The present study proposes multi-scale topology optimization for a two-phase composite considering hyperelasticity to minimize the end compliance of a macrostructure based on a decoupling multi-scale analysis. Much attention is paid to multi-scale topology optimization for its effectiveness in the field of the advanced material design dealing with a highly complex material behavior. However, most of the researches dealing with multi-scale topology optimization assume linear elasticity to avoid its complicated mathematical formulation and huge computational costs. The present study challenges to develop multi-scale topology optimization considering hyperelastic composite materials. In this context, we propose a two-scale adjoint sensitivity analysis utilizing a localization process.
In this paper, we propose a novel algorithm of two-dimensional wall boundary representation for the computational fluid dynamics using MPS method. The proposed method is based on the conventional mirror particle method, while it utilizes the visibility determination for the mirror particle generation and the neighbor particle selection. In the mirror particle generation, we consider mirror particle’s mirror particle to avoid lack of particle number density for concave wall boundary. This present algorithm can be applied to complex boundary shape. Furthermore, problems with zero thickness obstacle can faithfully be analyzed because the neighbor particle selection with the visibility determination can detect inappropriate particle connections across boundary. The proposed method is applied to several test problems, and it is found that the present mirror particle boundary representation is robust and applicable to practical problems.
Prevention of unstable ductile crack propagation is one of crucial issues in pipeline industry. Unstable ductile crack propagation in pipelines is complex coupling phenomenon among gas decompression inside pipelines, pipe deformation and crack propagation. Therefore, numerical methods are highly valuable for safety design against unstable ductile crack propagation. In this study, fluid-structure-fracture coupling 1D model for unstable ductile fracture in high-pressure gas pipelines was developed. The model describes gas decompression and pipe deformation by 1D partial differential equations, and judges whether or not a crack propagates using dynamic energy balance. Effect of soil backfill which constrains pipe deformation is formulated as added mass on a pipe wall. Because 1D partial differential equations in the model is solved by finite difference method, the model consumes lower CPU cost as compared to 3D finite element based model. Therefore, the model has a potential as a tool of pipeline design.
This paper presents fracture simulations of reinforced concrete involving crack propagation in concrete and plastic deformation in reinforcements. The simulation is based on the nonlinear finite element framework in which the von-Mises plasticity model and the modified von-Mises damage model are applied to reinforcement and concrete respectively. The method is also capable of simulating mesoscopic fracture behavior of reinforced concrete together with internally propagating cracks. We first show the material modeling of reinforcing bar and concrete based on the von-Mises and the modified von-Mises criterion. Several numerical experiments for material behavior are presented to verify the performance of the proposed model. The mesh sensitivity and objectivity of the proposed model is also verified in 4-point bend test of RC beam without shear reinforcements. Finally, the comparisons between numerical and experimental results show that the proposed method is able to simulate the failure behavior of RC beams with shear reinforcements and the simulation results are conformable with the experimental ones.
The aim of this study is that with consideration of geometrical fluctuation, robust design is made to assure performance of material more reliable to fabrication process. Firstly a target microstructure is defined as the optimum solution for coated particulate material. Then a slightly fluctuated computational models are generated in which some random variables are defined. Multiscale analysis is done to obtain homogenized Young’s modulus, shear modulus and an index with respect to strength. Probabilistic sensitivity for those quantities of interest against design variables is analyzed by means of response surface method. For response surface, this paper studies a case where the scattering of sampling points is clustered. The characteristics of cluster sampling points determine the response surface strategy as quadratic polynomial and least square regression method. Finally the numerical result of a specific robust design for coated particulate composite material reveals that when the mean radius of particle is bigger and mean coating thickness is smaller, the less sensitive index is. It will provide a reliable guidance and save cost in the development of wide range of composite materials.
To improve the total performance of numerical simulation on PC clusters or supercomputers, not onl parallel efficiency, but also performance per computing node is becoming more important than ever before. Here, we propose an new approach to optimize the performance of a finite element code based on domain-decomposition method (DDM) on the current multi-core architecture. We propose LSC (Local Schur Complement) approach, where the Schur complement matrix is explicitly computed. We demonstrate that our approach is not only more efficient in memory usage but also faster than existing approaches, which depend heavily on the forward- and back-substitution stage of a direct solver, with our performance prediction models and also numerical examples on K Computer and Intel architecture.
