Finite Element-meshless Coupling Method Of Dual Stress Theory And Its Application

Even higher-order continuous theories,such as the dual-stress theory,are increasingly used in engineering practice.Because it is difficult to obtain analytical solutions to the problem,numerical simulation plays a very important role in the application of high-order continuous theory.However,existing The finite element software basically has no function of simulating high-order continuous structures.In this paper,the high-order continuous feature of the moving least squares approximation is applied in the frame of the dual-stress elastoplastic theory,and the finite element-gridless coupling calculation method of the dual-stress theory is established.The program realizes numerical simulation,and numerical simulation can also be realized through the secondary development of finite element software.Subsequently,several numerical examples prove the effectiveness of the method in this paper.The main research work of this article includes:(1)Within the framework of the dual-stress elastoplastic theory,the elastoplastic incremental matrix is decomposed into a traditional term sub-matrix and a higher-order term sub-matrix,and the traditional term and the higher-order term are separated in a potential energy functional form.It is proposed that the traditional terms use the finite element method to perform discrete calculations,and the higher-order terms use the meshless method to perform discrete calculations,and then establish the finite element-meshless coupled calculation method for the even-stress elastoplasticity theory.(2)Use Ansys software to establish the calculation model,divide the unit,and calculate the traditional stiffness matrix and force vector.The node information of the finite element is derived.As the node of the meshless method,the moving least squares are used to construct the shape function.The strain gradient is approximated by the product of the second derivative of the shape function and the node displacement.The Fortran language programming is used to calculate the high-order term sub-matrix And force vector.The secondary development function of Ansys software is used to embed high-order term sub-matrix and force vector into Ansys software to realize the numericalcalculation of finite element-meshless coupling method.(3)In this paper,the finite element meshless coupling method of couple stress elastoplastic theory is used to simulate the simply supported thin plate.The validity of this method is proved,and the selection of joint influence domain is analyzed.The slope and slope under the effect of self-weight are calculated and simulated,and the influence of scale factor on the deformation of high-order continuous structures is studied.In this paper,the use of the meshless method can easily construct the characteristics of higher-order continuous shape functions,and the use of the finite element-meshless coupling method to solve the problem of higher-order continuous structures is theoretically innovative.It is proposed that through the secondary development of finite element software,the high-order items calculated by the meshless method are embedded in the software to realize the coupling calculation,which provides a new idea for the numerical simulation of related engineering practical problems.