POLYGON SCALED BOUNDARY FINITE ELEMENT NONLINEAR EFFICIENT ANALYSIS METHOD

The scaled boundary finite element method (SBFEM) is a high-precision semi-analytical numerical solution method, which is especially suitable for solving problems such as unbounded media and stress singularity, and the advantage of the polygon boundary element is more obvious to simulate the crack growth process and local mesh re-segmentation problems than the finite element method. At present, the scaled boundary finite element method is more concerned with the solution of the linear elasticity problem, while the research of the nonlinear scaled boundary element is in its infancy. An efficient inelasticity-separated scaled boundary finite element method (IS-SBFEM) is proposed based on the basic theory of the SBFEM and the inelasticity-separated theory. The proposed method considers that the sector sub-element of each boundary line covered domain is independent, and its shape function and strain-displacement matrix can be obtained by the semi-analytical elastic solution. Moreover, the nonlinearity strain field of each sector sub-element is establish by introducing nonlinear strain interpolation points, and the nonlinear constitutive relations can be introduced to achieve efficient nonlinear analysis of polygon scaled boundary element. The stiffness matrix of the polygon scaled boundary element can be obtained by assembling the stiffness of each sector sub-element, the numerical integration of each sector domain can be obtained by using Gaussian integration scheme, and its accuracy remains unchanged. Because more nonlinear strain interpolation points are introduced, the dimension of the Schur complement matrix is larger. The Woodbury approximation approach is used to solve the governing equations of the inelasticity-separated scaled boundary element. This method has efficiency advantages for the calculation of large-scale nonlinear problems. Numerical examples are adopted to verify the correctness and efficiency of the algorithm. Popularize this method that is important to practical engineering analysis.