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.

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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.

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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.

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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.

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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.

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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.

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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.

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In this paper, a numerical implementation of solid element and shell element with the Ogden material model is presented. This formulation derives the efficient constitutive law of Ogden material using invariants of the right Cauchy-Green tensor in the extension form of the Mooney-Rivlin's law, without solving eigenvalue problems or coordinate system transformations. This paper also validates the relationship between the present expression of the constitutive law and numerical stability. The convergence rates using the Newton-Raphson method are also illustrated through some numerical examples.

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This paper proposes a structural optimization method for obtaining mechanical structures that maximize structural stiffness, based on the level set method and topological derivatives. First, the basic concepts of a structural optimization method based on the level set method are briefly explained, and the minimum mean compliance problem is formulated. The concept of topological derivatives for cases where mean compliance is to be minimized is also explained. The specific values of such derivatives can provide crucial information concerning whether or not a hole can be created in a specified portion of the design domain. Next, a new optimization algorithm for a structural optimization based on the level set method is constructed by integrating the concept of topological derivatives. A new type of filtering scheme is also developed in order to obtain a clear optimal configuration. Finally, several examples are provided to confirm the usefulness of the proposed structural optimization method.

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Topology optimization for structures with linear behaviors has been very well studied but the number of studies on this optimization is relatively small when the structure is subjected to elasto-plastic deformations. One reason may be the computational cost to determine the design variables, however, this problem is getting less crucial due to the rapid development of computers. In this paper the density method is applied to the topology optimization of thin walled structures subjected to crashing deformations and availability of it is discussed through several numerical examples conducted with the explicit time integration scheme and the one point quadrature shell element.

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We present a distinct element method implementation algorithm which can be computed entirely on GPUs. In distinct element method simulation, force on a particle is calculated as contacting force between particles. To calculate contacting force, we have to detect collision between particles. The computational burden of this process is very high when a large number of particles are used in simulation. In recent years, the growth of computational power of GPUs is tremendous. If we can use GPUs for computation of distinct element method, it may accelerate computation speed. However, collision detection between particles is a difficult task when we use GPUs for simulation because GPUs are not designed to execute such a operation. In this study, we developed a method which makes it possible to use GPUs for collision detection. Bucket data structure is generated in four rendering passes by using depth test, stencil test, color mask and vertex texture fetch, and then collision detection is done with the bucket data. We measured calculation speed of our method and then it was compared with that of CPU implementation. The comparison shows that our method accelerates computation drastically.

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Boundary element analysis of K-values at the inclined surface crack tip under rolling contact fatigue (RCF) conditions have been performed. The RCF conditions include an accurate model of friction between the faces of cracks and the three possible effects of fluid trapped inside the crack. Comparisons were made on calculated K-values by present analyses and that by the other numerical procedures when different mechanisms are applied to the same conditions. Significant differences were shown between the results about the amplitude of the variations of both K_I- and K_II-values and their degree of overlap that were considered to be originated from the other procedures, which could not detect the contact of crack face. Since those are key factors for the crack to be propagated co-planar or arrested and branched under RCF conditions, the iteration procedure that specified the extent and location of locked, slipped and separated regions on the crack faces must be used for the calculations.

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Grid computing is increasingly influencing scientific computation practice. However, very few users can harness the power of today's Grid to run their partial differential equation (PDE) based physical simulations with desktop applications. In this paper, we present our recent finished work of GridPSi, a new problem solving environment, which automatically generates Matlab code and simplifies Grid computing for 3D finite element. With GridPSi, a user does not have to manually write finite element Matlab code, hence greatly reducing programming errors and improving efficiencies. In addition, the user needs to learn only one modeling method while enjoying multiple PDE tools (currently Matlab and PSILAB) and comparing results in a Grid environment. Finally, the simplified Grid computing pattern facilitates problem solving in a Grid environment and thus will appeal a broader user base.

