A unified formulation and the boundary discontinuous Fourier method for clamped functionally graded shells

Abstract

In the present work, analytical numerical solutions of the static behavior of fully clamped functionally graded (FG) doubly-curved panels are presented. The mechanical model is based on the Carrera Unified Formulation (CUF) under the Equivalent-Single-Layer (ESL) approach. The governing equations, in their strong form, are derived from the Principle of Virtual Displacements (PVD). The main novelty of this work is the integration of CUF and the Boundary-Discontinuous solution methodology. This merging yields a remarkably accurate and robust procedure that can handle different shell theories with arbitrary order of expansion. Besides, a new branch of future interesting applications of this purely analytical procedure is discussed. Several ceramic-metal graded shells with two different distribution-law variations subjected to uniform distributed load (UDL) are studied. Various thickness ratios, radius-to-thickness ratios, and order of expansion of the displacement field are considered. The accuracy of the proposed solution in predicting static displacements and stresses of thick and thin FG panels is evaluated and discussed by comparing it with those of the literature for various case problems. As the proposed approach solution presented in this paper is unique, the numerical results might be useful as benchmarks for validating new FG shell theories.