Research On Quasi-Conforming Triangular Plate/Shell Elements Based On Rotation Free

Sheet metal forming is a complex large deformation process influenced by many factors, relating material, geometry and contact nonlinearity. In order to simplify the research of sheet metal forming problems, the researchers usually start from the linear small deformation problem, and its numerical simulation is carried out by constructing the finite element model. Since the shell element considers the tensile and bending effect, it can exactly simulates the deformation process of material. Currently, the shell element is commonly used to analyze deformation of sheet. However, each node of the shell element has six degrees of freedom in the current finite element method, in particular the three rotational degrees of freedom has brought many difficulties to study, because the rotational degrees of freedom will often lead to non-convergence problems and simulation computation efficiency will decrease due to the increment of degrees of freedom. At the same time, since the material dimension becomes larger and shape becomes more complicated, the disadvantage of the node degree of freedom is more obvious, it is extremely urgent to construct an efficient finite element. This paper is aimed at the construction of efficient finite element to make the following work:(1) We have constructed a plate element with only translational degrees of freedom called "S3" based on the idea of non-rotational degrees of freedom. The element exists in the form of "patch", each main element has three adjacent triangle elements, the nodes of the element only have three translational degrees of freedom. Its bending effect is expressed by lateral displacement of adjacent cells.(2) We have realized the "RFDKT" plate element based on the combination of rotation-free and discrete Kirchhoff theory. The element is obtained by superimposing "S3" and "DKT6" element. Using adjacent relation of "S3"to remove the rotation value of DKT6 at the midpoint, we have constructed a "patch" of 18 degrees of freedom.(3) Referring to the construction of RFDKT plate element, starting from the quasi-conforming method, we have implemented "RFQC" plate element by combining constant-moment six parameter triangle plate element with rotation-free plate element. The element is similar to RFQC, but the formula is simpler and clearer, and has the advantages of the both two elements. The element also has higher computational efficiency.The above mentioned three elements are based on the thought of rotation free. They remove rotational degrees of freedom of each node, in order to greatly reduce the stiffness matrix. Although we remove rotational degree of freedom, the accuracy and its computational efficiency have significant advantage. The numerical results show that these three elements have good accuracy and convergence. The computational efficiency of "RFQC" element in this paper is higher.