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Whether the so-called Tag System can support to emerge cooperation is investigated concerned on 2 × 2 games. As the Tag System, what Riolo et al. (2001) proposed is assumed fundamentally, in which an agent has both Tag and Tol defined by [0,1] real numbers. Tol is a tolerance to recognize an opponent as a company. Both Tag and Tol are assumed to be evolving. Results show that tag's effectiveness depends on whether we allow AllD strategy in the system. If we allow AllD that implies Green Beard Effect does not work in the system, following things are implied; (1) the tag's effectiveness is meager than Riolo et al. reported, (2) Tag System can bring significant Alternating Reciprocity than the analytic solution in a Leader game; (3) the system using 2D tag space is more effectively support a cooperation that the usual Tag System.

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We examine the performance of the node-based approximation with constant strain triangular (CST) finite elements employed in the nodal-integration finite element method (NI-FEM). First, the NI-FEM, which is characterized by the node-based approximation with CST FE mesh, is briefly reviewed and is extended by means of a penalty-based mesh connection technique at material interfaces. Then, we examine its performance against shear locking and volumetric locking problems with the increase of DOFs and the sensitivity of the approximation to the distortion of elements in comparison with the standard FEM. Also, the studies are made on the capabilities of reproducing the stress concentration at free surfaces and the displacement/traction continuity as well as the discontinuous strains at material interfaces in composite materials.

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The solid-fluid mixture homogenization method enables us to simulate micro-macro coupled behaviors of incompressible permeation flows in elastic porous media. However, it needs a complex interface-fitted finite element mesh for micro scale computations of the solid-fluid two-phase unit cell. An extended finite element (X-FE) discretization technique based on the level set method and enriched interpolation is proposed for an alternative approach to the geometrical problem that can handle the solid-fluid two-phase unit cell with a simple non-interface-fitted mesh. Its homogenization and localization performances are demonstrated in a typical two-dimensional bench mark problem with a hole, and its three-dimensional application to the body-centered cubic unit cell is shown in this paper. The 3D application is prepared forward the computer-aided design of fluid permeation filters fabricated by partial sintering of the powder ceramics.

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Using a parallel FE solver, a 3-D structural analysis, whose degrees of freedom may exceed 100 million, can be performed on a supercomputer such as the Earth Simulator and the IBM BlueGene/L. To dive into such a huge scale structural model with a complicated geometry and search for a specific feature out of massive result data, we propose walkthrough visualization on a client PC terminal. This walkthrough system incorpolates advenced realtime rendering algorithms such as view volume culling, occlusion culling and VRAM management, using a hierarchical domain decomposition data structure. We applied the walkthrough system for the visualization of a structural analysis with 200 million DOFs, and rendering speed of near-realtime level was obtained.

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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.

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A dynamical model of coal and gas outbursts is presented for a parametric study of the phenomena. Identical solid plugs, which are identified with a body of coals, are placed in a row at equal intervals in a semi-infinitely long pipe with one dimension (so it is called the plug row model). Rooms between plugs are filled with the gas and the pressure change in an adiabatic change by assuming locally isolated system. Each plugs can move in the pipe with the pressure gradient force and finally eject to the outside. Through the simulation of the plug row model, the relationship between the dynamical characteristic of coal and gas outbursts and various parameters into coal mines is grasped.

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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.

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Moving particle semi-implicit method is widly used for the free surface and multi-phase flow analysis. In micro scale problems the surface tension is dominant. There have been two ways to calculate surface tension. One is based on CSF model, which is derived from continuum mechanics. The other is inter-particle force, which is similar to the inter-molecular force. The force is repulsive in short range and attractive in long range. We reveal the theoretical relation between this force and the surface tension coefficient. Oscillation of a droplet is analyzed by the present model. We also introduce the same inter-particle force between solid wall and fluid, which are represented by particles. Various wettabilities can be calculated by changing the ratio of inter-fluid and fluid-solid forces. The relation between the ratio and the contact angle is revealed theoretically. Droplet shape is calculated on a wall using the present model.

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The advent of various kinds of multi-core scalar CPUs had changed the rule of the HPC world again. To improve the total performance of a PC cluster or a MPP, not only the parallel efficiency, but also the performance per computational node is becoming more important than ever before. Here, we propose a new design and programming style to optimize the performance of a finite element code on a multi-core CPU node, considering its multimedia extension instruction set and cache hierarchy. Using element-by-element operations of solid tetrahedral 2nd order elements for linear structural problems, we demonstrate that our EBE matrix storage-free iterative solver is not only more efficient in memory usage but also faster than standard non-zero component storage solvers on a multi-core PC.

