In this paper, a topology optimization method to create damping mechanism of a building is shown. The topology is created on continuum divided in finite elements. In the optimization problem, the densities of the elements are chosen as design variables. The stiffness between the input point and the output point is maximized under the constraints of the displacement of the output point, the relativity displacement of the output point and input point, and the material usage. The optimization problem with different initial design variables is solved using the SLP optimizer, because the solution of this problem depends on the initial design variables. The initial design variables are given by random numbers. Some examples are shown to demonstrate the effectiveness of the present method.

In this paper, a shape optimization method for shell structures is shown. The present method is based on the traction method proposed by Azegami. However, the algorithm of the present method is very simple in comparison with the original method. The sensitivity analysis is not need in the present method. The method is similar to large displacement analysis based on update Lagrange, and it is named "deformation method" in this paper. The reliability of the present methods is shown by comparing with the original traction method and other shape optimization methods. Several examples are shown to demonstrate the effectiveness of the present methods for shell structures.

In this paper, the topology optimization method of link mechanisms is shown. In the link mechanisms composed of rigid bodies and hinges, the displacement of the output point can be controlled by the load of the input point. In the present method, the ground structure composed of beams is used in order to obtain the optimum topology of the link mechanisms. In the optimization problem, the sectional areas of the beams are chosen as design variables. The stiffness between the input point and the output point is maximized under the constraints of the displacement of the output point, the relativity displacement of the output point and input point, and the material usage. The optimization problem with different initial design variables are solved using the SLP optimizer, because the solution of this problem depends on the initial design variables. The initial design variables are given by random numbers or GA. Some examples are shown to demonstrate the effectiveness of the present method.

本論文では、 重合メッシュ法においてグローバルモデルとローカルモデルの構成式を変えた場合の場の支配方程式を求め、 ローカルモデルの材料定数のみで、 その部分の剛性を評価することが可能であることを示した。

本論文では、 節点の概念を用いない有限要素を提案し、 これを連続体の位相最適化問題に適用することにより、 最適位相を不鮮明にするチェッカーボード現象を回避できることを示している。

In this paper, a topology optimization method of elastic link mechanisms is shown. In these mechanisms, the displacement of the output point can be controlled by the load of the input point. The mechanism obtained by the present method is composed of the frame structure with elastic members and semi-rigid connections. The ground structure approach is used in order to obtain the optimum topology of the mechanism. In the optimization problem, both of the sectional area of the members and the rigidity of the connections are chosen as design variables. The stiffness between the input point and the output point is maximized under the total weight constraint and the displacement constraint of the output point. The optimization problem is solved using the SLP optimizer. Several examples are shown to demonstrate the effectiveness of the present method.

In the structural design of ship hull, the shell element is used for the analysis of the global model. However, the analysis using the solid elements is necessary for the analysis of the stress concentration zone or the crack vicinity. Therefore, we proposed the mixed method for assembling the shell elements and the solid elements using the overlay method. In this paper, the effectiveness of the presented method for the bending problem is investigated. In the bending analysis for the shell-shell assembling using the presented method, it was proven that a numerical instability occurs. In this paper, it is shown that such numerical instability occurs in the shell-solid assembling, and the solution about this problem is presented. In addition, a problem in which the bending deformation is generated in the effect of local model is shown. The numerical instability in such problem is also investigated, and its solution is presented. Some simple examples are shown to demonstrate the present solutions.

In this paper, the Finite Cover Method, which is unified analysis method of discrete model and continuum model, is extended for the plate-bending problem for the analysis of progressive failure of sea level ice. The solid element with assumed stress is employed to avoid the shear locking in Mindlin plate, and good accuracy is obtained for the case of large aspect ratio. The method to introduce discrete plane in Finite Cover Method to model the failure of ice is shown, and penalty spring is introduced to analyze the progressive failure of ice. One-dimensional examples and two-dimensional examples are solved to show the capability of the method.

The Convex Linearization method (CONLIN), that is a dual optimizer based on the convex approximation concepts, is often used to solve the structural optimization problem, recently. The CONLIN optimizer has many benefits, for example, the handling of constraint conditions is easy as well as the SLP method, and the performance of convergence is excellent as well as the optimality criteria method (OC). In this paper, the CONLIN optimizer is applied to the topology optimization problem of frame structures in order to investigate the performance of this optimizer in the topology optimization analysis. The ground structure method is used to obtain the optimum topology of frame structures. The characteristics of the CONLIN optimizer are clarified by comparing with the SLP method and OC method. Several examples are shown to demonstrate the effectiveness of the CONLIN optimizer for the topology optimization analysis.

