Coupling of element free Galerkin and hybrid boundary element methods using modified variational formulation

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182

The meshless local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using moving least squares (MLS) interpolants and local weak forms. In this paper, a MLPG formulation is proposed for free and forced vibration analyses. Local weak forms are developed using weighted residual method locally from the dynamic partial differential equation. In the free vibration analysis, the essential boundary conditions are implemented through the direct interpolation form and imposed using orthogonal transformation techniques. In the forced vibration analysis, the penalty method is used in implementation essential boundary conditions. Two different time integration methods are used and compared in the forced vibration analyses using the present MLPG method. The validity and ef®ciency of the present MLPG method are demonstrated through a number of examples of two-dimensional solids.

Section: Introductionmentioning

confidence: 99%

A meshless local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids

Gu¹,

Liu²

2001

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182

“…The Galerkin meshless methods, which are proposed much later than SPH, have been successful widely used in computational mechanics. In addition, techniques for coupling meshless methods with other established numerical methods have also been proposed, such as the coupled EFG/FEM (Belytschko and Organ, 1995), EFG/ BEM Liu and Gu, 2000a).…”

Section: Introductionmentioning

confidence: 99%

Comparisons of two meshfree local point interpolation methods for structural analyses

Liu

2002

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As truly meshless methods, the local point interpolation method (LPIM) and the local radial point interpolation method (LR-PIM), are based on the point interpolations and local weak forms integrated in a local domain of very simple shape. LPIM and LR-PIM are examined and compared with each other. They are also compared with the established FEM and the meshless local Petrov-Galerkin (MLPG) method. The numerical implementations of these two methods are discussed in detail. Parameters that influence the performance of them are detailedly studied. The convergence and efficiency of them are thoroughly investigated. LPIM and LR-PIM formulations are developed for structural analyses of 2-D elastodynamic problems and 1-D Timoshenko beam problems in the first time. It is found that LPIM and LR-PIM are very easy to implement, and very efficient obtaining numerical solutions to problems of computational mechanics.

“…However, there exist some disadvantages in using EFG. Strategies have been developed for the alleviation of the drawbacks of EFG Liu, 1999;Liu and Yang, 1998). A meshless method, called point interpolation method (PIM), has been proposed Wang et al, 2001).…”

Section: Introductionmentioning

confidence: 99%

A boundary point interpolation method for stress analysis of solids

Gu¹,

Liu²

2002

Self Cite

136

A boundary point interpolation method (BPIM) is proposed for solving boundary value problems of solid mechanics. In the BPIM, the boundary of a problem domain is represented by properly scattered nodes. The boundary integral equation (BIE) for 2-D elastostatics has been discretized using point interpolants based only on a group of arbitrarily distributed boundary points. In the present BPIM formulation, the shape functions constructed using polynomial basis function in a curvilinear coordinate possess Dirac delta function property. The boundary conditions can be implemented with ease as in the conventional boundary element method (BEM). The BPIM for 2-D elastostatics has been coded in FORTRAN, and used to obtain numerical results for stress analysis of two-dimensional solids.