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The improved SCGS method which has stability of convergence compared with the conventional CGS method has been proposed. However, the amount of computational cost per one iteration is increased. BiCR-types of iterative methods whose residual vector is based on that of the original BiCR method were recently proposed. The BiCR-types of iterative methods exhibit stable convergence in the process of iteration. In this article, we propose the preconditioned SCRS and Modified SCRS methods which reduce the computational cost. Numerical experimets indicate that the preconditioned SCRS and MSCRS methods are very effective for solving realistic problems.

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Generalized Interpolation-based Lattice Boltzmann method (GILBM) is one of the numerical analysis methods developed from a basically Lattice Boltzmann method in order to apply to body fitted grids. By transformation of coordinate system, GILBM overcomes a fundamental problem in the LBM. However, the GILBM has a same problem as other CFD methods, that computational time increase in case applying to high Reynolds number and large-scale analysis. So, this paper investigates applications of GILBM to parallel computing for a means of reduction on computational time. In the present study, incompressible two-dimensional cavity flow is calculated in MPI environments for parallel computing system based on domain decomposition. By the system, improvement of calculation speed and parallel efficiency is investigated to verify effectiveness of parallelization GILBM and high performance technique. It will be shown that the present method is verified be effective extremely by comparisons with other CFD results.

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This paper proposes a new topology optimization method for the structural design of electromagnetic waveguides that perform according to specified guiding characteristics, where the design target of the constructed methodology pertains to waveguide cross-sections. First, the concept of topology optimization and a way to apply it to electromagnetic problems are explained. Design requirements for the waveguide cross-sections are then clarified and corresponding objective functions are formulated. A new multi-objective function is formulated to reduce grayscales since using a penalization parameter for physical property interpolation is ineffective in electromagnetic problems. For the eigen-value analysis, the Finite Element Method with hybrid edge/nodal elements is used, to avoid undesirable nonphysical, spurious solutions. The optimization algorithm is constructed based on these formulations and Sequential Linear Programming. Finally, several design examples of waveguide cross-sections are presented in order to confirm the usefulness of the proposed method.

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In this paper, a Mach-uniform pressure-correction method for the compressible Euler equations is validated. Usually the accuracy of the numerical solution becomes lower in the low Mach number regime because of the stiffness problem. In order to improve this low accuracy, the nondimensionalization based on the pressure is adopted in the Mach-uniform pressure-correction method. The compressible Euler equations are solved by the second order method of lines with artificial viscosity. Two dimensional flows past a circular cylinder are considered. A Mach-uniform approach shows the very good results in supersonic, transonic and subsonic regimes in comparison with the standard Euler solutions. Also the pressent approach gives the reasonable solution in quasi-incompressible and incompressible regimes. Then, it is concluded that the present Mach-uniform pressure-correction method is very hopeful to solve the compressible Euler equations in the almost all Mach number regimes.

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This paper deals with 3D time-harmonic eddy current analyses using the A-φ method with the continuity of the excitation current density that uses the magnetic vector potential A and the electric scalar potential φ as unknown functions. To analyze large-scale problems with over 10 million complex degrees of freedom (DOF) in parallel environments, Hierarchical Domain Decomposition Method (HDDM) is introduced, together with the data handling type “Parallel processor mode (P-mode)”. Furthermore, we research the characteristics of HDDM in time-harmonic eddy current analysis and obtain the knowledge for large-scale time-harmonic eddy current analysis. To confirm the efficiency of our method, we analyze a simple model changing its DOF several times up to 44 million complex DOF. The computations are performed with a PC cluster that consists of 32 PCs. As a result, a time-harmonic eddy current problem with 44 million complex DOF is successfully solved in less than five hours.

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We present a sliced data structure that is effective for neighboring particle search of particle-based simulations. In the method, a grid is constructed dynamically to fit to a particle distribution. Rather than computing the grid fitting perfectly to a particle distribution where there are no voxels which does not store particle indices, we compute a grid with some margin to the distribution. This lowers the computation cost of generating the data structure. Before storing indices of particles to a grid, key values which are used to compute the index of a voxel are computed. The present data structure can be introduced to particle-based simulations on the Graphics Processing Unit (GPU) because the construction of this data structure and access to stored values can be also performed entirely on the GPU. The present data structure free us from a restriction of computation region with a fixed grid and so that we can simulate particle motions in a larger area. Moreover, the cost of the present method is low enough to be able to use for real-time applications. In this paper, we first introduce the sliced data structure and then describe how to implement it on the GPU. Then the present method is applied to particle-based simulations and quantitative evaluations are presented.

