CMES-Vol. 64, No. 1, 2010

Open Access

ARTICLE

Higher-Order Stress-Strain Theory for Damage Modeling Implemented in an Element-free Galerkin Formulation
Yang Yang¹, Anil Misra²
CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.1, pp. 1-36, 2010, DOI:10.3970/cmes.2010.064.001
Abstract Gradient theories have found wide applications in modeling of strain softening phenomena. This paper presents a higher order stress-strain theory to describe the damage behavior of strain softening materials. In contrast to most conventional gradient approaches for damage modeling, the present higher order theory considers strain gradients and their conjugate higher-order stress such that stable numerical solutions may be achieved. We have described the derivation of the required constitutive relationships, the governing equations and its weak form for this higher-order theory. The constitutive coefficients were obtained from a granular media approach such that the internal More >

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ARTICLE

Algebraic Formulation of Elastodynamics: the Cell Method
E. Tonti, F. Zarantonello¹
CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.1, pp. 37-70, 2010, DOI:10.3970/cmes.2010.064.037
Abstract This paper completes a preceeding paper on the algebraic formulation of elastostatics [Tonti, Zarantonello (2009)]. It shows how to obtain a numerical formulation for elastodynamics by avoiding any process of discretization of differential equations, i.e. PDE-free formulation. To this end, we must analyse in more detail the discretization of time by highlighting the need to introduce a dual subdivision of the time axis, as we did for a space cell complex. The mass matrix obtained with the direct algebraic formulation is diagonal. More >

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On the Solution of an Inverse Problem for an Integro-differential Transport Equation
Ismet Gölgeleyen¹
CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.1, pp. 71-90, 2010, DOI:10.3970/cmes.2010.064.071
Abstract In this paper, the solvability conditions for an inverse problem for an integro-differential transport equation are obtained and a numerical approximation method based on the finite difference method is developed. A comparison between the numerical solution and the exact solution of the problem is presented. Experimental results show that proposed method is robust to data noises. More >

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A Simple OpenMP Scheme for Parallel Iteration Solvers in Finite Element Analysis
S.H. Ju¹
CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.1, pp. 91-109, 2010, DOI:10.3970/cmes.2010.064.091
Abstract This study develops an OpenMP scheme to parallel the preconditioned conjugate gradient methods (PCG) in shared memory computers. The proposed method is simple and systematic, so a minor change in traditional PCG methods may produce effective parallelism. At first, the global stiffness matrix is re-numbered in order to produce a parallel three-line form matrix, and a subroutine only needs to be called once in the finite element analysis. Several basic OpenMP commands are then added into the traditional incomplete Cholesky factorization (ILU) and symmetric successive over-relaxation (SSOR) codes to make the procedures of matrix multiplication, More >

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