A novel complex variable element-free Galerkin method for two-dimensional large deformation problems

Based on complex variable theory and moving least-squares (MLS) approximation, the improved complex variable moving least-squares (ICVMLS) approximation is discussed in this paper. Compared with complex variable moving least-squares (CVMLS) approximation, the function in the ICVMLS approximation has an explicit physics meaning. By using a new basis function, the ICVMLS approximation can obtain greater precision and computational efficiency. Based on the ICVMLS approximation, an improved complex variable element-free Galerkin (ICVEFG) method, which belongs to a novel element free Galerkin (EFG) method, is presented for two-dimensional large deformation problems. The Galerkin weak form is employed to obtain the equations, while the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the ICVEFG method for two-dimensional large deformation problems are obtained. Compared with the EFG method, the ICVEFG method has greater precision and efficiency.

► A novel complex variable moving least-squares approximation (ICVMLS) is proposed.
► The function used in ICVMLS approximation has an explicit physical meaning.
► The ICVEFG method for two-dimensional large deformation problems is presented.
► The ICVEFG method has great precision and efficiency.