Finite Element-meshless Coupling Method For High-order Continuous Structures And Its Numerical Implementation

The higher-order continuum theory considers the effect of higher-order strains,which brings great trouble to the numerical calculation method of finite elements,and the traditional finite element software does not have the simulation function of higher-order continuum structure.In this paper,the typical higher-order continuum theory of even-stress theory is taken as the theoretical basis to establish a framework for the calculation of the finite-element-meshless coupling method and to investigate its numerical implementation process.The main research contents include.(1)A finite-element-gridless coupled computational framework for the even-stress theory.The conventional and higher-order terms in the principle of minimum potential energy of the even-stress theory are separated,and the conventional terms are discretized by the finite element method,while the higher-order terms are discretized by the meshless method.Since the nodal variables calculated by the meshless method are not nodal displacements,the total stiffness matrix and the total force vector cannot be calculated by directly coupling the higher-order terms and the traditional terms,and special treatment is required to realise the coupling calculation.This paper proposes to apply the full transformation method to transform the stiffness matrix and force vector of the meshless method,and then calculate the total stiffness matrix and total force vector to establish the coupling calculation framework,which solves the problem that the finite element and meshless methods cannot be directly coupled.(2)Numerical implementation of a coupled finite-element-gridless computational method for the theory of coupled stresses.The same node arrangement is proposed for the finite element and meshless methods to achieve the coupled calculation of both methods.ANSYS software is used to dissect the cells and output node information as well as traditional term stiffness matrix and force vector information to solve the node arrangement problem in the numerical implementation of the coupled method,effectively reducing the pre-processing workload and improving the research efficiency.Based on the output information,the corresponding stiffness matrix and force vector of the higher order terms are written in Fortran,and the total stiffness matrix and force vector are then calculated and finally solved numerically.(3)Study on the influence of the scale of high-order continuous structure.A finite element-gridless coupled numerical calculation program is used to numerically simulate a uniform planar thin plate,a tensile rectangular thin plate with a circular hole in the centre and a laminated rock cavity.The results show that the method of this paper can well describe the displacement of the laminated rock cavity chamber and the stress concentration phenomenon of the tensioned rectangular sheet with circular hole in the centre by the intrinsic scale factor,and the numerical simulation results of the coupled method and the meshless method in this paper have less error.