This paper presents a formulation for the Cam-clay model based on the finite deformation theory with the multiplicative decomposition of the deformation gradient. We developed an implicit stress-update scheme using the return-mapping algorithm and derived the consistent tangent modulus analytically. We also demonstrated that the scheme had high accuracy and quadratic convergence. By conducting the finite element analysis, we obtained the following conclusions. 1) Even though the Cam-clay model has compressibility both elastically and plastically, volumetric locking occurs. That is because the model shows the nearly incompressible property in the vicinity of the critical state. 2) F-bar method is useful for avoidance of the volumetric locking.

This paper investigate the improvement of the failure load for lattice sandwich panels by using the linear buckling load factor. In our calculation, the lattice panel maximized the initial stiffness is used as a initial structure, and the buckling load factor is optimized by changing struts’ diameter. Also, in order to clarify the effectiveness of this optimization, the failure load was calculated by using the elastoplastic stress analysis, and compared with the buckling results. It has been shown that this approach can be useful for enhancing the failure load of the lattice panel under the small value of the volume constraint. However, when the value of the volume constraint is increased, the failure load of the optimized lattice panel cannot be improved, which is based on the fact that the plastic hinges would be observed at some connection points between strands before the occurrence of elastic buckling.

In this work, we propose the improved computational method to reduce the computaional time and the memory usage in GPU-based DEM simulations. Our method has simulteneously achieved performance improvement and reduction of memory usage by improvements of data structure of neighbor particle list. In the parallel algorithms of previous computational process in which one thread correspond to one particle, the warp-divergence frequently occurs because the number of neighbor lists is different. On the other hand, our method can reduce warp-divergence in calculation of particle-particle interaction, and we applied spatial-blocking to DEM calculation that is used in stencil computation to reduce cache miss in reference of neighbor particles. Then, we achieved 1.5x speed up and reduction of 35 ％ memory usage. We can also complete 20 million particles and 200000 time step simulation in 3.3 hours by single Nvidia GTX980 GPU. This result shows the feasibility of low-cost large-scale DEM simulation using our method.

This study proposes a topology optimization method to minimize the maximum stress of a structure for transient external loads. To deal with external loads with arbitrary waveforms, the equations of motion are solved using the Newmark’s β method of the step-by-step integration. Also, a new objective function is defined to minimize the maximum von mises stress occurring at all times of interest in the analysis. We formulate the analytical sensitivity of the transient response problems by applying the adjoint variable method and the idea of the Discretize then differential approach, which provides sensitivity with high accuracy. The formulated sensitivities are validated by an accuracy verification using the finite difference method as a benchmark. Finally, the effectiveness of the proposed method is confirmed by presenting several optimization calculations.

In this study, we propose a topology optimization method for unsteady heat conduction problems. To consider the historical dependence of the temperature field in unsteady heat conduction problems in the sensitivity analysis, we apply the Discretize then differential approach, which is the most versatile and can calculate the sensitivity with high accuracy regardless of analysis conditions, and formulate the sensitivity in detail. Also, to derive a structure that can be controlled to an arbitrary temperature distribution while ensuring the thermal conductivity, an objective function based on a weighted sum function of the thermal compliance and the squared error from target temperature is newly defined. The formulated sensitivity is validated through accuracy verification using the finite difference method as a benchmark. Finally, the validity of the proposed method is verified by showing several examples of optimization results.

The fundamental laws of physics, such as the second law of thermodynamics and the mass conservation law, cannot be satisfied for systems obtained after space discretization, even if the original governing equations satisfy them. To this end, a new weakly compressible particle method with physical consistency was developed in this study. Since the discrete formulations of this method can be fit into the extended Lagrangian mechanics for systems with dissipation, it satisfies the fundamental laws of physics, i.e., physical consistency. The formulations were mostly inherited from the previously developed strictly incompressible particle method, which is also physically consistent. Instead of the implicit algorithm employed in the previous method, an explicit algorithm is employed in the present method for improved calculation efficiency. Static pressure, droplet extension and dam break calculations were conducted, and the ability to predict the pressure and fluid motion was confirmed by comparing with the theory and experimental results. The calculation efficiency was found to be better than that of the implicit algorithm-based strictly incompressible method.

