Numerical assessment of interlaminar stresses in tapered composite laminates : A comparative analysis with FEM and VAM

Laminated composites with internal ply drop-off regions at specific locations, popularly known as tapered composite structures have found wide applicability, owing mainly to its weight savings and customizable mechanical properties. A detailed analysis is therefore vital to predict the mechanical response of these tapered laminates with plies terminating at specific locations. In the initial part of the study, a three-dimensional (3D) model of a flexbleam structure, which is a typical structural application of tapered composites is condensed to a two-dimensional (2D) model on certain assumptions. It is a symmetric ply-configuration structure exposed to a tensile load and analysis is carried out on a commercial finite element method (FEM) package, ANSYS 16.2. The study of induced interlaminar stress responses can aid in determining the factors influencing the strength and endurance of the laminate structure thereby, guide in the design of the ideal layout to maximize performance across various conditions and prevent delamination. The conventional 3D/2D analysis require high investment in terms of computational effort and time. Therefore, a mathematical asymptotic method, Variational Asymptotic Method (VAM) is introduced in second phase of this study in order to analyze the problem. It mainly involves decomposition of the 3D problem into a one-dimensional (1D) one, owing to the point that the thickness of rotating beams such as propellor, rotors, etc. is comparatively lower than the other two dimensions. The application of beam theory involves the introduction of variables depending only on beam axis co-ordinates. Unlike classical approaches, this is especially useful to capture non-linearities such as extension-twist coupling (trapeze effect). warping, etc. which may be dominating in thin-walled beam section found in rotor blades and turbomachinery. For this purpose, geometrically exact intrinsic beam theory derived using variational principle is adopted for the analysis. The solution obtained contains asymptotically exact static displacement and rotation variations of the structure for arbitrary loading and stacking sequence. Out of plane stresses (interlaminar) are recovered from global 3D equilibrium equations which can be further used for delamination studies.