Linear and geometrically nonlinear analysis of novel flat shell elements with rotational degrees of freedom

Based on Kirchhoff assumptions and generalized conforming theory, new 4-node quadrilateral flat shell element and 3-node triangular flat shell element are presented. They have vertical rotational degrees of freedom, and translation displacement field and rotation displacement field are mutually independent. Furthermore, the tangent stiffness matrix is constructed for the element using Update Lagrange formulation. The numerical examples have demonstrated that the present elements have good performance for linear and geometrically nonlinear shell/plate problems, and result in easy assembling beam element and shell element. At the same time, a feasible and versatile method with characteristic matrix of nodal displacements, characteristic matrix of generalized displacements and transfer matrix is proposed during deductive procedure.