On Simple and Efficient Shell and Solid Finite Elements with Rotational Degrees of Freedom

摘要

This paper is concerned with the investigation the original goal of which was to provide mixed variational principles for the derivation and development of simple and efficient finite elements with rotational degrees of freedom. These finite elements include isotropic and laminated composite flat triangular shell elements, flat triangular shell elements with embedded and distributed piezoelectric components, and lower order four-node tetrahedral solid elements. One common feature is that for shell finite elements their drilling degrees of freedom or for solid finite elements all their rotational degrees of freedom are hinged on the displacement formulation, while their remaining degrees of freedom are hybrid strain formulation based. For the solid finite elements, their translational degrees of freedom are based on the hybrid strain formulation but all their rotational degrees of freedom are derived using the displacement formulation. Every one of the finite elements chosen is capable of producing the correct number of rigid body modes and there are no zero-energy spurious modes. Another common feature of these finite elements is that explicit expressions for element matrices are obtained with manual and a symbolic algebraic package, MAPLE. Thus, these explicit expressions are relatively much more efficient and economical to apply in the analysis and design as well as control of large scale structural systems.