An Improved Complex Variable Reproducing Kernel Particle Method Based on Conjugate Basis Functions for Elasticity Problems

Based on conjugate basis functions, this paper proposes a novel improved complex variable reproducing kernel particle method (ICVRKPM) for elasticity problems. The approximation function of ICVRKPM is formulated using conjugate basis functions. Combining with the Galerkin weak form for elasticity problems and the implementation of displacement boundary conditions via the penalty function method, the governing equations of the ICVRKPM for elasticity problems are derived. Through three numerical examples, this paper analyzes the influences of the factors, such as the scale parameter of the influence domain and penalty factor, on numerical precision. Further, the relationship between node distribution and convergence is investigated, and then the convergence and effectiveness of the ICVRKPM are validated. The comparative analysis between the ICVRKPM and the complex variable reproducing kernel particle method (CVRKPM) is performed. Numerical results demonstrate that the ICVRKPM exhibits superior precision and speed over to the CVRKPM for elasticity problems.