A novel highly accurate Trefftz attitude towards bending and free vibration analysis of doubly-curved laminated and sandwich shallow shells

Ali Reza Motamedi, Nima Noormohammadi, Bijan Boroomand

Engineering Analysis with Boundary Elements

Abstract

This paper extends the meshless local exponential basis functions to the analysis of doubly curved laminated and sandwich shallow shells. The method discretizes the shell domain by some nodes at which the degrees of freedom are defined. A specific number of nearby nodes, only based on their distance, are selected as a cloud. Within every cloud, the total solution is set in homogeneous and particular parts. The former is adjusted by exponential basis functions to exactly satisfy the homogeneous governing equation, as in Trefftz approaches. Overlapping of adjacent clouds integrates the solution function over the entire domain. While Trefftz methods usually implement trial and error approaches for eigenvalue problems, we introduce a novel technique for the free vibration solution in one step by treating the frequency including part as a loading term. Three deformation theories, namely CST, FSDT and TSDT will be adopted for the formulation. Various boundary conditions such as simple, clamped and free are applied to the edges. It will be shown that the method benefits from high accuracy and fast convergence rate, not adversely affected by irregularity of the nodal grid. Additional results are also provided for interested researchers.