Research On Coupling Of Micro-beam Bond-based Peridynamics And Finite Element Method In Plate Bending Modeling

Plate and shell structures are widely used in aerospace,automobile,shipbuilding,civil engineering,chemical engineering and other fields.Therefore,efficient and accurate calculation of damage and destruction processes is of great significance for improving structural safety.The use of traditional finite element method for structural analysis can efficiently and accurately simulate material deformation,but it cannot deal with discontinuous fracture problems.The peridynamic(PD)theory uses spatial integration to avoid the shortcomings of the finite element method.It is suitable for simulating the initiation and expansion of cracks.However,the PD method has low efficiency,complex calculations,and large memory usage.In order to better combine the advantages of the finite element method and the PD method,the model calculation is usually carried out in the coupling strategy,which can better simulate the discontinuous crack problem and improve the calculation efficiency.In this paper,the discontinuous Galerkin element method is used to solve the PD equations based on the micro-beam bond-based PD plate bending model,and then PD plate bending model is coupled with the finite element one through a simplified coupling strategy.In order to verify the coupled plate bending model,several thin plate examples under different constraints and load conditions are selected.First,the definition of the PD micro-beam bond model and the formulation of the micro potential energy are explained.On this basis,the establishment process of the PD plate bending model is explained,and the expression of the key PD micromodulus is given,which provides the theoretical foundation for building the stiffness matrix of the PD plate bending model based on the discontinuous Galerkin finite element method.At the same time the discontinuous Galerkin element method is given in preparation for the coupling study of plate bending model.Then,the formula derivation and program realization process of the discontinuous Galerkin finite element method to solve the PD plate bending model are given.Subsequently,the PD fracture criterion is introduced,and the judgment basis,judgment method and program realization process of the energy fracture criterion are explained in detail.Based on the above-mentioned solution process,the coupling strategy by setting the influence function of the PD module and the finite element one is proposed and then the expression of the total stiffness matrix is given,the expression deformation result is obtained by solving the total stiffness equation.Finally,the verification is carried out.The bending deformation of the thin plate under different constraints and loads is compared with the analytical solution or the finite element simulation results to verify the accuracy of the established model.At the same time,the crack propagation path of the pre-cracked thin plate is analyzed,which further proves the applicability of this research to crack propagation analysis.The results show that the discontinuous Galerkin finite element method can improve the calculation accuracy of the PD plate bending model,and it is feasible to establish the plate bending coupling model by using a simplified coupling strategy.