Continuous inter-laminar stresses for regular and inverse geometrically non linear dynamic and static analyses of laminated plates and shells

This study presents an orthotropic laminated finite element with continuous stress distribution along transverse direction applied to geometrically non linear analysis of static and dynamic plates and shells. The kinematic description is total Lagrangian based on positions and generalized vectors which avoids the use of the finite rotation concept. Therefore, the loss of precision that may appears when reference updating takes place is not present. Moreover, there is no necessity to transform velocity and acceleration from the spatial to the material reference frame and the Newmark method can be applied.Using generalized vectors introduces constant thickness variation and complete 3D constitutive relation. Without increasing the number of degrees of freedom, the equilibrium of laminas parallel to the reference surface is applied to achieve continuous stress distribution along transverse direction. A curved triangular finite element with cubic approximation is adopted also avoiding membrane locking.Static examples are designed to check the absence of locking and to verify the quality of transverse stress distribution for thin and moderately thick orthotropic plates and shells. Dynamic examples show the ability of total Lagrangian formulations on solving general and inverse dynamic problems with energy conservation.