Unified Complex Variable Element-Free Methods: A Comprehensive Framework of Complex Variable Meshless Approaches

Abstract

There are long-term traditions and efforts to apply the complex variable methods to the theoretical and numerical solutions of applied mechanics. Based on the aim of establishing a unified format of the complex variable meshless approximation, this paper proposes a unified complex variable moving least-squares (UCVMLS) approximation for any pair of independent real field variables. In the UCVMLS approximation, based on the complex variable form of real variable pair and the adopted complex variable basis, four independent approximation functions can be constructed, in which two different improved complex variable moving least-squares (ICVMLS) approximations developed before are included. The four trial functions in UCVMLS are proved to be able to construct two different approximations to the same real variable pair. The unified complex variable element-free Galerkin (UCVEFG) method for elasticity is established. Numerical examples are provided by applying UCVEFG method in three elastic problems to show its accuracy.