Nonlinear Finite Element Static and Dynamic Analyses of Stiffened Plates

In the present work, finite element method is used to study the behaviour of arbitrary shaped thin stiffened plates. The nonlinear static and dynamic analyses are carried out for both bare as well as stiffened plates. The formulation is generalised using a mapping technique so that the analysis is performed in a square domain. It uses a superparametric element in which the displacement field is defined by the shape functions of an ACM plate bending element along with in-plane displacements and geometry by cubic serendipity shape functions. The concentric and eccentric stiffeners, whether straight or curvilinear are ideally modelled so that they can be placed anywhere on the plate and not necessarily along the mesh grids as usually presented in the conventional methods. The formulation accommodates different boundary conditions which can be applied along the curved/straight boundary of the plate and for various types of loadings. To account for the nonlinearity, von Karman’s large deflection theory is used, and the formulation is performed in the total Lagrangian coordinate system. The nonlinear equations of large deformation are solved using Newton Raphson technique whereas the nonlinear equations of large amplitude free flexural vibration are solved by direct iteration method that uses the linear mode shape as a starting vector. The time-dependent equation in the transient analysis is solved using the average acceleration method of Newmark’s scheme. Various numerical examples of arbitrary shapes and boundary conditions are presented to show the versatility of the formulation and its efficacy is validated with the published results. Some new results obtained by the proposed method are also presented