Open Access
ARTICLE
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 length scale parameter reflects the… More >
Open Access
ARTICLE
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 >
Open Access
ARTICLE
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 >
Open Access
ARTICLE
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, decomposition, forward substitution, and backward… More >
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