Large rotation theory for static analysis of composite and piezoelectric laminated thin-walled structures

• A large rotation theory is developed based on FOSD hypothesis.
• Six parameters are considered in LRT56, but expressed by five DOFs.
• Electro-mechanical coupling effects are involved in the nonlinear FE model.
• A nonlinear equilibrium equation and a sensor equation are obtained.
• The results obtained by LRT56 agree quit well with those in the literature.

A fully geometrically nonlinear finite element (FE) model is developed using large rotation shell theory for static analysis of composite and piezoelectric laminated thin-walled structures. The proposed large rotation theory is based on the first-order shear deformation (FOSD) hypothesis. It has six independent kinematic parameters which are expressed by five mechanical nodal degrees of freedom (DOFs). Linear electro-mechanically coupled constitutive equations with a constant electric field distribution through the thickness of each smart material layer are considered. Eight-node quadrilateral plate/shell elements with five mechanical DOFs per node and one electrical DOF per smart material layer are employed in the FE modeling. The present large rotation FE model is implemented into static analysis of both composite and piezoelectric laminated plates and shells. The equilibrium equation is solved by Newton–Raphson algorithm with system matrices updated in every iteration. The results are compared with those presented in the literature and others calculated by various simplified nonlinear shell theories. They indicate that large rotation theory has to be considered for the calculation of displacements and sensor output voltages of smart structures undergoing large deflections, since other simplified nonlinear theories fail to predict the static response precisely in many cases.