Analysis and shape optimisation of variable thickness prismatic folded plates and curved shells — Part 1: Finite strip formulation

Abstract

This paper deals with the linear elastic analysis of prismatic folded plate and shell structures supported on diaphragms at two opposite edges with the other two edges arbitrarily restrained. The analysis is carried out using curved, variable thickness, Mindlin-Reissner finite strips. The theoretical formulation is presented for a family of C (0) strips and the accuracy and relative performance of the strips are examined for curved situations. Some variable thickness and elastically supported plates are considered and the interesting phenomenon of the occurence of boundary layers in the twisting moments and shear forces is highlighted for a common boundary condition. Other examples analysed include box girders and cylindrical shells. In all cases transverse shear deformation effects are included and the contributions to the strain energy from membrane, bending and transverse shear behaviour noted. In a companion paper these accurate and inexpensive finite strips are used for structural shape optimisation.