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A novel complex variable element-free Galerkin method for two-dimensional large deformation problems. (English) Zbl 1253.74106

Summary: 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.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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