Geometric nonlinear formulation of plate buckling structure

Abstract

The analytical or exact mathematical formulation of stresses and displacements for plate buckling structure become impossible to develop if the plate geometry is so complicated. Numerical technique is one another approach to solve this problem and it is chosen in this study for plate structure under in-plane and out-plane load. The formulation of elastic stiffness matrix (k_e) and geometric nonlinear stiffness matrix (k_g) of the plate structure due to buckling is presented and based on virtual displacement principle. The geometric nonlinear stiffness matrix (k_g) is found function of internal stresses. The direct iteration technique is applied to find nodal displacements. Under this technique, the Gauss points stresses are initialized as zeros, then the k_g matrix is updated, and then a new nodal displacement vector is found for the next approximation of internal stresses. Iterative process is done until convergence of displacement is satisfied. The rectangular plate with one fixed edge supported is used to test the proposed nonlinear formulation and procedure. The compressive in-plane load and moment is considered and applied for the tested plate. The plate is discretized with appropriate number of triangular finite element mesh. It is found that, the convergence of displacement is satisfied by using direct iteration technique. The load - deflection curve shows nonlinear relationship and approach to critical load. This finding shows that the direct iteration method can be accepted for the analyzing of plate buckling by considering geometric nonlinear assumption.