Two-dimensional incompressible materials analysis using standard formulation in a meshless style

Abstract

In this paper, exponential basis functions (EBFs) are used in a boundary collocation style to solve elasticity and steady Navier-Stokes equations in problems with fully incompressible materials. In the presented method, the approximate solution of the standard form of elasticity and Navier-Stokes equations is expressed by a linear combination of EBFs with complex-valued exponents multiplied by polynomials. Constant coefficients of the solution series are evaluated through a point collocation method on the domain boundaries via a complex discrete transformation technique. With these basis functions, the standard equations can be solved with Poisson's ratio equals to 0.5. Furthermore, Pressure basis functions can be straightforwardly evaluated by calculating the limit of bulk modulus multiplied by volumetric strain when Poisson's ratio approaches to 0.5. Some benchmark problems have been solved to show the capabilities of the method. © 2010 Civil-Comp Press.