The fracture morphologies of mud pastes show significantly complicated patterns in nature. The mud pastes have initially fluid-like properties, but gradually change from “fluid” to porous “solid” in their drying process. However, although it has been considered that this phenomena may be induced by the differences between shrinkage ratios of soil skeletons, the mechanical details remain unknown. In this work, we attempt to develop a novel numerical model based on three dimensional finite element method for crack propagation phenomena in bentonite pastes. In order to validate the proposed method, Hausdorff’s fractal dimension of the numerical cracking patterns was compared with those of the experiments. As a result, the numerical results showed reasonable cracking patterns, and the fractal dimension of the patterns by numerical simulation was almost consistent with the experimental results.
Conventional integration methods do not guarantee preservation of sound frequencies when they are applied to the sound ray equations treating the acoustic scattering by an isolated vortex. On the other hand, symplectic integration algorithms (SIAs) are known to preserve conservative quantities for long time integration. Even if it is so, results of our numerical experiments indicate that in the scattering problems, the frequency error increases substantially when the ray computed by SIA passes through the vortex core region. In order to decrease this error, a variable-time-stepping method (VTM) is introduced to the SIAs whose variation strategy is based on the estimation of vorticity of the background fluid flow. A total of nine SIAs are compared and the VTM is combined with the SIA which performs best among the SIAs considered. Proposed method, i.e., symplectic integration algorithm with variable-time-stepping method (SIA-VTM) is capable of preserving sound frequency at higher accuracy than the conventional integration methods for the scattering problems: numerical error of sound frequencies computed by SIA-VTM is approximately two-orders of magnitude smaller than the corresponding value computed by the SIA without VTM at the cost of only a slight increase in the CPU time. The scattered sound rays are computed for several model vortices.
There is an increasing need to automate handwork by highly-skilled workers in industry. However, human’s motion contains time and spatial perturbations, and it makes the automation difficult. In author’s previous study(19), the handwork was precisely expressed in dynamical system, and a mathematical model was established to analyze the time and spatial perturbation of an individual. In this report, the mathematical method is expanded by Lattice theory to deal with interpersonal spatial perturbation between individuals. The mathematical model is then applied to brush stroke motions of Japanese calligraphy to verify its effectiveness. As a result, a methodology is established to quantitatively evaluate proficiency levels of highly-skilled handwork based on intrapersonal and interpersonal spatial perturbation, and to provide guidelines for workers learning the handwork.
A method of isogeometric analysis (IGA) based on NURBS basis functions is applied to homogenization problems for periodic heterogeneous media and composite plates with in-plane periodicity. Since the treatment of the combination of different materials in IGA models is not trivial especially for periodicity constraints and has not been reported in the literature, the first priority is to clearly specify points at issue in the numerical modeling, or equivalently mesh generation, for IG homogenization analysis (IGHA). The most awkward, but important issue is how to generate patches for NURBS representation of the geometry of a rectangular parallelepiped unit cell to realize appropriate deformations in consideration of the convex-hull property of IGA. The issue arises from the introduction of multiple control points located at angular points in the heterogeneous unit cell, which must satisfy multiple point constraint (MPC) conditions associated with periodic boundary conditions (PBCs). Although some countermeasures may be conceivable, we suggest the use of multiple patches along with double MPC that impose PBCs and the continuity conditions between different patches simultaneously. Several numerical examples of numerical material and plate tests are presented to demonstrate the validity of the proposed method of IG unit cell modeling for IGHA.
A cohesive-force embedded damage model is proposed in this study to realize both crack nucleation and propagation. As in the existing smeared crack model and rotating crack model, the crack opening is introduced at each material point, but is treated as an internal variable to be determined implicitly. To work with the proposed damage model in crack propagation analyses, the Nested Tangent Secant Method (NTSM) is proposed as a proper alternative to the method with approximate tangent moduli. After verifying that the proposed model provides equivalent performance to the traditional cohesive zone models for cracking behavior under uniform tensile loading, we demonstrate its superiority over them in simulating crack nucleation and propagation in a plate with hole and in a beam-like structure subjected to bending. Here, the superiority of the NTSM over the Explicit Secant Method (ESM) is also discussed. Also, we studied the characteristics of the exiting cohesive zone models that do not have the crack opening as an internal variable and pointed out their limitation in history-dependent problems by taking the mixed-mode condition crack propagation analysis as an example.