In the structural design of ship hull, the shell element is used for the analysis of the global model. However, the analysis using the solid elements is necessary for the analysis of the stress concentration zone or the crack vicinity. Therefore, we proposed the mixed method for assembling the shell elements and the solid elements using the overlay method. In this paper, the effectiveness of the presented method for the bending problem is investigated. In the bending analysis for the shell-shell assembling using the presented method, it was proven that a numerical instability occurs. In this paper, it is shown that such numerical instability occurs in the shell-solid assembling, and the solution about this problem is presented. In addition, a problem in which the bending deformation is generated in the effect of local model is shown. The numerical instability in such problem is also investigated, and its solution is presented. Some simple examples are shown to demonstrate the present solutions.

In the topology optimization analysis based on the homogenization design method or the density approach, the checkerboards, that is the formation of regions of altemating solid and void elements ordered in a checkerboard-like fashion, often appear in the optimum solutions. Therefore, the filtering method is necessary for these approaches. In this paper, we present an effective filteing method for the topology optimization analysis using the optimality criteria method as optimizer. In this method, the value of the gravity control function is controlled as a constrained condition. The gravity control function, which was presented by the author in the topology optimization analysis using the S LP method , is defined from the relations of the density of an element with that of its neighbor elements. This function imposes the penalty in the checkerboards and the gray scale density, that is, if the fuction is high, the checkerboards and gray scales disappear in the optimum solution. In this paper, this filtering method is applied in the topology optimization using the homogenization design method and the density approach. Several examples of 2D and 3D problems are shown to demonstrated the effectiveness of the present method.

In this paper, we present an effective method for designing the composite material by the topology optimization technique using the homogenization design method. The composite material is made of two or three different material phases. Designing the composite material consists of finding a distribution of material chases that minimizes the mean compliance of the macrostructure subject to volume fraction constraints of the constituent phases, within a unit cell of periodic microstructures. At the start of the computational solution, the material distribution of the microstracture is represented as a pure mixture of the constituent phases As the iteration procedure unfolds, the component phases separate themselves out to form distinctive interfaces. The optimization problem is solved using the SLP method. Several examples of optimal topology design of composite material are presented to demonstrate the validity of the present numerical algorithm.

In this paper, we present an effective method for designing the compliant mechanisms by the topology optimization technique using the homogenization design method. In this method, a new multi-objective function which maximizes the relative compliance between input at the loading point and output at a prescribed point is defined. The topology optimization problem formulated using the homogenization design method is solved by SLP method. In this algorithm, with the size of the hole of unit cell, the angle of unit cell is made to be a design variable. The local minima occurring in topology optimization in which SLP method is used and the gray scale densities of optimal solutions are improved by .our presented methods. The effectiveness of the present method is demonstrated by numerical examples of the topology optimization on a short cantilever plate.

In this paper, an analysis method by computers based on optimum design of frames with semi-rigid connection is shown. This method evaluates the connection stiffness and the member sizes as design variables. The discrete member sizes are evaluated by referring to the database system as continuous function. The optimization algorithm minimizes the cost of not only members but also the connections of the structure subjected to constraints on stresses and displacements under specified design loads. Four examples are presented to illustrate features of this optimization method.

In this paper, the method of the optimal design for plane steel frame structures is presented. The sectional areas are automatically selected so as to be a minimum weight frame under the restraint conditions of the limited angle between the layers and the allowable stress in the composed members. In the present method, the sensitivity coefficients are numerically calculated by the finite difference method and the actual members on the market are selected by using the error functions between the obtained numerical solution and the discrete actual sectional properties of members. The interesting optimal solutions, which have the three local solutions, are obtained in an example of the plane steel frame with 5 floors and 3 spans.

A computer program which is developed for the optimal design of reinforced concrete buildings is presented. By using this program, it is possible to design of the sections of RC frame members under constraint conditions of new seismic design in Japan. Fairly good results are obtained through calculation example which is referred from the Japanese standard for structural calculation of RC structure.

In this paper, we investigate three characteristics of seismic response in the friction systems. First contents are base isolation systems containing mass on the base floor. We compare the response of these systems with one in the case of no mass on the base floor. Second contents are friction coefficients depended on the sliding velocity. We explain the method to simulate, and show response waves calculated using four kinds of these characteristics. Third contents are non-directional friction forces on the sliding plane surface. We propose one method to analyze the response of friction systems including those forces. In addition, we show the locus of ground motion and sliding motion using single or two mass model subjected to horizontal bi-axial earthquake.

