Geometric nonlinear tangent stiffness matrix with uniform expression for plane truss, beam and plane elements

摘要

The calculus of variations is employed to derive the geometric nonlinear tangent stiffness matrices for truss, beam and plane elements by considering the large deformation and small strain based on the virtual work principle. It is found that the stiffness matrices can be written as a uniform expression. Then, a FEM program is developed. A beam structure is calculated by considering the structural geometric nonlinearity to justify the validity of the proposed uniform expression.