the crack growth under thermal and residual stress fields. For evaluation of stress intensity factor, virtual crack closure integral method (VCCM) is employed. In order to confirm the validity of this analysis, numerical results are compared with previously-reported numerical results. Then, crack growth analysis in piping structure with welding joint was conducted. The residual stress data was provided by JAEA, Japan Atomic Energy Agency, based on their numerical simulation. Using S-FEM, two- and three-dimensional analyses are conducted, and crack growth behavior under thermal stress field is studied and discussed.

Mixed mode fatigue tests are conducted using surface cracked specimen. Slant surface cracked specimens are made where crack angle is 15 degrees, 30 degrees, 45 degrees and 60 degrees. It is shown that factory roof is made at deepest point of surface crack due to Delta K-III, and crack growth rate decreases by the factory roof. Fatigue crack growth is simulated using S-version FEM( Finite Element Method) using crack growth criteria. It is shown that conventional crack growth criteria are not available to predict fatigue crack growth with factory roof In this study, modified criterion for the prediction of crack growth rate is proposed. By using this criterion, fatigue crack growth simulation is conducted, and results are compared with those or experiments and discussed.

Fatigue crack growth under mixed mode loading conditions is simulated using S-version FEM. By using S-FEM technique, only local mesh should be re-meshed for new crack configuration, and it becomes easy to simulate crack growth. By combining with auto-meshing technique, local mesh easily re-meshed and curved crack path is modeled easily. Fully automatic crack growth simulation system in 3-dimensional problem is developed. Using this system, several kinds of plural surface cracks problems are simulated. It is shown that intereaction effect between two surface cracks appear in complicated manner depending on intial distances between two cracks. © (2010) Trans Tech Publications, Switzerland.

This paper describes a surface crack growth simulation using a new mesh generation technique. The generated mesh is constituted of all hexahedral elements. Hexahedral elements are suitable for an analysis of fracture mechanics parameters, i.e. stress intensity factor. The advantage of a hexahedral mesh is good accuracy of an analysis and less number of degrees of freedoms than a tetrahedral mesh. In this study, a plural crack growth simulation is computed using the hexahedral mesh and its distribution of stress intensity factor is investigated.

Fatigue crack growth under mixed mode loading conditions is simulated using S-version FEM. By using S-FEM technique, only local mesh should be re-meshed for new crack configuration, and it becomes easy to simulate crack growth. By combining with auto-meshing technique, local mesh easily re-meshed and curved crack path is modeled easily. Fully automatic crack growth simulation system in 3-dimensional problem is developed. Using this system, a basic slant surface crack problem is solved, and it is shown that surface crack grows under pure mode I condition, which is similar to 2-dimensional problem. It is also shown that this system is available for complicated structures, for example, surface crack at inner surface of pipe. Finally, interaction effect of two surface cracks is evaluated. Copyright © 2009 by ASME.

Mixed mode fatigue tests are conducted using surface cracked specimen. Slant surface cracked specimens are made where crack angle is 15°, 30°, 45° and 60°. It is shown that factory roof is made at deepest point of surface crack due to ΔKIII, and crack growth rate decreases by the factory roof. Fatigue crack growth is simulated using S-version FEM (Finite Element Method) using crack growth criteria. It is shown that conventional crack growth criteria are not available to predict fatigue crack growth with factory roof. In this study, modified criterion for the prediction of crack growth rate is proposed. By using this criterion, fatigue crack growth simulation is conducted, and results are compared with those of experiments and discussed.

Fatigue crack growth under mixed mode loading conditions is simulated using S-FEM. By using S-FEM technique, only local mesh should be re-meshed and it becomes easy to simulate crack growth. By combining with re-meshing technique, local mesh is re-meshed automatically, and curved crack path is modeled easily. Fully automatic crack growth simulation system in 3-dimen- sional problem is developed. At first, a basic slant surface crack problem is solved, and it is shown that surface crack grows under pure mode I conditions, which is similar in 2-dimensional problem. It is also shown that this system is available for complicated structure, for example, surface crack at inner surface of pipe. Finally, interaction effect of two surface cracks is evaluated.

