Linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method

Abstract

In the present study we apply the Natural Mode Method and formulate an appropriate linear and geometrically nonlinear theory which is implemented on a model three-node multilayered triangular facet element which incorporates the effect of transverse shear deformation and is intended for the nonlinear analysis of large and complex isotropic and composite structures. In this context, we discuss the derivation of the elastic and geometrical elemental stiffnesses which are based on appropriate kinematic as well as physical idealizations, which constitute basic elements of the method of Intelligent Physical Lumping. Subsequently, we present the ARIBAN scheme (accumulation of the rigid-body and natural modes) for geometrically nonlinear analysis. It is emphasized that both the triangular facet element and the nonlinear algorithm are developed for the analysis of large and complex structures for which higher order formal finite elements cannot provide answers inexpensivelly. In addition, the structure of the algorithm and its matrix language are ideally suited for modern parallel computers. We conclude our study with numerical examples for isotropic and composite plates. All the numerical experiments show the accuracy and potential of the developed methodology for extensive structural engineering computations.