An energy conserving non-linear dynamic finite element formulation for flexible composite laminates

Finite element formulation for non-linear dynamic analysis of flexible composite laminates is presented. A first-order shear-deformation theory, capable of modelling finite deformations and finite rotations in geometrically exact manner, is developed. A model allows simulation of a general elastic material with varied mass density, degree of orthotropy and elastic material parameters and is suitable for non-linear elasto-dynamic analysis of relatively thin and flexible laminates composed of fibre-reinforced composites. Coupling of mid-surface and shell-director fields is exactly taken into account, so that the kinetic energy is not of simple quadratic form. An implicit, one-step, second-order accurate numerical time-integration scheme is applied. In particular, the energy and momentum conserving algorithm, which exactly preserves the fundamental constants of the shell-like body motion, is accomodated for composite laminates. Spatial finite element discretization is based on the four noded multilayered shell finite element with isoparametric interpolations. Fully discrete weak form of the initial boundary value problem is consistently linearized in order to achieve a quadratic rate of asymptotic convergence typical for the Newton–Raphson based solution procedures. Numerical examples are presented.