This paper presents a layout design method of a noise filter that simultaneously optimizes an arrangement of electrical components and a conductor pattern. A conductor design method has been proposed based on topology optimization, but its solutions are limited to sub-optimal under the viewpoint of overall optimality, because the arrangement of components is treated as a given condition. For integratively optimizing both of them, this study extends a topology optimization framework incorporating external variables with metamodeling, where the external variables correspond to the arrangement of components. A face-centered cubic design and sequential addition of samples are introduced to efficiently perform its metamodeling even under large number of external variables. Two numerical examples of noise filter design problems are demonstrated, and their results show that the integrative optimization significantly improves the filter performance as compared with non-integrative optimization.

The objective of this study is to propose cohesive-traction embedded damage-like constitutive law based on non-local approach and its numerical implementation using Petrov-Galerkin method to improve dependence of directional mesh bias in crack propagation problem. The extension from local approach to non-local approach is made by the introduction of weak formulation of balance equations between principal stresses and cohesive traction vectors. In addition, Petrov-Galerkin method is employed for numerical implementation that allows us to obtain proper crack propagation without dependence of directional mesh bias caused by C⁰ continuity of shape functions. To represent propagation of crack surface between finite elements, the weighting function of the balance equations is shifted from conventional one, which is the first derivative of a test function, to the same order function as test function, which is obtained by finite difference approximation. After verifying the equivalence of the proposed non-local approach to conventional one, we investigate the sensitivity of an additional numerical parameter to shift the weighting function. Finally, the capability of the proposed method is demonstrated by comparing the numerical results of the crack propagation problem obtained by finite element method and isogeometric analysis between two different meshes.

In this paper, we propose an optimization method for a unit cell structure of electromagnetic metamaterials using a level set-based topology optimization method incorporated with a high contrast homogenization method. The high contrast homogenization method can express wave propagation behaviors in metamaterials for a wide range of frequencies, and it can capture unusual properties caused by local resonances, which cannot be estimated by the conventional homogenization approaches. An optimization problem is formulated with an objective function composed of the homogenized coefficients, and a sensitivity analysis is conducted based on the concept of the shape derivative and the topological derivative. As numerical examples, we offer optimal configurations of unit cells exhibiting negative permeability. We examine wave propagation behaviors on the electromagnetic metamaterials composed of the optimized unit cells using the Helmholtz equation, and we confirmed that the obtained unit cell structures function as bandgap structures.

Reduced order model based on the Galerkin Projection was applied to the 2D cavity flow under high Reynolds number conditions and the swirling flow analysis in pipings, and the calculation accuracy and the effect of shortening the calculation time of the flow analysis using the reduced order model were examined. (1) The calculation accuracy of the reduced order model constructed with 40 bases was 2.64% for the 2D cavity flow under the condition of Reynolds number=10⁵, which was 87 times faster than the three-dimensional fluid analysis. (2) The calculation accuracy of the reduced order model constructed with 6 bases was 0.43% for the simulated piping flow under the condition of Reynolds number=10⁴, which was 38 times faster than the three-dimensional fluid analysis.

In this paper, we develop a polygon wall boundary model with consideration of corners of wall domain that is suitable for semi-implicit particle method, such as Incompressible Smoothed Particle Hydrodynamics (ISPH) method. The polygon model is based on Explicitly Represented Polygon (ERP) model, and definition of reflecting operation for surface polygon is extended in order to eliminate error occurred near corners in the original ERP model. Besides, volume of wall domain expressed near corners are modified using an approximate formula based on planer angle and solid angle of corners to improve accuracy of the calculation. We introduce the improved ERP model to ISPH method, and solve three-dimensional hydrostatic and dam break problems as numerical examples. According to the results, it is confirmed that the improved ERP model can obtain more accurate and smoothed distributions of pressure than the previous ERP model.

