Mohammad Mashayekhi¹, Hossein M. Shodja^1,2, Reza Namakian¹

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.1, pp. 19-60, 2011, DOI:10.3970/cmes.2011.076.019

Abstract A meshless method called reproducing kernel particle method (RKPM) is exploited to cope with elastic-plastic fracture mechanics (EPFM) problems. The idea of arithmetic progression is assumed to place particles within the refinement zone in the vicinity of the crack tip. A comparison between two conventional treatments, visibility and diffraction, to crack discontinuity is conducted. Also, a tracking to find the appropriate diffraction parameter is performed. To assess the suggestions made, two mode I numerical simulations, pure tension and pure bending tests, are executed. Results including J integral, crack mouth opening displacement (CMOD), and plastic zone size More >

Sunilkumar N¹, D Roy^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.3, pp. 249-284, 2010, DOI:10.3970/cmes.2010.066.249

Abstract We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and 1D NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested… More >

Sunilkumar N¹, D Roy^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.2, pp. 107-154, 2010, DOI:10.3970/cmes.2010.065.107

Abstract The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries. Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials. There is thus a case for combining these advantages in a so-called hybrid scheme or a 'smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C^p(p ≥ 1) continuity. One… More >

Yue-Ting Zhou¹, Xing Li², De-Hao Yu³, Kang Yong Lee^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.2, pp. 163-190, 2010, DOI:10.3970/cmes.2010.063.163

Abstract In this paper, a coupled crack/contact model is established for the composite material with arbitrary periodic cracks indented by periodic punches. The contact of crack faces is considered. Frictional forces are modeled to arise between the punch foundation and the composite material boundary. Kolosov-Muskhelisvili complex potentials with Hilbert kernels are constructed, which satisfy the continuity conditions of stress and displacement along the interface identically. The considered problem is reduced to a system of singular integral equations of first and second kind with Hilbert kernels. Bounded functions are defined so that singular integral equations of Hilbert More >

H.M. Shodja^1,2,3, M. Khezri⁴, A. Hashemian¹, A. Behzadan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.2, pp. 171-204, 2010, DOI:10.3970/cmes.2010.062.171

Abstract An accurate numerical methodology for capturing the field quantities across the interfaces between material discontinuities, in the context of reproducing kernel particle method (RKPM), is of particular interest. For this purpose the innovative numerical technique, so-called augmented corrected collocation method is introduced; this technique is an extension of the corrected collocation method used for imposing essential boundary conditions (EBCs). The robustness of this methodology is shown by utilizing it to solve two benchmark problems of material discontinuities, namely the problem of circular inhomogeneity with uniform radial eigenstrain, and the problem of interaction between a crack More >

D. Asprone¹, F. Auricchio², G. Manfredi¹, A. Prota¹, A. Reali², G. Sangalli³

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 1-22, 2010, DOI:10.3970/cmes.2010.062.001

Abstract Particle methods represent some of the most investigated meshless approaches, applied to numerical problems, ranging from solid mechanics to fluid-dynamics and thermo-dynamics. The objective of the present paper is to analyze some of the proposed particle formulations in one dimension, investigating in particular how the different approaches address second derivative approximation. With respect to this issue, a rigorous analysis of the error is conducted and a novel second-order accurate formulation is proposed. Hence, as a benchmark, three numerical experiments are carried out on the investigated formulations, dealing respectively with the approximation of the second derivative More >

Shih-Wei Yang¹, Yung-Ming Wang¹, Chih-Ping Wu^1,2, Hsuan-Teh Hu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.1, pp. 1-40, 2010, DOI:10.3970/cmes.2010.060.001

Abstract A differential reproducing kernel (DRK) approximation-based collocation method is developed for solving ordinary and partial differential equations governing the one- and two-dimensional problems of elastic bodies, respectively. In the conventional reproducing kernel (RK) approximation, the shape functions for the derivatives of RK approximants are determined by directly differentiating the RK approximants, and this is very time-consuming, especially for the calculations of their higher-order derivatives. Contrary to the previous differentiation manipulation, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. A meshless collocation method based on More >

Hossein M. Shodja^{1, 2, 3}, Alireza Hashemian^{2, 4}

The International Conference on Computational & Experimental Engineering and Sciences, Vol.13, No.3, pp. 57-58, 2009, DOI:10.3970/icces.2009.013.057

Abstract Gradient reproducing kernel particle method (GRKPM) is a meshless technique which incorporates the first gradients of the function into the reproducing equation of RKPM. Therefore, in two-dimensional space GRKPM introduces three types of shape functions rather than one. The robustness of GRKPM's shape functions is established by reconstruction of a third-order polynomial. To enforce the essential boundary conditions (EBCs), GRKPM's shape functions are modified by transformation technique. By utilizing the modified shape functions, the weak form of the nonlinear evolutionary Buckley-Leverett (BL) equation is discretized in space, rendering a system of nonlinear ordinary differential equations More >

Mani Khezri¹, Alireza Hashemian¹, Hossein M. Shodja^1,2,3

The International Conference on Computational & Experimental Engineering and Sciences, Vol.11, No.4, pp. 99-108, 2009, DOI:10.3970/icces.2009.011.099

Abstract Meshless methods using kernel approximation like reproducing kernel particle method (RKPM) and gradient RKPM (GRKPM) generally use a set of particles to discretize the subjected domain. One of the major steps in discretization procedure is determination of associated volumes particles. In a non-uniform or irregular configuration of particles, determination of these volumes comprises some difficulties. This paper presents a straightforward numerical method for determination of related volumes and conducts a survey on influence of different assumption about computing the volume for each particle. Stress intensity factor (SIF) as a major representing parameter in fracture of More >

Hua Li¹, Shantanu S. Mulay¹, Simon See²

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.1, pp. 43-82, 2009, DOI:10.3970/cmes.2009.048.043

Abstract Differential Quadrature (DQ) is one of the efficient derivative approximation techniques but it requires a regular domain with all the points distributed only along straight lines. This severely restricts the DQ while solving the irregular domain problems discretized by the random field nodes. This limitation of the DQ method is overcome in a proposed novel strong-form meshless method, called the random differential quadrature (RDQ) method. The RDQ method extends the applicability of the DQ technique over the irregular or regular domains discretized using the random field nodes by approximating a function value with the fixed… More >