Tracing equilibrium paths of elastic plates under different loading path

nlew algorithm for tracing equilibrium paths of simply supported rectangular thin plates in the nonlinear elastic range under different loading paths is developed. In the algorithm, different loading paths are expressed as different functions of path parameter TV [O, l] ; the nonlinear algebraic equilibrium equations are derived by a semi-analytical method and solved by applying Broyden’s method ; locating critical points is realized by applying a determinant-based bisection method; tracing primary equilibrium paths and bifurcated equilibrium paths is controlled by specifying the incremental arc length of the paths ; and switching from primary equilibrium paths to bifurcated equilibrium paths at bifurcation points is controlled by specifying the incremental amplitude of critical modes. The algorithm is applied in some representative examples of imperfect plates under six different loading paths of inplane compressive stresses and transverse load. Through these examples., the following phenomena are observed : different loading paths sometimes lead to different final equilibrium states; under some loading paths with special final loads, there exist bifurcation points on fundamental equilibrium paths even for imperfect plates, and through a bifurcation point there are two stable bifurcated equilibrium paths which approach different final equilibrium states