Hong-Hua Dai^1,2, Jeom Kee Paik³, S. N. Atluri²

CMC-Computers, Materials & Continua, Vol.23, No.2, pp. 155-186, 2011, DOI:10.3970/cmc.2011.023.155

Abstract The application of the Galerkin method, using global trial functions which satisfy the boundary conditions, to nonlinear partial differential equations such as those in the von Karman nonlinear plate theory, is well-known. Such an approach using trial function expansions involving multiple basis functions, leads to a highly coupled system of nonlinear algebraic equations (NAEs). The derivation of such a system of NAEs and their direct solutions have hitherto been considered to be formidable tasks. Thus, research in the last 40 years has been focused mainly on the use of local trial functions and the Galerkin method, applied to the piecewise… More >

Hamad F. Al-Harbi¹, Marko Knezevic^1,2, Surya R. Kalidindi^1,3

CMC-Computers, Materials & Continua, Vol.15, No.2, pp. 153-172, 2010, DOI:10.3970/cmc.2010.015.153

Abstract In recent work, we have demonstrated the viability and computational advantages of DFT-based spectral databases for facilitating crystal plasticity solutions in face-centered cubic (fcc) metals subjected to arbitrary deformation paths. In this paper, we extend and validate the application of these novel ideas to body-centered cubic (bcc) metals that exhibit a much larger number of potential slip systems. It was observed that the databases for the bcc metals with a larger number of slip systems were more compact compared to those obtained previously for fcc metals with a smaller number of slip systems. Furthermore, we demonstrate in this paper that… More >

P. B. Wang¹, Z. H. Yao^1,2, T. Lei¹

CMC-Computers, Materials & Continua, Vol.3, No.2, pp. 65-76, 2006, DOI:10.3970/cmc.2006.003.065

Abstract The fast multipole method (FMM) is applied to the dual boundary element method (DBEM) for the analysis of finite solids with large numbers of microcracks. The application of FMM significantly enhances the run-time and memory storage efficiency. Combining multipole expansions with local expansions, computational complexity and memory requirement are both reduced to O(N), where N is the number of DOFs (degrees of freedom). This numerical scheme is used to compute the effective in-plane bulk modulus of 2D solids with thousands of randomly distributed microcracks. The results prove that the IDD method, the differential method, and the method proposed by Feng… More >

T. Tsangaris¹, Y.–S. Smyrlis^{1, 2}, A. Karageorghis^{1, 2}

CMC-Computers, Materials & Continua, Vol.1, No.3, pp. 245-258, 2004, DOI:10.3970/cmc.2004.001.245

Abstract The Method of Fundamental Solutions (MFS) is a boundary-type method for the solution of certain elliptic boundary value problems. In this work, we develop an efficient matrix decomposition MFS algorithm for the solution of biharmonic problems in annular domains. The circulant structure of the matrices involved in the MFS discretization is exploited by using Fast Fourier Transforms. The algorithm is tested numerically on several examples. More >