In this paper, two analysis models for the coupled torsional-bending responses of thin-walled beam with discontinuously variable cross-sections are presented. These models are based on a thin-walled beam theory which takes into account shear deformation by the 2D or 3D shear warping function. A C1 continuous finite element with boundary contraction technique is used for the discretization. The compatibility condition of warping, which is automatically satisfied in the 3D shear warping model, is satisfied approximately in the 2D shear warping model by use of warping error minimization technique. By an example of box girder with open section, the accuracy and efficiency of present models are shown.

The finite element formulation of nonuniform shear warping model for thin-walled beam's flexural-torsional behavior, which can show the precise distribution of normal stress and shear stress on the beam section including the shear lag phenomena, is developed. In order to realize the acual end conditio of the beam, a boundary contraction method for the additional degress freedom of out-plane warping due to shear is applied. By some examples of the closed and open thin-walled sectin beams, te accuracy and convergency of the numerical solutions are compared with the analytical solutions.

In this paper, a new non-comforming 4-node quadrilateral plate bending element is developed. This finite element is formulated on the basis of Reissner's plate bending theory. The displacement fields in this theory consist of the two kinds of rotations. One is the differentiation of the deflection, the other is the shear angle of the plate. However, after the discretization procedure in finite element method, these two rotations at each node are unified to the one rotation of the cross section by the contraction method. This contruction is achieved by using the mechanical relations between the bending moment and shear force at each node. Several numerical experiments are performed, and show that the present element gives excellent results in the analysis of both thin and thick plate bending.

In this paper, two analysis models, a uniform shear warping model and a nonuniform shear warping model for the thin-walled beam's flexural behavior are developed, which can show the precise distribution of normal stress and shear stress within the beam section including the shear lag phenomena. The mechanism of boundary condition of the developed shear warping models and their relation for the Timoshenko's beam model are discussed and clearly verified. By using the St. Venant's semi-inverse method, the uniform and nonuniform warping functions are defined. By two examples, the usefulness of the proposed analysis model is shown.

We presented an effective finite element method based on the thin-walled beam theory for the structural analysis of highrise building. However, the story deformation angles and shear forces obtained by this method are not acculate in the lowest story. In this paper, we show the matrix condensation methods based on the Uetani's idea in order to solve this problem. By numerical example of analysis of a highrise building, we show the validity of this methods, and we show it is possible to apply the present method to actual structural design.

This paper presents the new analytical method for the three-dimensional dynamic interaction problem between a layered soil and embedded foundations with arbitrary shapes. A soil domain is devided into the two subdomains by an artificial cylindrical boundary. A general dispacement field of the outer domain is expanded in a Fourier series and analyzed by the indirect boundary integral equation method which has been developed by authors in a thin layered soil model. The inner domain is discretized by ordinary boundary element method. Combining equations for the total domain are obtained by applying the Fourier inverse technique to the stiffness equations of the outer domain. The method is illustrated by the analysis of a rigid rectangular foundation embedded in an elastic uniform soil. The impedance functions and the foundation input motions are discussed as well as the distribution of soil pressure and the local effects of the side wall.

This paper presents a procedure for the finite element analysis of high-order elastic fundamental solutions in two-and three-dimensional bodies. Three-dimensional fundamental solutions can be expressed by the Fourier's Series expansion with respect to the Coordinate ψ. Its Second-order solution correspond to the plane symmetric fundamental solution (Cerruti's solution) and is formulated in this paper by finite element method. Two-dimensional higher-order fundamental solutions under following load conditions are analysed by finite element method: (1) a couple, (2) equal and opposite moment of couples, acting on the straight boundary of an infinite plane. It is clarified that the usual two-dimensional fundamental solution can be solved by a simultaneous equation, however, the above higher-order two-dimensional fundamental solutions are analysed as eigen-value problem. By the present finite element method, the numerical fundamental solutions were obtained with good convergence.

The effect of the backfilled soil on the dynamic response property of the foundation is investigated. For this purpose the new analytical method is also presented. The outer domain of a soil is analyzed by the indirect boundary integral equation method in the thin layered soil model which has been developed by authors. The inner domain which contains an irregular soft soil is discretized using the axi-symmetric isoparametric finite elements. Combining equations for the total domain are obtained by applying the principle of virtual displacements to the stiffness equation of the outer domain. The three types of the foundation are chosen as analytical models. The first is rested on the elastic base through a surface stratum. The second and third are floating in the homogeneous half space soil and the upper layer of the two layered soil respectively. The results obtained by numerical analyses are as follows. 1) The rigidly backfilled soil reduces the maximum response of the superstructure within the natural period of 0.3 or 0.4 second. Conversely the softly backfilled soil is usefull for the structure with the natural period of longer than it. 2) The maximum response of the foundation bonded to the elastic base becomes lower in a soft backfill rather than a rigid one.