In the viewpoint of design efficiency in the development of an oil jet-cooling electric vehicle motor, the simulation technology of the particle-based method, which is suitable for free-surface flows with moving walls, is desired. However, it is not so easy to simulate the heat transfer with high accuracy and short computing time, so that it is especially difficult to apply it to impinging-jet cooling engineering design. Therefore, in the present study, a heat transfer model for an impinging jet flow is developed, based on the flow field obtained with the particle-based method. The analogy between the heat and momentum transfers is assumed in the model, and the impinging jet velocity, and the characteristic length scales of Reynolds and Nusselt numbers in the stagnation region. The model is constructed through comparing with the impinging jet flow experimental correlation expression formula. The model validity by comparing with the oil-cooling rotor experimental results is confirmed. It is found that the model-implemented simulations agree well with the correlation expression formula and the experimental results.

Computation performance has rapidly increased by equipping a large number of cores. To use effectively these high-performance computers, the domain decomposition method, which divides a space domain into sub-domains, has been widely employed in large-scale simulations, in which each core carries out parallel computing. On the other hand, the parallel in time integration has been proposed to further utilize massive cores in high performance computer more efficiently. Although theoretical studies on the method have been reported, its adaptability for engineering applications has still been under investigation. To investigate this, the parareal method, one of the methods of the parallel in time integration methods, is adapted into a general-purpose groundwater simulator TOUGH2 in this study. The developed code is applied to groundwater simulations with water injection in a radially symmetrical model. The results show that the parareal method can reduce the computation time down to one-eighth, compared with that from serial in time method.

This study aims to enhance the crack phase-field model for ductile fracture by introducing a novel degrading fracture toughness to reflect damage evolution based on the phenomenological justification for the failure mechanism in elastoplastic materials. The free energy consists of elastic, pseudo-plastic and crack components. The governing equations are derived as stationary conditions for the corresponding local and global optimization problems within the continuum thermodynamics framework. Then, we introduce a degrading fracture toughness to reflect the evolution of micro-defects and their coalescences that are caused by both plastic deformation and negative hydrostatic pressure. Equipped with this implement, the proposed crack phase-field model realizes the reduction of both stiffness and fracture toughness to simulate the failure phenomena of elastoplastic materials. Two numerical examples are presented to demonstrate the capability of the proposed model in reproducing typical ductile fracture behaviors.

Compact and boundary compact schemes are often combined under non-periodic boundary conditions to simulate numerically the fluid flow near a wall. Because compact schemes are implicit schemes, computational results are influenced by the choice of boundary compact schemes. Thus, the grid convergence of a combination of compact and boundary compact schemes should be considered. This study reveals that selecting boundary compact schemes significantly affects the relationship between grid spacing and computational error for dozens of nodes close to boundaries when the same compact scheme is used throughout a region, excluding near boundaries. This study also reveals that using explicit high order finite difference schemes near boundary nodes is effective at improving grid convergence.

A new implicit solver in the moving particle hydrodynamics (MPH) method for high-viscous incompressible flows was developed. Since the incompressible MPH (MPH-I) method can calculate strictly incompressible flows in the physically consistent manner, it is useful for calculating fluid which shows little compression even under high pressure load as in molding. In this study, the large linear system to be solved in the original MPH-I method was converted to the one with a positive definite symmetric coefficient matrix with less dimensions by substituting the pressure equation into the motion equation. With keeping the mathematically identical calculation, the efficiency was largely improved. The calculation speed with the present implicit solver was compared with the existing MPH methods such as weakly compressible MPH through a calculation of colliding high-viscous object. The present method was the fastest in the cases with large diffusion numbers. Furthermore, the performance of the method under high pressure load was demonstrated using a molding-like calculation.

