Jan Sladek¹, Vladimir Sladek¹, Chuanzeng Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 637-648, 2003, DOI:10.3970/cmes.2003.004.637

Abstract A new computational method for solving transient elastodynamic initial-boundary value problems in continuously non-homogeneous solids, based on the meshless local Petrov-Galerkin (MLPG) method, is proposed in the present paper. The moving least squares (MLS) is used for interpolation and the modified fundamental solution as the test function. The local Petrov-Galerkin method for unsymmetric weak form in such a way is transformed to the local boundary integral equations (LBIE). The analyzed domain is divided into small subdomains, in which a weak solution is assumed to exist. Nodal points are randomly spread in the analyzed domain and More >

E. J. Sellountos¹, D. Polyzos²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 619-636, 2003, DOI:10.3970/cmes.2003.004.619

Abstract A new meshless local Petrov-Galerkin (MLPG) method for solving two dimensional frequency domain elastodynamic problems is proposed. Since the method utilizes, in its weak formulation, either the elastostatic or the frequency domain elastodynamic fundamental solution as test function, it is equivalent to the local boundary integral equation (LBIE) method. Nodal points spread over the analyzed domain are considered and the moving least squares (MLS) interpolation scheme for the approximation of the interior and boundary variables is employed. Two integral equations suitable for the integral representation of the displacement fields in the local sub- domains are… More >

Q. Li¹, S. Shen¹, Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 571-586, 2003, DOI:10.3970/cmes.2003.004.571

Abstract In this paper, a truly meshless method, the Meshless Local Petrov-Galerkin (MLPG) Method, is developed for three-dimensional elasto-statics. The two simplest members of MLPG family of methods, the MLPG type 5 and MLPG type 2, are combined, in order to reduce the computational requirements and to obtain high efficiency. The MLPG5 method is applied at the nodes inside the 3-D domain, so that any domain integration is eliminated altogether, if no body forces are involved. The MLPG 2 method is applied at the nodes that are on the boundaries, and on the interfaces of material More >

Yiorgos-Sokratis Smyrlis¹, Andreas Karageorghis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 535-550, 2003, DOI:10.3970/cmes.2003.004.535

Abstract In this study, we investigate the application of the Method of Fundamental Solutions for the solution of biharmonic Dirichlet problems on a disk. Modifications of the method for overcoming sources of inaccuracy are suggested. We also propose an efficient algorithm for the solution of the resulting systems which exploits the symmetries of the matrices involved. The techniques described in the paper are applied to standard test problems. More >

Adnan Ibrahimbegovic¹, Catherine Knopf-Lenoir²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 337-344, 2003, DOI:10.3970/cmes.2003.004.337

Abstract In this work we present an unconventional procedure for combining the optimal shape design and nonlinear analysis in mechanics. The main goal of the presented procedure is to enhance computational efficiency for nonlinear problems with respect to the conventional, sequential approach by solving the analysis and design phases simultaneously. A detailed development is presented for the chosen model problem, the 3d rod undergoing large rotations. More >

I. S. Raju¹, D. R. Phillips²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 141-160, 2003, DOI:10.3970/cmes.2003.004.141

Abstract An accurate and yet simple Meshless Local Petrov-Galerkin (MLPG) formulation for analyzing beam problems is presented. In the formulation, simple weight functions are chosen as test functions as in the conventional MLPG method. Linear test functions are also chosen, leading to a variation of the MLPG method that is computationally efficient compared to the conventional implementation. The MLPG method is evaluated by applying the formulation to a variety of patch tests, thin beam problems, and problems with load discontinuities. The formulation successfully reproduces exact solutions to machine accuracy when higher order power and spline functions More >

Jin Yeon Cho¹, Seung Jo Kim²

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.6, pp. 687-698, 2002, DOI:10.3970/cmes.2002.003.687

Abstract In this work, an explicit solution procedure for the recently developed discontinuous time integration method is proposed in order to reduce the computational cost while maintaining the desirable numerical characteristics of the discontinuous time integration method. In the present explicit solution procedure, a two-stage correction algorithm is devised to obtain the solution at the next time step without any matrix factorization. To observe the numerical characteristics of the proposed explicit solution procedure, stability and convergence analyses are performed. From the stability analysis, it is observed that the proposed algorithm gives a larger critical time step More >

Yansong Wang¹, Q. Jane Wang¹, Chih Lin²

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.4, pp. 517-530, 2002, DOI:10.3970/cmes.2002.003.517

Abstract Many mechanisms, such as computer hard drives, gear trains, and machine tool spindle systems, operate under both axial and radial loads, which should be respectively supported by a thrust and a journal bearing. By utilizing the end face of the shaft of a journal bearing as a thrust bearing, a coupled journal-thrust bearing system can be formed. This paper presents a mixed lubrication model developed to investigate the lubrication of this coupled bearing system. A conformal-mapping method is used in the model formulation to facilitate a universal flow description. The performance of typical coupled bearing More >

Weimin Han, Xueping Meng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 65-76, 2002, DOI:10.3970/cmes.2002.003.065

Abstract Interests in meshfree (or meshless) methods have grown rapidly in the recent years in solving boundary value problems arising in mechanics, especially in dealing with difficult problems involving large deformation, moving discontinuities, etc. Rigorous error estimates of a meshfree method, the reproducing kernel particle method, for smooth solutions have been theoretically derived and experimentally tested in Han, Meng (2001). In this paper, we provide an error analysis of the meshfree method for solving problems with singular solutions. The results are presented in the context of one-dimensional problems. The error estimates are of optimal order and More >

António Tadeu, Julieta António¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 477-496, 2001, DOI:10.3970/cmes.2001.002.477

Abstract This paper presents analytical solutions, together with explicit expressions, for the steady state response of homogeneous three-dimensional layered acoustic and elastic formations subjected to a spatially sinusoidal harmonic line load. These formulas are theoretically interesting in themselves and they are also useful as benchmark solutions for numerical applications. In particular, they are very important in formulating three-dimensional elastodynamic problems in layered fluid and solid formations using integral transform methods and/or boundary elements, avoiding the discretization of the solid-fluid interfaces. The proposed Green's functions will allow the solution to be obtained for high frequencies, for which More >