Date of Award

Spring 1-1-2013

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

First Advisor

Widera, G. E. Otto

Second Advisor

Kim, Kyuil

Third Advisor

Kyuil Kim


The present work is concerned with the finite element structural analysis of laminated anisotropic plates and shells. New elements based on a modified complementary energy principle are proposed to improve the analysis of such composite structures. Third order deformation plate and shell models incorporating a convergence parameter are developed to govern the general displacement field.

An eight-node isoparametric quadrilateral element with two independent cross-sectional rotations and three normal displacements is utilized to describe the displacement field. The present modified complementary energy formulation incorporates a number of in-plane strain functions of various orders. The corresponding in-plane stresses for each lamina are derived from the constitutive relations. The transverse stresses are then computed from the application of equilibrium equations. The element comprises an arbitrary number of lamina rigidly bonded together.

The analysis technique employed, although using a higher order formulation, does not increase the number of variables associated with each lamina. Moreover, the use of a convergence parameter permits one to achieve excellent results for very thin as well as thick composite plates and shells. The static bending analysis of several example problems for various geometries, transverse loads and material properties is analyzed via a code written in MATLAB. The results are compared with those from technical theories, other finite element models and three-dimensional elasticity solutions available in the literature. It is demonstrated that marked improvements in the results for stress and displacement can be achieved by the use of the new modified complementary energy elements incorporating a convergence parameter.