Analysis and optimization of prismatic plate and shell structures with curved planform—I. Finite strip formulation

Abstract

This paper deals with the linear elastic analysis of prismatic folded plate and shell structures with curved planform. The analysis is carried out using Mindlin-Reissner variable thickness finite strips of curved cross-section and the theoretical formulation is presented for a family of C(0) strips. Curved plates on elastic foundations are also considered. Further, the interesting phenomenon of the occurrence of boundary layers in the twisting moments and shear forces is highlighted for plates subjected to a common boundary condition. All the features of the curved planform strip formulation are tested using known solutions for right structures first 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 further test the formulation, comparisons are provided with known solutions for structures with curved planform. Finally, some new solutions are presented for structures with curved planform. In a companion paper these accurate and inexpensive strips are used for structural shape optimization of prismatic structures with curved planform.