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.
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.
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.
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.