K. Wang¹, S.J. Zhou^2,3, Z.F. Nie⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.1, pp. 77-102, 2011, DOI:10.3970/cmes.2011.073.077

Abstract The natural neighbour Galerkin method is tailored to solve boundary value problems of the couple-stress elasticity to model the size dependent behaviour of materials. This method is based on the displacement-based Galerkin approach, and the calculation of the global stiffness matrix is performed using gradient smoothing technique combined with the non-Sibsonian partition of unity approximation scheme. This method possesses the following properties: the complex C1-continuous approximation scheme is avoided without using either Lagrange multipliers or penalty parameters; no domain integrals involved in the assembly of the global stiffness matrix; and the imposition of essential boundary conditions is straightforward. The validity… More >

Htike Htike¹, Wen Chen¹, Yan Gu¹, Junjie Yang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.4, pp. 247-272, 2011, DOI:10.3970/cmes.2011.072.247

Abstract This paper makes the first attempt to employ the Radial Basis Function (RBF) interpolation in the material point method (MPM), in which the shape function is based on RBF and polynomial function and satisfies the partition of unity and possesses Delta-function property. It is worthy of stressing that the RBF interpolation has the merit of high smoothness and is very accurate and can easily be applied to the MPM framework for mapping information between moving particles, known as material point in the MPM, and background grids. The RBF-based MPM is designed to overcome the unphysical results, such as shear stress… More >

H. T. Wang^1,2, Z. H. Yao³

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.2, pp. 115-148, 2011, DOI:10.3970/cmes.2011.072.115

Abstract A fast boundary element solver for the analysis of three-dimensional general crack problems is presented. In order to effectively model the embedded or edge cracked structures a dual boundary integral equation (BIE) formulation is used. By implementing the fast multipole method (FMM) to the discretized BIE, structures containing a large number of three-dimensional cracks can be readily simulated on one personal computer. In the FMM framework, a multipole expansion formulation is derived for the hyper-singular integral in order that the multipole moments of the dual BIEs containing the weakly-, strongly- and hyper-singular kernels are collected and translated with a unified… More >

Shuncai Li^1,2,3, Zhengzhu Dong², Dan Ma²

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.2, pp. 93-110, 2011, DOI:10.3970/cmes.2011.071.093

Abstract Weak local support is a very common phenomenon in roadway support engineering. It is a problem that needs to be studied thoroughly at the theoretical level. So far, the literature on stress field theory of rock surrounding a roadway is largely restricted to analytical solutions of stress for roadways with a uniform support or no support at all. The corresponding stress solution under conditions of local or weak local support has not been provided. Based on a mechanical model of weak local support at the boundary of a circular roadway and the boundary element method on boundary value problems of… More >

Xue-Qian Fang¹, Jin-Xi Liu¹, Ming-Zhang Chen¹, Li-Yong Fu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.2, pp. 101-116, 2010, DOI:10.3970/cmes.2010.066.101

Abstract In the authors' previous work (Zhang et al., 2010), the dynamic stress resulting from two cavities in exponential functional graded materials subjected to non-homogeneous shear waves has been studied. In this paper, the wave function expansion method is further developed to the case of two cylindrical inclusions embedded in functional graded materials, and the incident angle is also considered. The multiple scattering and refraction of non-homogeneous shear waves around the two inclusions are described accurately. The dynamic stress concentration factors around the two inclusions are presented analytically and numerically. The multiple effects of geometrical and physical parameters on the dynamic… More >

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 >

Ching Kong Chao^1,2, Chin Kun Chen¹, Fu Mo Chen³

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.1, pp. 1-28, 2010, DOI:10.3970/cmes.2010.063.001

Abstract A general analytical solution for a reinforced elliptical hole embedded in an infinite matrix subjected to a point heat source is provided in this paper. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and stresses in the reinforcement layer and the matrix are derived explicitly in a series form. Some numerical results are provided to investigate the effects of the material combinations and geometric configurations on the interfacial stresses. The solution obtained can be treated as Green's functions which enable us to formulate… More >

R. Valisetty^1,2, A. Rajendran^1,3, D. Grove²

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.1, pp. 41-72, 2010, DOI:10.3970/cmes.2010.060.041

Abstract A multi-scale model exhibiting progressive damage is considered for a 3D-woven composite. It is based on the evolution of some fundamental damage modes in a representative volume element (RVE) of a composite's woven architecture. The overall response of a woven composite due to a variety of damage modes is computationally obtained through a transformation field analysis (TFA) that is capable of quantifying the effects of spatial distribution of micro stresses and strains on strength. Since the model is computationally intensive, its numerical requirements are to be understood before it can successfully be used in design studies or in conjunction with… 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 the present DRK approximation is… More >

Baskaran Bhuvaraghan¹, Sivakumar M Srinivasan², Bob Maffeo³, Om Prakash⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.2, pp. 137-158, 2010, DOI:10.3970/cmes.2010.057.137

Abstract Shot peening is a complex and random process which is controlled by many input parameters. Numerical methods, which are normally used for impact problems will prohibitively put strain on the computing resources since a large number of impacts are involved in the computations. In this paper, a simplified analytical approach is used to predict the residual compressive stress that includes strain-rate effects. This is based on the method proposed by with a simple modification to include the strain rate effects. The residual stresses are predicted in materials SAE1070 and Inco718. In the computations, the random variation of the input parameters… More >