Free vibration analysis and shape optimization of variable thickness plates and shells—I. Finite element studies

Abstract

This paper deals with the free vibration analysis of plate and shell structures. The formulation presented caters for shells with arbitrary thickness variation and support conditions. The shape and the thickness distributions of the structure are represented using Coons patches and the analysis is carried out using the nine-noded, degenerated, Huang-Hinton element with assumed strain fields. Several benchmark problems are considered to check the convergence and accuracy of the implementation. Additional shell examples are included to demonstrate the versatility of the formulation. In a companion paper, the studies initiated here are extended to structural sensitivity analysis and shape optimization.