FEM And S-FEM Study Of The Three Dimensional Complex Structures In Solid Mechanics

Finite Element Method(FEM)is an efficient numerical simulation method which has been widely used in various practical engineering fields such as thermology,electromagnetism,solid mechanics and so on.However,the FEM numerical solution based on linear element is not accurate because the problem domain has a variety of geometric structures and usually has curved boundaries,for three-dimensional(3D)solid mechanics problems.Therefore,the paper conducts the following researches to solve this problem:on the one hand,a set of higher-order elements with curved boundaries is proposed to solve the 3D solid mechanics problems with curved boundaries.On the other hand,the Smoothed Finite Element Method(S-FEM)is used to solve the 3D solid mechanics problems with complex structure.In addition,a 3D preprocessor of FEM and S-FEM is developed to ensure that mesh of FEM and S-FEM can be better constructed,so as to improve the operation efficiency of the algorithm.The work of this paper can be detailed as follows:First of all,FEM based on four-noded linear tetrahedron(Te4)cannot simulate the 3D solid mechanics problems with curved boundaries accurately,which leads to the decrease of solution precision.In order to overcome this problem,a class of novel tetrahedral elements with curved edges is proposed.These new elements can simulate the changing trend of the curved boundaries by adding new nodes to curved edges.According to the number of nodes in the curved element,the new tetrahedral elements can be divided into five-noded tetrahedral element(Te5),six-noded tetrahedral element(Te6)and seven-noded tetrahedral element(Te7).They are applied to FEM by constructing the shape functions of their isoparametric elements.Then,the problem domain is discretized by combining Te4 element and the curved elements for the solid mechanics problems with curved boundaries.In this hybrid mesh,curved elements are used at the curved boundaries,and Te4 element is used elsewhere.In this manner,the accuracy of numerical results is improved and the running speed of the algorithm could also be ensured.A large number of numerical examples have shown that the FEM using the hybrid mesh proposed in this work can solve the 3D solid mechanics problems with curved boundaries very well.Next,the complex 3D solid mechanics problems are studied using S-FEM.This method is a numerical method combining the advantages of FEM and Meshless method.Based on the weakened weak(W~2)form and the G-space theory,it can significantly improve the accuracy of stress solution.In the first step,a variety of smoothing domains are constructed on the background mesh of FEM,then the smooth Galerkin weak form of the corresponding method is established,and finally the displacement solution and stress solution can be obtained.The examples with complex problem domain have shown that S-FEM has high-accuracy solution.Furthermore,a 3D S-FEM preprocessor is developed to facilitate the construction of smoothing domains.The preprocessor has a simple and easy-to-operate Graphical User Interface(GUI).It can automatically discretize the problem domain and create the smoothing domains by using the geometric model generated by this GUI or geometric files provided by existing commercial software,such as ABAQUS?and Hyper Mesh?.Meanwhile,the preprocessor is connected with a variety of numerical solvers,including:FEM,Face-based S-FEM(FS-FEM),Edge-based S-FEM(ES-FEM)and Node-based S-FEM(NS-FEM).The effectiveness,accuracy and stability of the preprocessor are verified by a large number of experiments.The results show that the preprocessor can automatically generate the FEM mesh and the smoothing domains of S-FEM with arbitrary complex geometry without manual intervention.