Co-Rotational Formulation-Based Analysis of Shell Buckling

In order to solve the nonlinear problem in analyzing the bulking of thin-walled structures, an updated Lagrangian co-rotational method for the nonlinear analysis of shell structures was presented. A program based on this method was developed, and 2 numerical examples of the buckling analysis of shell structures were given. In this method, an updated Lagrangian formulation is adopted to build the equilibrium equation of shell elements under large displacements, and then the tangent stiffness matrix is get with the energy theory. The polar decomposition theory is applied in the computations of the new co-rotational coordinates of elements and the rigid body rotations of nodes, and the finite rotation theory is introduced to separate rigid displacements from total displacements to get deformations of the nodes. As a result, stresses of an element can be calculated based on the deformations by using the small-strain theory to obtain the element state for the current load step. The numerical examples indicate that the nonlinear analysis method based on co-rotational (CR) formulation is efficient and accuracy in solving the buckling of shell structures.