Xiaojing Liu¹, Jizeng Wang^1,2, Youhe Zhou^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.3, pp. 225-238, 2013, DOI:10.32604/cmes.2013.094.225

Abstract A wavelet method is proposed for solving a class of nonlinear timedependent partial differential equations. Following this method, the nonlinear equations are first transformed into a system of ordinary differential equations by using the modified wavelet Galerkin method recently developed by the authors. Then, the classical fourth-order explicit Runge-Kutta method is employed to solve the resulting system of ordinary differential equations. To justify the present method, the coupled viscous Burgers’ equations are solved as examples, results demonstrate that the proposed wavelet algorithm have a much better accuracy and efficiency than many existing numerical methods, and the order of convergence of… More >

Qiang Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.3, pp. 207-224, 2013, DOI:10.32604/cmes.2013.094.207

Abstract In this paper, an immersed boundary method (IBM) has been developed to simulate three-dimensional (3D) complex flows in the injection molding process, in which the irregular boundary of mould is treated by a level set function. The melt front (melt-air interface) is captured and treated using the coupled level set and volume of fluid (CLSVOF) method. The finite volume method on the nonstaggered meshes is implemented to solve the governing equations, and the melt filling process is simulated in a rectangular mould with both thick- and thin-wall sections. The numerical result shows good agreement with the available data. Finally, the… More >

Chia-Cheng Tsai^1,2, D. L. Young³

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.2, pp. 175-205, 2013, DOI:10.3970/cmes.2013.094.175

Abstract It is well known that the method of fundamental solutions (MFS) is a numerical method of exponential convergence. In this study, the exponential convergence of the MFS is demonstrated by obtaining the eigensolutions of the Helmholtz equation. In the solution procedure, the sought solution is approximated by a superposition of the Helmholtz fundamental solutions and a system matrix is resulted after imposing the boundary condition. A golden section determinant search method is applied to the matrix for finding exponentially convergent eigenfrequencies. In addition, the least-squares method of fundamental solutions is applied for solving the corresponding eigenfunctions. In the solution procedure,… More >

Dan Dumitriu¹, Ligia Munteanu¹, Cornel Brişan², Veturia Chiroiu¹, Rǎzvan-Vlad Vasiu², Octavian Melinte¹, Victor Vlǎdǎreanu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.2, pp. 159-173, 2013, DOI:10.3970/cmes.2013.094.159

Abstract The continuum modeling of tire/road vibro-contact dynamics is developed in this paper by assuming continuum relationship between the contact force and the deformation. An important aspect of this model is that the damping depends on the indentation. In the continuum approach, no difference is made between impact and contact, and the friction law can be other than the Coulomb’s law. Since the road is rocky, a bristle model was chosen to take into account the effect of the road irregularities. The identification of the contact domain is performed by checking the minimum distance between bodies. More >

Guizhong Xie¹, Jianming Zhang^1,2, Cheng Huang¹, Chenjun Lu¹, Guangyao Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.2, pp. 139-157, 2013, DOI:10.3970/cmes.2013.094.139

Abstract In this work, an improved exponential transformation is presented for nearly singular boundary element integrals in problems of thin structures. Accurate evaluation of nearly singular integrals is an important issue in the implementation of boundary element method (BEM) for thin structures. In this paper, the exponential transformation, which was firstly developed to evaluate nearly singular integrals arising in 2D BEM, is extended into 3D BEM to deal with nearly singular integrals. Firstly, a novel (α,β) coordinate system is introduced. Then, the conventional distance function is modified into a new form in (α,β) coordinate system. Based on the refined distance function,… More >

Cao Guohua¹, Zhu Zhencai¹, Peng Weihong², Wang Jinjie¹, Liu Zhi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.2, pp. 119-138, 2013, DOI:10.3970/cmes.2013.094.119

Abstract The single helical structure is twisted by surrounding helical units with clearance or not between two layers. In order to master the thermal expansion behavior, the theory has been developed for the analysis of these helical structures. The previously deduced linear expressions of thermal expansion coefficients for the gapless structure model (GM) is used and the analytical method is applied to the clearance structure model (CM) and clearance-gapless structure model(CGM) under two boundary conditions. For further evaluating the analytical expressions of two models, the finite element models of the single helical structure surrounding by helical units with lang lay and… More >

Jun-Sheng Duan^1,2, Randolph Rach³, Abdul-Majid Wazwaz⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.1, pp. 77-118, 2013, DOI:10.3970/cmes.2013.094.077

Abstract In this paper, we propose a new modification of the Adomian decomposition method for solution of higher-order nonlinear initial value problems with variable system coefficients and solutions of systems of coupled nonlinear initial value problems. We consider various algorithms for the Adomian decomposition series and the series of Adomian polynomials to calculate the solutions of canonical first- and second-order nonlinear initial value problems in order to derive a systematic algorithm for the general case of higher-order nonlinear initial value problems and systems of coupled higher-order nonlinear initial value problems. Our new modified recursion scheme is designed to decelerate the Adomian… More >

Yixian Du^1,2,3,4, De Chen¹, Xiaobo Xiang¹, Qihua Tian¹, Yi Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.1, pp. 53-75, 2013, DOI:10.3970/cmes.2013.094.053

Abstract Topological design of continuum structures usually involves numerical instabilities, such as checkerboards and mesh-dependency, which degenerate the manufacturability, the efficiency and the robustness of the optimal design. This paper will propose a new topology optimization method to suppress numerical instabilities occurred in the topology optimization of continua, according to the principle of error amplifier and feedback control in the control system. The design variables associated with topological design are updated based on the Cellular Automata (CA) theory. A couple of typical numerical examples are used to demonstrate the effectiveness of the proposed method in effectively suppressing numerical instabilities occurred in… More >

Changqing Miao¹, Yintao Wei², Xiangqiao Yan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.1, pp. 29-52, 2013, DOI:10.3970/cmes.2013.094.029

Abstract This paper is concerned with periodic collinear circular-hole cracks in an infinite plate in tension. A numerical approach to this type of circular-hole cracks is presented. Numerical examples are included to illustrate the accuracy of the numerical approach. By means of a generalization of Bueckner's principle and by using a displacement discontinuity method, periodic collinear circular-hole cracks in an infinite plate in tension are investigated in detail by using the numerical approach. Many numerical results are given and discussed. More >

Tao Zhang^1,2, Leiting Dong^2,3, Abdullah Alotaibi⁴, Satya N. Atluri^2,5

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.1, pp. 1-28, 2013, DOI:10.3970/cmes.2013.094.001

Abstract In this paper, a novel Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed for solving the inverse Cauchy problem of linear elasticity, wherein both the tractions as well as displacements are prescribed/measured at a small portion of the boundary of an elastic body. The elastic body may be isotropic/anisotropic and simply connected or multiply-connected. In the MLPG mixed collocation method, the same meshless basis function is used to interpolate both the displacement as well as the stress fields. The nodal stresses are expressed in terms of nodal displacements by enforcing the constitutive relation between stress and the displacement gradient… More >