This paper proposes a bottom boundary-fitted moving particle semi-implicit/simulation (MPS) method in transformed space for viscous flow problems. The proposed method contains a novel mixed partial derivative model to represent the viscosity term. The mixed partial derivative model is introduced by a novel comprehensive derivation of the differential operator models of the MPS method. The verification of the proposed method is conducted by the numerical convergence of mixed partial derivative and Laplacian in curvilinear space. Moreover, accurate numerical results of the proposed method are confirmed in a hydrostatic pressure problem with a curve bottom boundary. Its applicability to dynamic problems is demonstrated by solving a wave propagation over a triangular bottom sill.

This research presents a level set-based topology optimization method involving user-specified parting surfaces for the molding process. First, the concept of topology optimization and the level set-based method is briefly described. Second, certain geometrical features needed for molds to be decomposed are clarified. Then, an extended normal vector is defined via Partial Differential Equation (PDE) of geometrical shape features, and such geometrical requirements for mold forming are expressed using the normal vector. Based on the PDE, the geometrical constraint for the molding process is formulated. Next, a topology optimization problem of the linear elastic problem is formulated considering the mold forming constraint. A level set-based topology optimization algorithm is constructed where the Finite Element Method (FEM) is applied to solve the governing equation of the linear elastic problem and the PDE for geometrical constraint and to update the level set function. Finally, numerical examples are offeblack to illustrate the mold releasability of the design, confirming the validity and the utility of the proposed method.

To obtain the conceptual structure of an automobile frame from a large area of metal blocks by topology optimization, a volume constraint of less than 1% and sufficient element resolution are required. By using the building cube method framework, usually a finite volume method solver using hierarchical orthogonal lattices, as a voxel finite element method solver for orthogonal lattices with connectivity, we perform iterative topology optimization in a massively parallel environment. Topology optimization of billions of elements intended for a vehicle frame is performed using tens of thousands of processors and its parallel performance is measured.

This paper proposes a nonlinear computational model for predicting flexural fracture behavior of reinforced concrete beam based on Euler-Bernoulli beam theory. The model is verified by showing the convergence rate to the theoretical solution, and then validated by the comparison between the numerical and experimental results. The material nonlinearity of steel and concrete brings two nonlinear problems for finding the bending moment, stress, strain and curvature, and the problems are solved by coupling the bisection algorithm and Newton method. After formulating the four-point bend problem of reinforced concrete beam based on Euler-Bernoulli beam theory, several numerical examples are presented to verify and validate the proposed nonlinear computational model.

The simultaneously iterative procedure for elastic-plastic boundary value problems proposed by the authors is extended to elastoplastic problems under plane stress state. The authors define a coupled problem of the equilibrium equation, the yield equation, and the plane stress condition at every material points, and develop a numerical procedure based on the block Newton method to solve them with simultaneous linearization. In the proposed block Newton method, the tangent moduli can be constructed algebraically by eliminating the internal variables, which are also updated algebraically without local iterative calculation. In addition, the residuals of yield criterion and plane stress state are incorporated into the linearized equilibrium equation. Hence, the proposed procedure enables us to decrease the residuals in the coupled boundary value problems simultaneously. Some numerical examples illustrate the validity and the effectiveness of the procedures under plane stress state with material nonlinearity.

The performance of the extended B-spline-based implicit material point method (EBS-MPM) in elastic-plastic problems is assessed in terms of accuracy and numerical stability. In order to examine the calculation accuracy and the capability in suppressing the volumetric locking and/or pressure oscillation due to plastic incompressibility, we carry out several verification analyses, in which both low and higher-order polynomials are adopted for the basis functions, in comparison with the result by the finite element method. It is also worth mentioning that the Nitsche’s method employed to impose an arbitrary boundary condition for the EBS-MPM enables us to carry out the present numerical verification.