Failure in heat affected zone (HAZ) in welding has been a serious problem for the integrity of nuclear power plant. Trediction of crack behavior affected by the residual stress field in HAZ is important. In this paper, S-Version FEM (S-FEM) is applied to simulate the crack growth under thermal and residual stress fields. S-FEM is applied because the mothod enables us to generate cracked models flexibly. For evaluation of stress intensity factor, virtual crack closure integral method (VCCM) is employed. In order to confirm the validity of this analysis, numerical results are compared with previously-reported analytical and experimental results. Then, crack growth analysis in piping structure with welding joint was conducted. The residual stress data was provided by JAEA, Japan Atomic Energy Agency, based on their numerical simulation. Using S-FEM, two- and three-dimensional analyses are conducted, and crack growth behavior under thermal stress field is studied and discussed.

Fatigue crack growth under mixed mode loading conditions is simulated using S-FEM. By using S-FEM technique, only local mesh should be re-meshed and it becomes easy to simulate crack growth. By combining with re-meshing technique, local mesh is re-meshed automatically, and curved crack path is modeled easily. Plural fatigue crack problem is solved by this technique. For two through crack problems, crack coalescence condition is proposed by JSME standard. By simulating this problem by S-FEM, it is shown that thid criterion depends on initial crack size. Then more than 160 cases are simulated by changing several parameters. Results are summarized by normalized form, and new criterion is proposed. © 2008 by ASME.

Fatigue crack growth under mixed mode loading conditions is simulated using S-FEM. By using S-FEM technique, only local mesh should be re-meshed and it becomes easy to simulate crack growth. By combining with auto-meshing technique, local mesh is re-meshed automatically, and curved crack path is modeled easily. Plural fatigue crack problem is solved by this technique. For two parallel crack problelm, criteria of crack coalescence are proposed. By simulating this problem by S-FEM, it is verified these criteria are conservative ones.

There are several studies for developing web-based CAE applications to substitute existing CAE applications. CASOW is the web-based CAE system developed by the author. The approach for implementation of the system is to use fundamental technologies, for instance, HTML, HTTP, CSS and so on, because we cannot know whether new technologies will be alive or not. Certain technologies bring specific advantages to the applications, but a life time of the application would be short. Recently a great advantage of web interface is developed. Such a representative application is Google Maps which doesn't require any special software components; however the application realizes interactiveness of the application. The technology is called Ajax which drastically overcomes the bad interactiveness on the web browser. On the other hand, high efficiency of analysis work with high performance computers produces many kinds of knowledge and a large amount of information. We are confronted with inefficient knowledge and information management in the network system. This paper presents the new web-based CAE system using Ajax and knowledge sharing framework with compatibility to web interface. The system is presented, and advantages of the interface, effectiveness of the API in the system and knowledge sharing framework are discussed.

Due to more complex and severe design restrictions, more effective and faster finite element analyses are demanded. There are several ways to compute FE analysis efficiently: parallel computing, fast iterative or direct solvers, adaptive analysis and so on. One of the most effective analysis ways is the combination of adaptive analysis and multigrid iterative solver, because an adaptive analysis requires several meshes with difference resolutions and multigrid solver utilizes such meshes to accelerate its computation. However, convergence of multigrid solver is largely affected by initial shape of each element. An effective mesh improvement method is proposed here. It is the combination of mesh coarsening and refinement. A good mesh can be obtained by the method to be applied to an initial mesh, and better convergence is achieved by the improved initial mesh.

Fatigue crack growth under mixed mode loading conditions is simulated using S-version FEM (Superposition FEM, S-FEM). By using S-FEM technique, only local mesh should be re-meshed and it becomes easy to simulate crack growth. By combining with re-meshing technique, local mesh is re-meshed automatically, and curved crack path is modeled easily.

A non-triangulation inserting particle method is presented to prevent numerical fractures of SPH Computations. The particles in those regions in which numerical fractures may occur are chosen at the beginning of SPH computations. And, the chosen particles are arrayed by the two different rules respectively according to the particle position relations. When the distance between each two chosen connected particles exceeds a certain value and neither of the corresponding two particles has fractured in SPH computations, a new particle is generated between those two ones and the position relation of particles is updated. The physical quantities that the new particle carries are obtained according to some given rules. The method and the same type of method in the reference are compared. The application of the method is analyzed. Conservation of mass and Conservation of momentum of the whole system are kept in this method. Several examples are given to validate the efficiency of the method to prevent numerical fractures.

