Open Access
ARTICLE
J. Sladek1, V. Sladek1, P. Stanak1, Ch. Zhang2
CMC-Computers, Materials & Continua, Vol.15, No.1, pp. 1-26, 2010, DOI:10.3970/cmc.2010.015.001
Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve laminate plate problems described by the Reissner-Mindlin theory. Both stationary and transient dynamic loads are analyzed here. The bending moment and the shear force expressions are obtained by integration through the laminated plate for the considered constitutive equations in each lamina. The Reissner-Mindlin theory reduces the original three-dimensional (3-D) thick plate problem to a two-dimensional (2-D) problem. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the center of a circle surrounding this node. The weak-form on small subdomains with a Heaviside step… More >
Open Access
ARTICLE
Rasa Kazakevičiũtè-Makovska1
CMC-Computers, Materials & Continua, Vol.15, No.1, pp. 27-44, 2010, DOI:10.3970/cmc.2010.015.027
Abstract The phenomenon of stress softening observed in the cyclic inflation of spherical balloons or membranes is quantitatively and qualitatively examined. A new measure of the stress softening extent is proposed which correctly captures the main feature of this phenomenon. This measure of the stress softening is related to the relevant response functions in the constitutive models proposed in the literature to describe this effect. Using these relationships, the predictive capability of the theoretical models is examined. It is shown that only those theoretical models which admit a non-monotone character of the stress softening can properly describe this phenomenon. More >
Open Access
ARTICLE
Chih-Wen Chang1, Chein-Shan Liu2, Jiang-Ren Chang3
CMC-Computers, Materials & Continua, Vol.15, No.1, pp. 45-66, 2010, DOI:10.3970/cmc.2010.015.045
Abstract In this article, we propose a semi-analytical method to tackle the two-dimensional backward heat conduction problem (BHCP) by using a quasi-boundary idea. First, the Fourier series expansion technique is employed to calculate the temperature field u(x, y, t) at any time t < T. Second, we consider a direct regularization by adding an extra termau(x, y, 0) to reach a second-kind Fredholm integral equation for u(x, y, 0). The termwise separable property of the kernel function permits us to obtain a closed-form regularized solution. Besides, a strategy to choose the regularization parameter is suggested. When several numerical examples were tested,… More >
Open Access
ARTICLE
Chia-Ming Fan1,2, 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 >
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