Chia-Ming Fan^1,2, Chein-Shan Liu³, Weichung Yeih¹, Hsin-Fang Chan¹

CMC-Computers, Materials & Continua, Vol.15, No.1, pp. 67-86, 2010, DOI:10.3970/cmc.2010.015.067

Abstract In this study, the nonlinear obstacle problems, which are also known as the nonlinear free boundary problems, are analyzed by the scalar homotopy method (SHM) and the finite difference method. The one- and two-dimensional nonlinear obstacle problems, formulated as the nonlinear complementarity problems (NCPs), are discretized by the finite difference method and form a system of nonlinear algebraic equations (NAEs) with the aid of Fischer-Burmeister NCP-function. Additionally, the system of NAEs is solved by the SHM, which is globally convergent and can get rid of calculating the inverse of Jacobian matrix. In SHM, by introducing a scalar homotopy function and… More >

Wen Chen^1,2, Zhuo-Jia Fu^1,3, Qing-Hua Qin³

CMC-Computers, Materials & Continua, Vol.13, No.3, pp. 201-218, 2009, DOI:10.3970/cmc.2009.013.201

Abstract This paper presents high-order Trefftz functions for some commonly used differential operators. These Trefftz functions are then used to construct boundary particle method for solving inhomogeneous problems with the boundary discretization only, i.e., no inner nodes and mesh are required in forming the final linear equation system. It should be mentioned that the presented Trefftz functions are nonsingular and avoids the singularity occurred in the fundamental solution and, in particular, have no problem-dependent parameter. Numerical experiments demonstrate the efficiency and accuracy of the present scheme in the solution of inhomogeneous problems. More >

S. Mukherjee¹, S. Chakraborty², I. Manna^1,3

CMC-Computers, Materials & Continua, Vol.10, No.3, pp. 217-228, 2009, DOI:10.3970/cmc.2009.010.217

Abstract Influence of power density and interaction time for austenitisation during laser surface hardening of plain carbon eutectoid steel has been investigated. The analysis involves numerical prediction of thermal and solute diffusion profiles and thereby, the time needed for homogenization of austenite for different processing conditions. Experimental results provide qualitative validation. More >

G. Haasemann¹, M. Kästner¹ and V. Ulbricht¹

CMC-Computers, Materials & Continua, Vol.3, No.3, pp. 131-146, 2006, DOI:10.3970/cmc.2006.003.131

Abstract Novel textile reinforced composites provide an extremely high adaptability and allow for the development of materials whose features can be adjusted precisely to certain applications. A successful structural and material design process requires an integrated simulation of the material behavior, the estimation of the effective properties which need to be assigned to the macroscopic model and the resulting features of the component. In this context two efficient modelling strategies - the Binary Model (Carter, Cox, and Fleck (1994)) and the Extended Finite Element Method (X-FEM) (Moës, Cloirec, Cartraud, and Remacle (2003)) - are used to model materials which exhibit a… More >