Von Karman Nonlinear Theory of Composite Plates

The von Karman plate theory is used to analyze geometrically nonlinear small strain, large deflection response of composite laminated plates. The 3D elasticity equations are reduced to 2D problem using kinematical assumptions based on layerwise displacement field of Reddy. With the assumed displacement field, nonlinear Green-Lagrange small strain large displacements relations and linear orthotropic material properties for each lamina the total Lagrangian formulation is used to derive the weak form of the problem. The weak form or nonlinear integral equilibrium equations are discretized using isoparametric finite element approximation. The obtained nonlinear incremental algebric equilibrium equations are solved using the Newton Raphson’s method. The originally coded MATLAB computer program for the finite element solution is used to investigate the effects of geometrical nonlinearity on displacement field of thick anisotropic laminated composite plate