Fatigue crack growth under mixed mode loading conditions is simulated using Superimposed-FEM (S-FEM). By using S-FEM technique, only local mesh should be re-meshed and it becomes easy to simulate crack growth. By combining with re-meshing technique, local mesh is re-meshed automatically, and curved crack path is modeled easily. At first, slant crack problem is solved. It is shown that results agree with conventional solutions, and verified the availability of this technique.Then two-crack problems are solved in several cases by changing each crack location. Stress intensity factors are evaluated and interaction effect between two cracks is discussed. Results are compared with crack coalescence criteria, and it is verified that these criteria are reasonable ones.

Fatigue crack growth under mixed mode loading conditions is simulated using S-FEM. By using S-FEM technique, only local mesh should be re-meshed and it becomes easy to simulate crack growth. By combining with re-meshing technique, local mesh is re-meshed automatically, and curved crack path is modeled easily. In the previous paper, basic problems were solved, and availability of this method was verified. In this paper, interaction of two parallel cracks with different level is studied. By changing relative locations of two cracks, totally 161 cases are solved, and results are summarized by normalized form. It is shown that there is a clear area in which interaction between two cracks is not neglected. A new criterion to evaluate interaction effect between two parallel cracks is proposed.

We have proposed a cell based parallel computing system using a cellular automaton model. The proposed system is designed by object-oriented technique to realize extensibility for parallel cellular automaton model. Because the system needs only information of model as cells which are represented by pixel and voxel mesh, model generation is very easy from any data formats. We implement several applications, which are I-D life game, 2-D life game, 2-D diffusion, 2-D parallel diffusion, 2-D wave propagation, 3-D wave propagation and 3-D parallel wave propagation on the system. Status of cells is updated by adjacent status of cells. In other worth, behavior of system is completely specified in terms of a local relation. Cells can hold many properties to represent its status. Cellular automata system can calculate physical phenomena and discrete problem like a life game simultaneously. We present some results of a physical analysis and discrete analysis, and discuss effectiveness and parallel efficiency of proposed system.

Bone is a complex system with adaptation and repair functions. To understand how bone cells can create a structure adapted to the mechanical environment, we proposed a simple bone remodeling model, iBone, based on a reaction-diffusion system [1]. A 3-dimensional mandibular bone model consisting of approximately 1.4 million elements was constructed from sequential computer tomography (CT) images of a 14-year old female. Both teeth and bone were modeled with isoparametric voxel elements with Young's Modulus = 20 GPa and Poisson's ratio = 0.3. Both heads of the mandible were fixed allowing rotation and horizontal movement. Teeth were fixed vertically allowing horizontal movements. Incisor, right/left group, and right/left molar biting conditions were simulated. The locations and directions of muscles, and their forces were predicted from the CT images. Remodeling simulation was performed by 10 sets of finite element method analysis and reaction-diffusion remodeling simulation to obtain internal structure adapted to each loading condition. As a result, the major part of the corpus of the simulated mandibular bone showed similar internal structures under different biting conditions. Moreover, these simulated structures were satisfactorily similar to that of the real mandible. Computer simulation of three-dimensional bone structures based on CT images will be very useful for understanding the patho-physiological state of bone under various mechanical conditions, and may assist orthopedic doctors to predict the risk and efficacy of surgical therapies.

MG (multigrid) method is one of the most promising solvers for large scale problems. Hexahedral mesh generation and its adaptation are not enough to use for practical applications, because its mesh generation is very difficult and still labor intensive work by hand. We have developed hexahedral local refinement technique controlled by posterior error estimation. We have proposed a MG technique for unstructured hexahedral meshes with local mesh refinement. In this paper, the proposed technique is evaluated to check its performance and severe analyses of bending cantilevers. Performance of MG for unstructured hexahedral meshes is compared with that of the PCG (preconditioned conjugate gradient) through several benchmark examples of 3-D static elastic analysis. Proposed MG is faster than PCG for all problems as number of freedoms increases. Finally limitation of the proposed technique is presented.

Bone is a complex system with functions including those of adaptation and repair. To understand how bone cells can create a structure adapted to the mechanical environment, we propose a simple bone remodeling model based on a reaction-diffusion system influenced by mechanical stress. Two-dimensional bone models were created and subjected to mechanical loads. The conventional finite element method (FEM) was used to calculate stress distribution. A stress-reactive reaction-diffusion model was constructed and used to simulate bone remodeling under mechanical loads. When an external mechanical stress was applied, stimulated bone formation and subsequent activation of bone resorption produced an efficient adaptation of the internal shape of the model bone to a given stress, and demonstrated major structures of trabecular bone seen in the human femoral neck. The degree of adaptation could be controlled by modulating the diffusion constants of hypothetical local factors. We also tried to demonstrate the deformation of bone structure during osteoporosis by the modulation of a parameter affecting the balance between formation and resorption. This simple model gives us an insight into how bone cells can create an architecture adapted to environmental stress, and will serve as a useful tool to understand both physiological and pathological states of bone based on structural information.

