Multilayered plate elements with node-dependent kinematics for electro-mechanical problems

In the present work,a new class of finite elements(FEs)for the analysis of composite and sandwich plates embedding piezoelectric skins and patches is proposed.By making use of node-by-node variable plate theory assumptions,the new finite element allows for the simultaneous analysis of different subregions of the problem domain with different kinematics and accuracy,in a global/local sense.As a consequence,the computational costs can be reduced drastically by assuming refined theories only in those zones/nodes of the structural domain where the resulting strain and stress states,and their electro-mechanical coupling present a complex distribution.The primary advantage is that no ad-hoc techniques and mathematical artifices are required to mix the fields coming from two different and kinematically incompatible adjacent elements,because the plate structural theory varies within the finite element itself.In other words,the structural theory of the plate element is a property of the FE node in this present approach,and the continuity between two adjacent elements is ensured by adopting the same kinematics at the interface nodes.The finite element arrays of the generic plate element are formulated in terms of fundamental nuclei,which are invariants of the theory approximation order and the modeling technique(Equivalent-Single-Layer,Layer-Wise).In this work,the attention is focused on the use of Legendre polynomial expansions to describe the through-the-thickness unknowns to develop advanced plate theories.Several numerical investigations,such as composite and sandwich multilayered plates embedding piezoelectric skins and patches with various load,boundary conditions,and piezoelectric material polarizations,are carried out to validate and demonstrate the accuracy and efficiency of the present plate element,including comparison with various closed-form and FE solutions from the literature.

Electro-mechanical analysis of composite and sandwich multilayered structures by shell elements with node-dependent kinematics

In this work,a new class of finite elements for the analysis of composite and sandwich shells embedding piezoelectric skins and patches is proposed.The main idea of models coupling is developed by presenting the concept of nodal dependent kinematics where the same finite element can present at each node a different approximation of the main unknowns by setting a nodewise through-the-thickness approximation base.In a global/local approach scenario,the computational costs can be reduced drastically by assuming refined theories only in those zones/nodes of the structural domain where the resulting strain and stress states,and their electro-mechanical coupling present a complex distribution.Several numerical investigations are carried out to validate the accuracy and efficiency of the present shell element.An accurate representation of mechanical stresses and electric displacements in localized zones is possible with reduction of the computational costs if an accurate distribution of the higherorder kinematic capabilities is performed.On the contrary,the accuracy of the solution in terms of mechanical displacements and electric potential values depends on the global approximation over the whole structure.The efficacy of the present node-dependent variable kinematic models,thus,depends on the characteristics of the problem under consideration as well as on the required analysis type.