Analysis of Linear Two-Dimensional Equations by Hermitian Meshfree Collocation Method

Document Type: Persian

Authors

1 Lecturer, Islamic Azad University, Ravansar Branch

2 Assistant Professor, Department of Mechanical Engineering, Razi University, Kermanshah

Abstract

Meshfree Collocation Method is used to solve linear two-dimensional problems. This method differs from weak form methods such as Galerkin method and no cellular networking and no numerical  integration. Therefore, this method has no constraints such as the integration accuracy and the integration CPU time, and equations can be isolated directly from the strong form of governing PDE. The fundamental problem of this method is unstable solution especially in the case, including derivative boundary conditions. In this paper hermite type shape functions are used to impose boundary conditions. These shape functions have improved the solution accuracy. also, In this paper  effects of various parameters such as type weight functions, order based vector, dilation parameter, distribution nodal on the solution accuracy have been studied.

Keywords


[1] Thoma P.F., Hermann G.M., Classification and Overview of Meshfree Methods, Institute of Scientific Computing Technical University Braunschweig Brunswick, 2004, Germany.

[2] Yong-Ming Guo., Kenji Nakanishi., Yasuto Yokouchi.,A nonlinear rigid-plastic analysis for metal forming problem using the rigid-plastic point collocation method, Advances in Engineering Software 36, 2005, pp.234–242.

[3] Liu. W.K, Li. S, Belytschko T. , Moving Least Square Reproducing Kernel Methods (I) Methodology and Convergence, Comp. Methods. Appl. Mech. Eng. 1996.

[4] G.R. Liu., Gu Y.T. , An Introduction to Meshfree Methods and Their Programming, National University of Singapore, Singapore., 1981.

[5] Liszka T.J., Duarte C.A. , Tworzydlo W.W. ,  Hp-meshless cloud method, Comput, Methods Appl. Mech. Eng. 139, 1996, pp. 263-288.

[6] Foroutan Mehrdad., Bahrami Mohammad Amin, Analysis of Plane Strain Upsetting by Hermitian Meshless Collocation Method, Steel Research Int.81, No.9, 2010, pp. 1462-1465.