We develop a particle method for nonlinear elastodynamics of compressible and incompressible materials from a direct discretization of their Lagrangian. This particle method is a Hamiltonian system with which holonomic constraints are accompanied in incompressible case. Symplectic schemes (the Störmer/Verlet scheme in compressible case and the RATTLE algorithm in incompressible case) are adopted to improve the quality of the particle method. Some numerical tests indicate the exellence of the method in conservation of mechanical energy besides that of linear and angular momenta.
The objective of this paper is to develop a finite strain shell element with its material restricted to hyper-elasticity. This shell element is based on the MITC shell element developed by Bathe in 1984 to perform locking-free behavior using assumed transverse shear strains. In addition to this MITC formulation, an assumed transverse normal strain is introduced to treat thickness change. In this formulation, the transverse normal strain is assumed to be uniform throughout the element, and evaluated at the middle surface using incompressibility condition. Indeterminate pressure, which occurs in incompressible materials, is eliminated at the element level using the plane stress condition. The advantage of this technique is that well-conditioned tangent stiffness for a large strain shell element can be obtained without any additional variables. Numerical analysis was conducted to assess the performance of the present shell element using several examples.
We present the new grid system called ”Voronoi Reduced grid” on the sphere. The Voronoi Reduced grid is a kind of Reduced grid, and is characterized by grid control volume defined by the Voronoi region of the spherical Voronoi diagram. Voronoi Reduced grid shows uniform grid aspect ratio over the whole grid on the sphere. Voronoi Reduced grid can dramatically decrease truncation error on divergence field around the pole, which has been an open problem noticed by Dey.(1) In adition, we show results of validation on numerical accuracy and computational stability on the Voronoi Reduced grid.
In the previous studies, the overall elastic moduli were theoretically determined for a composite material containing anisotropic ellipsoidal inhomogeneities randomly distributed in an isotropic matrix. In that study, as the macrostress which acts in an arbitrary direction had already been determined, an analytical theory in which local regions are considered was proposed, as well as a general analytical formula, and their validities were also proved. In this study, for the same composite material as used in the previous study, an analysis was performed on the interactions among inhomogeneities and on the interaction between those inhomogeneities and the matrix. Firstly, based on the Eshebly model, with a view to considering the interactions between the inside and the outer local boundaries, the influential factors on elastic compliance were determined. Secondly, using the factors based on the Reuss model, self-consistent conditions of the Kröner model were presented. Thirdly, general formulations were examined based on their conditions, and the overall elastic moduli of composite material were clarified. Furthermore, using the example of SiC fibers randomly distributed in an isotropic aluminum matrix, numerical results are provided.
In order to develop a lightweight plastic bottle, the application of optimal method to the plastic bottle design is investigated. The Statistical Design Support System (SDSS) which is the optimal design method combined with FE simulation is adopted. Five kinds of characteristic values are obtained by FE simulation. They are loads of vented and unvented longitudinal compression, reduction in volume or buckling pressure at reduced pressure, increase in volume at increased pressure, and squeeze load. The analysis of variances, response surface equations, and optimum dimensions for design factors are calculated by SDSS. The optimum dimensions for minimum bottle weight are found under some conditions constrained by the characteristic values and bottle size. It is shown that the application of the optimal method to the bottle design is effective for developing a lightweight bottle.
With the recent rapid progress in handsets, these antennas must keep pace with the downsizing of the handset unit. In this paper, we focus on topology design of magnetic materials for miniaturization of built-in antenna. In particular, the planer inverted F antenna are designed which allow for lowering resonance frequency. The density approach is applied to the topology optimization in order to analyze the topology of magnetic material. The FDTD method is used to analyze of electromagnetic field, and the adjoint variable method is used to analyze of the design sensitivity. As a result, it is confirmed that the optimal configuration of the magnetic materials can be obtained by using topology optimization approach.
