Construction Method And Programming Of Composite Finite Element

With the development of the finite element method theory and computer science, various finite elements are created. At present, every finite element consists of a single material. And then, make the element as a function module, and the elasticity, plasticity, creep, expansion, large deformation, large strain and other functions of the material are considered in the element. Because of the consideration of the nature of a material, it brings great convenience to the programming. However, the modern structure is getting more and more complex and the materials are becoming more and more various. When the engineers using the software of finite element to solve the structure problems, the process of making model becomes the most onerous task. In order to solve the complicated process caused by the single material in each element, the concept of the composite element method is proposed.The viewpoint of this thesis is that the element in the finite element method is not necessarily a single material. In this paper, the principle of virtual work from the four nodes rectangular element and the two nodes linear element is discussed, and the energy equation is used to integrate the two different elements. Using VC as the development tool, taking advantage of the parametric element characteristics, according to the inverse matrix construction method of functions written plane element shape function program, using Gaussian numerical integral method, the element stiffness matrix of the common elements of is formed.Then, according to the node displacement number of the element, the element stiffness is integrated, and a new type of finite elements is obtained. The following results are obtained through the research of this paper.(1) Pay particular attention to the number and location of the parent element node when using the method of the inverse matrix shape function.In order to ensure the smooth progress of the matrix inversion,the element in the local coordinate system of the element in the matrix must ensure that the matrix is non singular. In condition of the non singular matrix, moving the node location, the inverse matrix function method can well adapt to this kind of problem.(2) It is possible to integrate the elements which have different types of material together to form a new composite element. Through the combination of the element, the structure can reduce the number of elements, and the accuracy of the calculation results will not be reduced. The properties of different materials can be reflected in the structure. Through the calculation of examples, the results obtained by using the composite element method and ANSYS in the same conditions are compared, and the results show that the results of the two cases are very close.(3) The composite element with different materials has the same displacement of the joints. The element stiffness matrix of the composite element can be easily obtained by superposing the element stiffness matrix of the two different materials in the same natural coordinate system according to the nodal displacement number. This method has good maneuverability and stability.