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In this paper, an arbitrary Lagrangian-Eulerian (ALE) overlaying mesh technique is proposed for the computational solution of fluid-shell interaction problems with large deformations and complex geometries. In the proposed method, a fluid-shell strongly-coupled analysis is carried out only within the local mesh domain including a deformable shell structure by an interface-tracking ALE method, while a global domain mesh is solved under the immersed boundary (IB) forces which are evaluated from the local mesh solutions of fluid-structure coupling forces on their interface. Therefore, two kinds of fluid-structure coupling computations are interactively carried out between local and global meshes. A falling paper and a flapping filament are simulated to demonstrate the superior performance of the proposed method.

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It is very difficult to implement mesh-based method for underwater explosion (UNDEX) because large deformation and inhomogeneity occur in the whole domain. Therefore Smoothed Particle Hydrodynamics (SPH) method familiar as a particle method is applied to UNDEX problems and the effectiveness has been shown. However the standard SPH method has inconsistency problem, which often leads to remarkable reduction of the accuracy due to the boundary deficiency or unbalanced particle distribution in a support domain. In the UNDEX analysis using the SPH method, the numerical oscillation of pressure also arises from discontinuity at the gas-liquid interface. In this study, we make use of Moving Least Squares (MLS)-SPH method that always fulfills the first order consistency condition and Discontinuous-derivative Basis Function (DBF) in the MLS approximation and investigate into discontinuous-derivative treatment at the gas-liquid interface.

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The governing equation of elasticity is discretized into the motion equations of the particles using the least square method. Using the symplectic scheme for a Hamiltonian system, we can obtain energy conservation for discretized calculations. However, local particle oscillations occur, which excessively decreases low frequency motion. In this study, we propose an artificial force to suppress the local oscillations, without affecting the physical property. With and without the force, accuracies are compared using a loaded bar model and wave propagation models. The local oscillations are reduced by the proposed artificial force.

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The Cartesian grid method is very useful for CFD simulation around a complex geometry in terms of automatic and robust grid generation. However, it is difficult to simulate both large-scale and subgrid-scale flow simultaneously on the Cartesian grid because of the restriction of a computing resource. Therefore, an empirical formula is often employed on the Cartesian grid system to incorporate the subgrid-scale effect of fluid characteristics. For example, in the case of flow computation for heat exchangers, the detail of geometry is usually not represented. Instead, Darcy’s law is used to simulate the relationship between flow rate and pressure drop. Moreover, for the flow calculation around the unaligned heat exchanger with respect to the underlying Cartesian grid, a special technique is necessary to express the pressure drop along the normal direction of the inclined heat exchanger. In this paper, the empirical formula that describes macroscopic fluid properties is expressed as an external force in the incompressible Navier-Stokes equations. This formulation is also valid for unaligned heat exchangers. Special attention is paid to the iterative method of the pressure Poisson equation in order to satisfy the constraint of the fluid characteristics for the heat exchanger. To validate the proposed method, several examples were calculated. Finally, it was found that the proposed method could reasonably predict the pressure loss of the inclined heat exchanger. In addition, the convergence behavior of the iterative process was investigated.

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This paper presents a parallel computing technique for the multi-scale piezoelectric analysis based on the crystallographic homogenization method. In the finite element equation for the conventional piezoelectric analysis, coefficient matrix is not positive definite and ill-condition because of the piezoelectric coupling problem. A parallel computing technique for microscopic analysis is newly developed based on the iterative partitioned coupling method with the parallel conjugate gradient (CG) solver. The parallel iterative method improves the condition number of coefficient matrices without applying precondition technique. In the parallel analysis code, a hierarchical process distribution is introduced to reduce amount of data for communication. Numerical experiments show safe convergence of both the iterative partitioned coupling method and the CG method by using the partitioned solution procedure into structural and electrical fields.

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