SOLUTION OF CONTACT PROBLEM USING "MIXED" MLPG FINITE VOLUME METHOD WITH MLS APPROXIMATIONS

Meshless methods are became an alternative to most popular numerical methods used to solve engineering problems such as Finite Difference and Finite Element Methods. Because of element free nature, problems are solved using meshless methods depending on the general geometry and conditions of the problem. Mixed Meshless Local Petrov-Galerkin (MLPG) approach is based on writing the local weak forms of PDEs. Moving least squares (MLS) is used as the interpolation schemes. In this study contact analysis problem is modelled using Meshless Finite Volume Method (MFVM) with MLS interpolation and solved for beam contact problem. Meshless discretization and linear complementary equation of the 2-D frictionless contact problems are described first. Then the problem is converted to a linear complementary problem (LCP) and solved using Lemke’s algorithm. An elastic cantilever beam contact to a rigid foundation is considered as an example problem.

Anahtar Kelimeler:

Mixed Meshless Local Petrov-Galerkin, Moving least squares, Meshless Finite Volume Method, Linear Complimentary Problem, Cantilever beam contact.

PDF

___

Atluri S.N.: The Meshless Local Petrov Galerkin ( MLPG) Method for Domain & Boundary Discretizations, Tech Science Press, (2004), 680 pages.
Li Q., Shen S., Han Z.D., Atluri S.N.: Application of Meshless Local Petrov-Galerkin (MLPG) to Problems with Singularities, and Material Discontinuities, in 3-D Elasticity, CMES: Computer Modeling in Engineering & Sciences, vol. 4 no. 5, (2003), pp. 567-581.
Han Z.D., Atluri S.N.: On Simple Formulations of Weakly-Singular Traction & Displacement BIE, and Their Solutions through Petrov-Galerkin Approaches, CMES: Computer Modeling in Engineering & Sciences, vol. 4 no. 1, (2003) pp. 5-20.
Han Z.D., Atluri S.N.: Truly Meshless Local Petrov-Galerkin (MLPG) Solutions of Traction & Displacement BIEs, CMES: Computer Modeling in Engineering & Sciences, vol. 4 no. 6, (2003), pp. 665-678.
Han Z.D., Atluri S.N.: Meshless Local Petrov-Galerkin (MLPG) approaches for solving 3D Problems in elasto-statics, CMES: Computer Modeling in Engineering & Sciences, vol. 6 no. 2, (2004), pp. 169-188.
Han Z.D., Atluri S.N.: A Meshless Local Petrov-Galerkin (MLPG) Approach for 3-Dimensional Elasto-dynamics, CMC: Computers, Materials & Continua, vol. 1 no. 2, (2004), pp. 129-140.
Atluri S.N., Kim H.G., Cho J.Y.: A Critical Assessment of the Truly Meshless Local Petrov Galerkin (MLPG) and Local Boundary Integral Equation (LBIE) Methods, Computational Mechanics, 24:(5), (1999), pp. 348372.
Atluri S.N., Shen, S.: The meshless local Petrov-Galerkin (MLPG) method: A simple & less costly alternative to the finite element and boundary element methods. CMES: Computer Modeling in Engineering & Sciences, vol. 3, no. 1, (2002), pp. 11-52.
Xiao, J.R., Gama, B.A., Gillespie, Jr J.W., Kansa, E.J.: Meshless solutions of 2D contact problems by subdomain variational inequality and MLPG method with radial basis functions, Engineering Analysis with Boundary Elements, 29, (2005), 95–106.
Fasshauer G. E., Approximate moving least-squares approximation: A fast and accurate multivariate approximation method, in Curve and Surface Fitting: SaintMalo 2002, A. Cohen, J.-L. Merrien, and L. L. Schumaker (eds.), Nashboro Press, (2003), 139–148.
Atluri S.N., Han Z.D., Rajendran A.M., A new implementation of the meshless finite volume method, through the MLPG “mixed” approach, CMES: Computer Modeling in Engineering & Sciences, vol.6, no.6, (2004), pp.491513.
Kikuchi N, Oden JT. Contact problems in elasticity: a study of variational inequalities and finite element methods. Philadelphia: SIAM; 1988.