CMES-Vol. 60, No. 1, 2010

Open Access

ARTICLE

A Meshless Collocation Method Based on the Differential Reproducing Kernel Approximation
Shih-Wei Yang¹, Yung-Ming Wang¹, Chih-Ping Wu^1,2, Hsuan-Teh Hu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.1, pp. 1-40, 2010, DOI:10.3970/cmes.2010.060.001
Abstract A differential reproducing kernel (DRK) approximation-based collocation method is developed for solving ordinary and partial differential equations governing the one- and two-dimensional problems of elastic bodies, respectively. In the conventional reproducing kernel (RK) approximation, the shape functions for the derivatives of RK approximants are determined by directly differentiating the RK approximants, and this is very time-consuming, especially for the calculations of their higher-order derivatives. Contrary to the previous differentiation manipulation, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. A meshless collocation method based on More >

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ARTICLE

Mesh Effects in Predictions of Progressive Damage in 3D Woven Composites
R. Valisetty^1,2, A. Rajendran^1,3, D. Grove²
CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.1, pp. 41-72, 2010, DOI:10.3970/cmes.2010.060.041
Abstract A multi-scale model exhibiting progressive damage is considered for a 3D-woven composite. It is based on the evolution of some fundamental damage modes in a representative volume element (RVE) of a composite's woven architecture. The overall response of a woven composite due to a variety of damage modes is computationally obtained through a transformation field analysis (TFA) that is capable of quantifying the effects of spatial distribution of micro stresses and strains on strength. Since the model is computationally intensive, its numerical requirements are to be understood before it can successfully be used in design More >

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A Topology Optimization of Moderately Thick Plates Based on the Meshless Numerical Method
S.L. Li^1,2, S.Y. Long¹, G.Y. Li¹
CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.1, pp. 73-94, 2010, DOI:10.3970/cmes.2010.060.073
Abstract A new implementation of topology optimization for the plate described by the Reissner-Mindlin theory based on the meshless natural neighbour Petrov-Galerkin method (NNPG) is proposed in this work. The objective is to produce the stiffest plate for a given volume by redistributing the material throughout the plate. We try to couple the advantages of the meshless numerical method with the topology optimization of moderately thick plate. The numerical approach presented here is based on the solid isotropic material with penalization (SIMP) formulation of the topology optimization problem. The natural neighbour interpolation shape function is employed More >

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ARTICLE

Nonlinear Vibration of the Double-Beams Assembly Subjected to A.C. Electrostatic Force
Shueei-Muh Lin¹
CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.1, pp. 95-114, 2010, DOI:10.3970/cmes.2010.060.095
Abstract In this study, the mathematical model of double-beams assembly subjected to the a.c. electrostatic force is established. This is helpful for designing sensors and actuators. The boundary condition of this system is nonlinear and time-dependent. Obviously, this system is very complicated. A new solution method is here developed to derive the analytical solution. Because the a.c. electrostatic force includes the static and harmonic forces, the system is divided into the nonlinear static and dynamic subsystems. The exact static solution is presented. In the other hand, the boundary conditions of the dynamic subsystem are nonlinear and More >

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