In this paper, we present application of the algebraic multigrid method to a pressure Poisson equation that arises in the fluid flow simulation of the particle method. The solution method is based on the plain aggregation algebraic multigrid (PA-AMG), in which the double pairwise aggregation is employed for grid coarsening and K-cycle is adopted for multigrid cycle. The PA-AMG method is used as a preconditioner for BiCGSTAB method. The method is applied to fundamental test problems to examine the performance for solution of linear systems generated by discretizing a Poisson equation based on the MPS method. The numerical results showed that the present method is successful in coarsening grid with constant coarsening ratio and can solve Poisson equations faster than non-preconditioned BiCGSTAB method especially for large problems.
For granular particle simulations based on Discrete Element Method (DEM), we have a severe problem of its long computational time consuming. Using GPU (Graphics Processing Unit) is one of options to accelerate the computation with the high performance of floating-point operation. Since the amount of on-board high-speed memory on GPU cards is limited to several GB, we have to choose algorithms to save the memory usage. Four kinds of speed-up techniques have been proposed: a highly efficient method for neighbor-particle searching, sorting the particle order on their positions, an efficient memory usage for the tangential spring, and fusion of GPU kernel function to reduce the memory access. A benchmark test of the 3-dimentional dam-breaking problem is examined to evaluate their performances and their memory usages for four techniques, respectively. The computational performance of the code which all the four techniques are applied to is improved 14.86 times higher than the original one, and only 6% increase of the memory usage is required. It is shown that the four speed-up techniques are quite available for GPU computing to achieve higher performance and less memory usage for DEM computation. We have also demonstrated a large-scale dam-breaking test using 15,728,640 particles on a NVIDIA Tesla K20X and the simulation has completed within 5.5 hours.
A new directional-splitting CIP interpolation with the multi-dimensional Soroban mesh is proposed based on the Type-F CIP interpolation technique with a structured rectangular computational mesh. The proposed scheme does not need to treat the time evolution of the high-order derivatives and largely reduce the memory consumption. The proposed scheme applies to solutions of the two and three dimensional advection equation. The numerical results show that the proposed interpolation retains the third-order accuracy and realize the rapid solution with low memory consumption.
In this paper, a new anisotropic high viscosity model using a particle method is proposed to analyze the carbon fiber reinforced thermoplastics (CFRTP) press molding process. Anisotropy of viscosity is considered with fiber orientation vector, and LSMPS method is used to improve reliability and usability. Analysis of a simple cube pressing process demonstrates the capability of the present method to analyze anisotropic high viscosity flows without vitiating the incompressibility.
Since Particle Swarm Optimization (PSO) does not require gradient information of an objective function and its algorithm is simple, it is applied to various engineering fields. However, it is well known that in the case that the objective function is multimodal or that design parameters are high-dimensional, the search performance of PSO falls. In this article, the authors propose mPSO (modified PSO), for which the algorithm of PSO is slightly revised, and present that these problems are greatly improved in numerical experiment of benchmark problems. Furthermore, design parameters are digitized and multilevel optimization process is added to mPSO, which is applied to a three-dimensional truss structure and three-dimensional rigid frame structure, to present effectiveness of this method.
Dynamic stress intensity factor (DSIF) is analyzed based on two-dimensional (2D) ordinary state-based peridynamics (PD) theory. The equation of motion is formulated by an integral equation, and a body is discretized by a number of particles. An internal force is considered for each particle and the forces interact each other over finite distances. It is considered that the PD theory is a class of meshfree methods. In the present paper, a basic study is carried out for 2D plane stress/strain elastodynamic problems. DSIF is also evaluated for a stationary crack problem based on an equivalent domain integral form of J-integral. A moving least square method is introduced to calculate derivatives of the displacement components for evaluating the stress/strain components and the DSIF. The results are compared with the reference solutions and the path-independent property is critically examined to verify effectiveness of the discretization and DSIF evaluation.