The boundary integral equation method based on the Green's function obtained by the thin layer method is very useful for the analysis of the foundations embedded in multi-layered visco-elastic soil. However, two problems exist in this method;!) the calculation of the stress components of the Green's functions introduces substantial errors near the applied point, 2) the solution of the dynamic stiffness analysis is disturbed in the vicinity of fictitious eigen-frequencies. The latter problem can be resolved by putting several constraint panels in the internal region. The former problem can be also resolved by modifying the stress matrix under certain conditions. This paper presents new conditions to modify the stress matrix. This conditions are derived from the boundary integral equations which the Green's functions must satisfy in the internal region when a applied point is in the external region. In order to show the validity of the present method, this paper presents the dynamic horizontal and rocking stiffness analysis of the cylindrical foundations embedded in the homogenious visco-elastic soil. Also we calculate the dynamic response of the cylindrical foundations embedded in the two layered visco-elastic soil when subjected to S-wave excitation with vertical incidence, and we qualitatively investigate the effect of the side walls of the foundations on the response of the soil-structure system by considering a model of structure consisting of the embedded foundation and the lamped mass system with single degree of freedam.

The boundary integral equation method involving the Green's function by the thin layer method is very useful for the analysis of the excavated multi-layered visco-elastic soil. However, there exist two complexities in this method ; 1) the calculation of the stress components of the Green's functions introduces substantial errors near the applied point, 2) the solution of the dynamic stiffness analysis is disturbed in wide range near the natural frequency of the internal region. This paper resolves both of these complexities at once by putting several constraint panels in the internal region. Those panels are used for the purpose of taking away the internal resonance point from the frequency range of interest and deriving the conditions to modify the solution of the stress. In order to show the validity of the present method, this paper presents the dynamic torsional stiffness analysis of the axi-symmetric excavation.

The boundary integral equation method involving the Green's function of the multi-layered medium by the thin layer method is very useful to evaluate the foundamental physical quantities in the dynamic soil-foundation interaction problem. However, there exist two complexities in evaluating these quantities by this method ; 1) the calculation of the stress components of the Green's functions introduces substantial errors near the applied point, 2) the solution of the dynamic stiffness analysis is disturbed in wide range near the natural frequency of the fundation (the internal resonance). In spite of the complexity 1), both of the imaginary part of the impedance and static impedance are rather exactly calculated by the indirect integral formulation. So, the real part can be indirectly obtained from them by the Hilbert transform, and also it can be directly calculated by modifying the solutions of the stress from the condition that the internal stress might be real value. The complexity 2) is resolved by putting the internal constraint surface in the foundation to take away the internal resonance point from the frequency range of interest. In order to verify the accuracy of the proposed method, this paper presents the torsional impedance analysis of axi-symmetric foundation by use of the ring-line-load solutions in a thin layered soil.

There exist three fundamental physical quantities in the dynamic soil-foundation interaction problem. These are the real and imaginary parts of impedance, and the seismic exciting force. An integral equation formulation based on the dynamic Green's functions for an elastic medium is developed for use as a tool in analyzing the fundamental physical quantities. A limited number of the evaluation for them are available at present, most of which are restricted to the case of flat foundations because in case of the embedded foundation the enormous computational time is needed for calculation of the dynamic Green's functions. It is the objective of this work to remove the limitation by applying interrelations of the physical quantities to the boundary integral equation method. The displacement field is represented by the displacement component of the Green's functions and the source distribution at the interface of soil and foundations. Both of the imaginary part of the impedance and the static impedance are directly obtained by the source distribution. The real part of the impedance is indirectly calculated from them by the Hilbert transform. The seismic exciting force is represented as the product of the source distribution and the free-field motion through use of the reciprocal theorem. Therefore, the evaluation of the physical quantities reduces to the problem of determining the intensity of source distribution. The proposed method resolves a prevailing shortcoming in the analysis of the embedded foundation ; the necessity of calculation for the stress components of the dynamic Green's functions.

