Multiobjective Best Theory Diagrams for cross-ply composite plates employing polynomial, zig-zag, trigonometric and exponential thickness expansions

Abstract

This paper presents Best Theory Diagrams (BTDs) for plates considering all the displacement and stress components as objectives. The BTD is a diagram in which the minimum number of terms that have to be used to achieve the desired accuracy can be read. Maclaurin, zigzag , trigonometric and exponential expansions are employed for the static analysis of cross-ply composite plates. The Equivalent Single Layer (ESL) approach is considered, and the Unified Formulation developed by Carrera is used. The governing equations are derived from the Principle of Virtual Displacement (PVD), and Navier-type closed form solutions are adopted. BTDs are obtained using the Axiomatic/Asymptotic Method (AAM) and genetic algorithms (GA). The results show that the BTD can be used as a tool to assess the accuracy and computational efficiency of any structural models and to draw guidelines to develop structural models. The inclusion of the multiobjective capability extends the BTD validity to the recognition of the role played by each output parameter in the refinement of a structural model.

Consideration of interlaminar strain–energy continuity in composite plate analysis using improved higher order theory

“…Additionally, (Cho and Averill 2000;Thai et al 2014;Arani, Kolahchi, and Zarei 2015;Yarasca et al 2017)formulated a higher-order composite plate theory using a zigzag nonlinear in-plane displacement through the plate thickness. In that approach, the governing equations are derived from the zigzag nonlinear geometry, but the inter-laminar stress is not considered.…”

Static Analysis of Anisotropic Doubly-Curved Shell Subjected to Concentrated Loads Employing Higher Order Layer-Wise Theories

“…A milestone for the assessment of the kinematic field variable is its unified description [44,45], which incorporates both higher order theories and classical approaches like the First Order Shear Deformation Theory (FSDT) and the Third Order Shear Deformation Theory (TSDT), outlined in references [46,47]. Since it allows the introduction of a generalized set of thickness functions in both in-plane and out-of-plane directions, polynomials, non-polynomials and trigonometric functions can be employed to this purpose [48][49][50], depending on the material properties and relative thickness of the laminae embedded in the structure. Moreover, it is possible to develop an advanced set of axiomatic thickness functions, whose expressions is obtained from the mechanical shear properties of the lamination scheme, leading to the so-called refined zig-zag theories [51][52][53].…”