Incompressible hyper-elastic deformation is analyzed by FEM (Finite Element Method) based on GLS (Galerkin/Least-Squares) method. The incompressible condition is introduced by Lagrange multiplier method, and stabilizing term is obtained from the least squares of Euler’s equation of the functional on reference configuration. This method can use same interpolation function for displacement and pressure. Linear elements are used for two and three dimensional large deformation process by this method. The plane strain block compression problem is analyzed, and influence of stabilizing parameter is discussed. Three dimensional torsion-compression of slender rod is also calculated. Bending process after one-revolution twisting is simulated by linear elements. It is clarified that the GLS method can calculate severe deformation of hyper-elastic material, and good correlation beteen reference solution of past studies obtained from mixed interpolation FEM was found.
A new method of structural analysis is proposed for the solution of problems of response uncertainty. In this problem, the target structural model involves uncertainty in shape to follow the non-normal distribution. The proposed method makes use of an Hermite polynomial chaos expansion (PCE) to represent the uncertainty of shapes and the response surface, and involves a mathematical formulation which is a natural extension of the deterministic finite element concept to the space of random variables. In this paper, two cases of the example problems are investigated by the new method, i.e., (1) a plate with a circular hole at the center with uncertainty in shape to follow the normal distribution and the non-normal distribution respectively, and (2) the fillet welded cruciform joints with uncertainty in shape of the weld toe radius to follow the non-normal distribution. Then accuracy of the analysis will be discussed for the two cases. The validity of the new method of structural analysis is discussed using a result of uncertainty analysis through a Monte-Carlo simulation by solution of the deterministic problems.
In this study, we perform finite element analysis of swelling-induced pattern transformation in porous gel films. An inhomogeneous field theory for polymeric gels is implemented as a user-defined material subroutine into a commercial finite element package. Swelling process is analyzed by increasing the chemical potential of external solvent. To investigate the point of buckling and the buckling mode, eigenvalue buckling prediction is conducted using a quasi incremental loading pattern instead of using the chemical potential, because the chemical potential is not available in eigenvalue buckling analysis. This approach is verified by analyzing pattern transformation in gel films with a square lattice of holes. It is found that diamond plate patterns are successfully predicted regardless of including an increase of the chemical potential under the base state, while as the base state departs from the buckling point, the buckling stress is underestimated, especially in this study, by up to about 40%. It is further found that diamond plate patterns are the most dominant mode as a result of using a larger periodic unit.
In this paper, we develop the simulation method of crack propagation under nearly incompressible condition. The finite cover method (FCM), which defines the multiple covers, enables us to deal with the discontinuous deformation. However, the conventional FCM with the constant strain triangle (CST) element suffers from stress oscillation caused by the volumetric locking. Avoiding the volumetric locking and to simulate the crack propagations in incompressible materials, we implement the P1-iso-P2/P0 element into the FCM. Several illustrations show how to approximate the discontinuous displacement fields by FCM with P1-iso-P2/P0 element. Some representative numerical examples demonstrate the performance of the proposed method for crack propagation simulations.
In this study, we propose an extended Goodman’s joint element formulation and a graph theory based mesh generation method for geotechnical analysis. Although the geometric shape of conventional Goodman’s joint element is assumed to be rectangular, the extended Goodman’s joint element has arbitrary triangular or quadrilateral shape and it is possible to model faults or joints intersecting in a soil. Additionally, the proposed mesh generation method generates tetrahedral solid elements for a soil with intersecting faults or joints modeled by extended Goodman’s joint elements.
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.
The present study proposes a multiscale topology optimization method of cross-section structures that control the macroscopic thermal deformations of a thick composite plates. The proposed optimization method is based on the two-scale composite plate model, in which thick plate theory is employed at macro-scale, while three-dimensional solids are assumed for in-plane periodic microstructures (unit cells) whose scale is comparable with the plate’s thickness. The process of the in-plane homogenization in a two-scale analysis corresponds to numerical plate testings (NPTs) to compute the macroscopic plate stiffness of the thick plate. In addition, the co-rotational formulation is employed to account for large displacement and rotation of the macroscopic plate structure, whereas material models used in in-plane unit cells, are assumed to be linearly elastic. The optimization problem that controls a nodal displacement of the macrostructure is selected as numerical examples, and their solutions are provided to demonstrate the capability of the proposed method.