本研究では,位相最適化手法を利用した建築物の新しい構造デザインツールの開発を行った。位相最適化の手法としては,2次元または3次元連続体の位相最適化手法としての均質化設計法,密度法等があり,トラスや骨組などの1次元部材の位相最適化手法としてのグランドストラクチャー法がある。本研究では,これらの方法をさらに発展させ,建築物の構造デザインに利用できるツールとして一般に普及させることを目的とした。 本研究の研究成果としでは,グランドストラクチャー法を用いた接合部の剛性を自由に変化させることができる骨組の位相最適化ツール,均質化設計法を用いた2次元およびシェル構造の位相最適化ツール,密度法を用いた3次元構造の位相最適化ツールを開発し,教育用ツールとして一般に普及させるため,GUIを付加した使いやすいソフトとして完成させた。また,骨組構造の位相最適化ツールでは,剛性の高い構造を求められるだけでなく,リンク機構のように,変形を生じさせるメカニズムも創生できる手法を開発した,さらに,2次元および3次元構造の位相最適化では,より明解な位相が求められるよう,チェッカーボード状の分布が中間的な密度がなるべく残らないような手法を開発し,プログラムに実装した。そして,最適化問題の解法としても,より計算効率の良い最適性規準法,CONLIN法などを開発し,プログラムに実装した。 以上の成果は,建築学会,機械学会,海外のジャーナル等に発表し,広く公開した。また,最終的に,教育用として一般に普及させるためプログラム付きの著書として出版される。

本研究の成果として、まず、研究代表者らが提案しているせん断変形を3次元せん断ゆがみ関数で評価する薄肉はり理論にもとずく薄肉テ-パ-はりの有限要素解析法を提案した。本解析法は、はりのたわみおよびねじり角を3次関数で、せん断変形を1次関数で近似する有限要素法であり、要素間の境界条件の矛盾を解消するために定式化の過程で変位自由度の縮約を行う。本解析法は、はりの長さ方向だけでなく、はりの断面も有限要素で分割する必要があるため、通常のはりの解析法に比較して解析自由度が多くなるが、応力レベルまで非常に良好な解析精度が得られる。本研究では、既往の研究との比較により、本方法の有効性を検証し、また、本方法により、はりのテ-パ-度と固定端近傍の応力のshear-lag現象の相関を調査した。その結果、テ-パ-度を上げることにより、固定端近傍断面のshear-lagの効果は小さくなり、また、高層骨組を薄肉はりに置換したモデルのように、せん断変形が顕著に現れる場合は、隅部の応力集中度を軽減できることが明らかになった。 次に、以上の解析法にもとづく薄肉はり構造の形状および剛性分布の最適化を行う解析法を開発した。最適化の目的は、荷重作用時の仮想仕事量として定義されるコンプライアンスの最小化とし、制約条件は構造体の体積とした。設計変数は各断面の大きさおよびはり膜面の板厚分布とした。最適設計問題は逐次線形計画法によって解いている。そして、本方法を高層ビルの意匠計画、構造計画段階で利用することを目的として、高層骨組を薄肉はりに置換した例題によりその有効性を検討した。その結果、本方法は、高層ビルの構造計画では、ブレースの効果的な配置計画や、部材種別のグル-ピング等への利用が可能であり、また、意匠計画においても、デザインのコンセプトを得ること等に利用できる可能性が示された。

無限領域中の一点に集中荷重を受ける場合の荷重点近傍の弾性応力および変位の解は弾性基本解,または単に基本解と呼ばれ,近年著しい発展をとげている境界要素法の解析理論を構成する上で重要な役割を果たしている.本研究では,有限要素法を利用した半解析的手法によって,この弾性基本解の数値解を得る試みを行った. 本研究により,以下のことが明らかになった.(1)2次元および3次元弾性体において,集中荷重近傍の解(弾性基本解)を有限要素法によって解析する場合,一般には固有値解析問題になる.(2)しかしながら,2次元問題の弾性基本解のうち,通常の集中荷重を受ける問題(Kelvin解,Boussinesq解,Cerruti解)のみ例外で,この種の問題は,変位が対数型特異性をもつため,固有値解析問題とならず,荷重ベクトルを右辺とす連立方程式を解く問題となる.(3)有限要素法でKelvin解,Boussinesq解,Cerruti解を解析するとき,2次元問題では,この3つの解の対称性を議論することなく解くことができるが,3次元問題では,Kelvin解とBoussinesq解は,軸対称問題として,Cerruti解は面対称問題として,それぞれ区別して解析しなければならない.(4)弾性基本解の応力もクラック先端近傍の応力も,どちらもr^<λー1>の形のべき乗型の特異性をもつが,弾性基本解の場合は,λは0または負の整数であるのに対して,クラック先端近傍の応力解は,λは0<λ<1の値をとる.(5)弾性基本解を有限要素法によって解析したところ,2次元問題の場合も3次元問題の場合も,解は非常に良好な収束性をもっている. なお,当初の研究目的のうち,Mindlin解の解析法を確立とTransverselyーIsotropy問題への拡張および動的問題への発展については,本研究年度内に成果が得られなかった.