Basic Finite Strip Formulation for Prismatic Shells

Abstract

This chapter 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, MR FSs.

First, before discussing the finite strip formulation, Fourier-series-based solutions for simply supported beam will be considered for both Euler-Bernoulli and Timoshenko beam idealizations.

Next, the theoretical formulation is presented for a family of C(0) strips for right prismatic structures and the accuracy and relative performance of the strips are examined for some benchmark examples. Some variable-thickness and elastically supported plates are considered and the interesting phenomenon of the occurrence of boundary layers in the twisting moments and shear forces is highlighted for a common boundary condition. Other examples include box-girder bridges and cylindrical shells.

Later, the formulation is extended to prismatic folded plate and shell structures that are of curved planform. All the features of the curved strip formulation are first tested using known solutions for right structures to demonstrate that the formulation is working correctly. This is done by taking a very large radius in conjunction with a very small appropriate subtended angle to provide the correct span. To test the formulation further, comparisons are provided with known solutions for structures with curved planform. Finally, some new solutions are presented for structures that have curved planform. In all cases, transverse shear deformation effects are included and the contributions to the SE from membrane, bending and transverse shear behaviour noted.