Bone is a complex system with functions including those of adaptation and repair. To understand how bone cells can create a structure adapted to the mechanical environment, we proposed a simple bone remodeling model based on a reaction-diffusion system influenced by mechanical stress. When an external mechanical stress was applied, stimulated bone formation and subsequent activation of bone resorption produced an efficient adaptation of the internal shape of the model bone to a given stress, and demonstrated major structures of trabecular bone seen in the human femoral neck. By modulation of a single parameter affecting the balance between formation and resorption, deformation of bone structure during osteoporosis was also demonstrated. This simple model gives us an insight into how bone cells create a sophisticated architecture, and will serve as a useful tool to understand both physiological and pathological states of bone based on structural information.

3-D finite element method (FEM) is widely used as an effective numerical simulation technique. In the simulation technique, accuracy is one of the most significant issues. In case of FEM, the accuracy is affected by number of freedom and shape of each element. Generally, a fine mesh can provide more accurate result than a coarse one, and needs more time of calculation and more computer resources (memory, CPU time and disk space). Recently tetrahedral automatic mesh generation and adaptive mesh generation become advanced and practical. Hexahedral mesh generation and its adaptation are not enough to use for practical applications, because its mesh generation is very difficult and still intensive labor work by hand. In recent years local mesh refinement for a tetrahedral element is widely used in order to avoid failure of mesh regeneration. Therefore one of the best ways to control quality of a hexahedral mesh is applying local mesh refinement to existing hexahedral mesh. In this study we present a method to generate an appropriate mesh for user's demand using existing hexahedral mesh and hexahedron mesh and hexahedral automatic local refinement technique.

This paper describes a simple and effective adaptive technique for mesh refinement in finite-element method models. The proposed refinement method is based on a modified octree refinement approach, and can be applied to an arbitrary hexahedral unstructured mesh. The implementation, Hex-R, is used in conjunction with the finite-element viewer GPPView, and applied to a complex model. The proposed method is demonstrated to be capable of easily and reliably generating an adaptive mesh. Copyright (C) 2002 John Wiley Sons, Ltd.

This paper describes an automated mesh generation method named Intelligent Local Approach (ILA), which can control size and shape of hexahedral elements. A solid model created by a commercial solid modeler is first converted to quadrilateral surface patches. Second, considering local information on geometrical constraints, local connectivity of one to few hexahedral elements is determined step by step through some pattern matching tests with an element pattern database. Finally appropriate locations of new nodes are determined through a fuzzy knowledge processing technique. Fundamental performances of the present method are demonstrated through generating hexahedral meshes of some nuclear structures. (C) 2002 Published by Elsevier Science B.V.

This paper describes an automated generation method of a hexahedral mesh named Intelligent Local Approach (ILA). Here elements are generated sequentially, by taking account of both local information on geometrical constraints and user's demand on quality of elements. Topological connectivity is first determined based on a heuristic category-based method. Then a fuzzy knowledge processing technique is utilized to determine optimum positions of nodes, considering various complicated geometrical constraints for high quality hexahedral elements. The determination of hexahedral connectivity and nodes positions is important technique to overcome difficulty in generating a hexahedral mesh of an arbitrary shape. Fundamental performances of the ILA are demonstrated in detail through generating several hexahedral meshes.

This paper describes a new automated mesh generation method named Intelligent Local Approach (ILA), which well controls both size and aspect ratio of quadrilateral element in a two-dimensional plane. The ILA can be straightforwardly extended to hexahedral elements in a three-dimensional solid. Here elements are created sequentially, considering local information on geometrical constraints and user's demand on quality of elements. A user can specify the following two numerical fields, (a) a field of element size and (b) that of element aspect ratio. A field of priority of element creation is also specified within the ILA. To efficiently deal with various complicated geometrical constraints for high quality quadrilateral elements, a fuzzy knowledge processing technique is effectively utilized. The ILA is implemented using an object-oriented technique. Fundamental performances of the ILA are demonstrated in detail through generating several quadrilateral meshes. (C) 1999 Elsevier Science S.A. All rights reserved.