Many methods to simulate rigid body motion and collision have been developed in the computer graphics field recently. In most methods, polygons are used to represent a rigid body configuration. In this paper a novel particle based method is presented and some examples are calculated. A simple algorithm for collision detection is proposed using particles and Distinct Element Method (DEM) is used for collision response. In the case that a configuration of a rigid body is complicated, the quantity of data is reduced and the calculation is fast. It is also easy to couple with fluid motion using Moving Particle Semi-implicit (MPS) method.
近年，計算工学の発展や計算機性能の向上に伴い，複合構造物を詳細にモデル化・解析したり，材料の微視構造を解析して巨視的な挙動を評価したりすることが一般的になっている．これに伴い，構造解析や数値解析の対象は，より複雑化・大規模化する傾向にあり，継続的な技術革新が求められている．しかし，構造解析において最も多く利用される有限要素法(FEM)は，解析対象のメッシュ分割が現在においてもボトルネックとなっており，必ずしも解析対象の複雑化・大規模化の問題に適応しているとは言えない．具体的には，規模化を考えると低次要素の利用が望まれるが，高精度な高性能要素が提供されているのは，自動メッシュ生成に制限のある四角形・六面体要素のみであり，また自動メッシュ分割が可能な三角形・四面体要素では，高性能な低次要素は提供されておらず，高次要素の利用が前提となっている．Dohrmann et al.は，FEMにおける定ひずみ三角形要素・定ひずみ四面体要素の有限要素近似を，従来の要素ベースから節点ベースに応用した節点積分有限要素法(Nodal-Integration FEM; NI-FEM)を提案している．これによれば節点ベースの近似によって，低次近似にも関わらず要素ベースのCST近似よりも近似精度が向上するばかりか，三角形・四面体のメッシュをそのまま利用するので，FEMのプリプロセッサによる自動メッシュ分割(オートメッシュ)も利用可能である．したがって，NI-FEMを利用することにより，上で述べた，低自由度かつ自動メッシュ生成が可能な要素を用いて，精度の良い有限要素解析が期待される．しかし，NI-FEMの近似特性や変形性能についての基礎的な検討は，十分には行われておらず，様々な分野への適用に先立って把握しておく必要がある．そこで本研究では，Dohrmann et al.が提案したNI-FEMの近似特性や変形性能に関する基礎的な検討を行う．具体的には，低次の有限要素近似において重要な曲げ変形に伴うせん断ロッキングと非圧縮性に伴う体積ロッキングの問題や，円孔穴あき板における応力集中の問題，異種材料界面を含む複合構造の問題を設定し，自由度数や近似に利用する有限要素のゆがみに対する影響などを検討する．また最後に，節点近似に利用する有限要素の数の違いを考慮した例題を示し，その影響についても考察する．
Using a parallel FE solver, a 3-D structural analysis, whose degrees of freedom may exceed 100 million degrees of freedom, can be performed on a supercomputer such as the Earth Simulator (ES) and the IBM BlueGene/L. However, the data size of the analysis result also becomes huge. Server-side rendering capability is required for the visualization of such a huge scale structural analysis. We developed an off-line visualizer running on the ES and PC clusters. It is vectorized on the ES and scalar-tuned on the PC clusters. It is also parallelized. Here in this paper, we focus on our polygon rendering algorithm using a look-up table approach, which is required for image generation of surface scalar contour and deformation plots of our off-line visualizer.
In recent years, several CAE (Computer Aided Engineering) systems intended for a large scale parallel finite element analysis have appeared and their performance and functionality have also been improved. However, difficulty of system installation procedures and complexity of user operations have also become a heavy burden on CAE users. In this paper, we developed a client-server type CAE system based on a back-end PC cluster and a Java3D-based front-end Web interface. The system helps a user to utilize the remote high performance computational server through the Internet with a simple user interface. The user, sitting in front of a local PC terminal, can perform a large scale finite element analysis over ten million degrees of freedom with 3-D interactive operations from a Web browser.