CMES-Vol. 68, No. 2, 2010

Open Access

ARTICLE

MLPG analysis of Nonlinear Heat Conduction in Irregular Domains
Harishchandra Thakur¹, K. M. Singh², P. K. Sahoo³
CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 117-150, 2010, DOI:10.3970/cmes.2010.068.117
Abstract MLPG method is a meshfree method which removes the need of meshing of computational domain at any stage of numerical analysis. Current article extends MLPG method to nonlinear heat conduction in irregular domains including the problem of solid-liquid phase change. Moving least square (MLS) scheme is used to interpolate the trial function and a fourth order spline function is used as the test function. Method of direct interpolation is used to enforce essential boundary conditions. Nonlinearities in the problems are handled with an iterative predictor-corrector method. Time integration is performed using θ-method. MLPG method has More >

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Birefringence Simulations of Calcium Fluoride Single Crystal Used as Chamber Window of Gas Laser Light Source
Yuta Kitamura¹, Noriyuki Miyazaki¹, Takahito Kumazaki², Naoto Nagakura³, Yasuhiro Hashimoto³, Isao Masada³
CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 151-166, 2010, DOI:10.3970/cmes.2010.068.151
Abstract CaF₂ single crystal is used as high performance optical elements. We developed an analysis system for simulating birefringence of CaF₂ single crystal used as a chamber window of a gas laser light source. The analysis system consists of a stress analysis and a birefringence analysis. In the stress analysis, the finite element method was applied to obtain the mechanical stress caused by a window holder and gas pressure. In the birefringence analysis, the photo-elastic effect gives the change of refractive indices, from which the optical path difference and the fast axis are calculated by using the More >

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Evolutionary Algorithms Applied to Estimation of Thermal Property by Inverse Problem
V.C. Mariani¹, V. J. Neckel², L. S. Coelho³
CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 167-184, 2010, DOI:10.3970/cmes.2010.068.167
Abstract In this study an inverse heat conduction problem using two optimization methods to estimate apparent thermal diffusivity at different drying temperatures is solved. Temperature and moisture versus time were obtained numerically using heat and mass transfer equations with drying temperatures in the range between 20°C to 70°C. The solution of the partial differential equation is made with a finite difference method coupled to optimization techniques of Differential Evolution (DE) and Particle Swarm Optimization (PSO) used in inverse problem. Statistical analysis shows no significant differences between reported and estimated curves, and no remarkable differences between results More >

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Crack Analysis in Piezoelectric Solids with Energetically Consistent Boundary Conditions by the MLPG
J. Sladek¹, V. Sladek¹, Ch. Zhang², M. Wünsche²
CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 185-220, 2010, DOI:10.3970/cmes.2010.068.185
Abstract A meshless method based on the local Petrov-Galerkin approach is proposed to solve initial-boundary value crack problems of piezoelectric solids with nonlinear electrical boundary conditions on crack faces. Homogeneous and continuously varying material properties of the piezoelectric solid are considered. Stationary governing equations for electrical fields and the elastodynamic equations with an inertial term for mechanical 2-D fields are considered. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. The spatial variation of displacements and electric potential are approximated by the Moving Least-Squares (MLS) scheme. More >

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