This study describes a PC-based system to evaluate three-dimensional (3D) stress intensity factors (SIFs) using various simplified formulas found in literature. In general, this kind of system has to be flexible in extending its functions, and easy for ordinary engineers to use. It is also important to keep system compact by sharing common functions among various formulas for different crack and structure geometries. To meet these conditions, the present system is fully designed based on an object-oriented approach, and built in a PC/Windows environment using one of the object-oriented languages Visual C++. About 50 different formulas of 3D-SIFs are implemented in its first version. Better usability of the system is clearly demonstrated through actual usability tests for persons with and without experience on SIF evaluation. (C) 1999 Elsevier Science Ltd. All rights reserved.

In the present study, we have developed a system for evaluating numerous formulas of three-dimensional (3D) stress intensity factors (SIFs) found in literature.In general, this kind of system has to be flexible in extending its functions, and easy for ordinary engineers to use.In addition, it is important to keep system compact by sharing common functions among various cracks and structure geometries. To meet those requests, the present system has been fully designed based on an object-oriented programming approach, and built in a personal computer using one of object-oriented languages Visual C++.Its first version contains about 50 different formulas of 3D-SIFs.

Finite-element method codes for 2-dimensional and 3-dimensional structural analyses are reprogrammed using FEM code class libraries in an object-oriented language, C++. The readability and modifiability are improved by using C++ instead of FORTRAN. In this paper, two concepts are introduced in the construction of the class library for further improvement of modifiability. One is the application framework, which simplifies the process for FEM programming. Another is the action queue, which is an assembly of pointers of functions. It is shown that the database for action queue and functions is important for the further development of FEM class libraries

A high-performance computing and numerical methods to realize electromagnetic field analysis has been researched. In particular, by developing the COMINRES-QLP method of the iterative method for complex symmetric linear systems, theoretical studying on application of the balancing domain decomposition method to electromagnetic field analysis, developing and utility evaluating a mixed-precision IC(p) preconditioner, developing a mesh smoothing technique based on the centroidal Voronoi tessellation, a huge-scale electromagnetic field analysis with 130 billion degrees of freedom mesh of a full-scale human body model has been successfully performed.

S-version FEM code was updated. The crack closure effect is estimated by conventional method, and realistic fatigue crack growth simulation became possible. 3-dimensional crack growth simulation is applied to verify the alignment rule for nuclear power plant maintenance code. A new method estimating crack closure effect is proposed using AI technique. Basic research for the study by deep-learning is conducted. To improve the S-version FEM code, S-FEM seminars were organized. Research results have been published in the Journal and presented in domestic and international conferences

本研究の目的は、対象とする人の頭部周辺に「スポクト状」の高感度・高音圧分布を作り出してS/N比の高い集音・伝送を実現し、たとえその人が動いても、それに対してスポット状高感度・高音圧分布を追従可能な対象人物追従型遠隔伝声システムの実現を目指すことにある。このため具体的には多軸マイクアレイ・スピーカーアレイによる「スポットフォーミング」技術と、実時間追跡視覚による移動対象人物へのスポット実時間追従技術とを提案し、提案に基づく実験システム構築を通じてシステム構成法を明らかにする。これにつき、今年度は以下の3項目に取り組んだ。 1)多チャンネルスピーカーアレイと実時間視覚との結合 従来は、システム稼働中は、サウンドスポット位置が予め設定した位置に固定であったが、昨年度に、これを稼働中にも独立して変更可能となるよう機能拡張した。今年度は、昨年度に開発したこのサウンドスポット位置移動可能化技術と実時間視覚とを結合した。これにより、対象とする人物が動いてもそれに追随してサウンドスポットを追跡・移動させるような効果が実現できた。 2)直交3軸スピーカーアレイの構築と3次元空間中任意位置でのスポット形成 既設のスピーカーアレイを直交3軸に拡張し、空間中の任意の位置にスポットが形成できるようにし、3次元音場測定実験により確認した。3次元の音場測定には、きわめて多数の測定点での音圧測定が必要であり、そのための測定装置も構築した。 3)音圧分布の時間変化に関するシミュレーションの展開 計算力学的手法法を活用し、スピーカーアレイが生成する音圧の空間的分布の時間変化を数十マイクロ秒オーダの微少時間間隔でシミュレートする技術の開発に昨年度より着手した。2次元平面内に限定した、反射も吸収も無い状況のシミュレーションは実現できたので、今年度は反射、吸収の導入を図った。3次元への拡張についても検討を行った。