Session: 02-09-03: Computational Modeling and Simulation for Advanced Manufacturing-III

Paper Number: 73618

Start Time: Tuesday, 04:30 PM

73618 - Assessment of Interlaminar Stress Components in Laminated Composites Manufactured by Ply-Drop Technique of Interlaminar Stress Components in Laminated Composites Manufactured by Ply-Drop Technique 

Tapered composites have found applications in a wide spectrum of areas, mainly owing to its weight savings and ’tailoring’ options possible for its mechanical properties. This calls for a thorough analysis required to predict the response of the tapered laminates, which are formed by dropping some part of the plies at certain fixed locations. Initially, a three-dimensional model (3D) of a particular symmetric ply-configuration of the body, subjected to a tensile load is analyzed using a commercial package, ANSYS 16.2 and the results obtained are compared against established results. It is vital to obtain the various parameters affecting the strength and endurance of the material to external load conditions and obtaining an ideal configuration extending scope of maximum performance. The three-dimensional modelling and analysis would be computationally time-investing, and therefore a new mathematical asymptotic method, is applied in the second phase of this project, known as Variational Asymptotic Method (VAM), in order to analyze this problem. It mainly involves decomposition of the 3D problem into a 1D, owing to the point that the thickness of rotating beams such as propellers, rotors, etc.is comparatively lower than the other two dimensions, width and length. The application of beam theory involves the introduction of variables depending only on beam axis co-ordinates. For the case of general deformation, at least 4 variables depending on 1-D beam dimension have to be introduced, one extensional, one torsional and two flexural variables for the two orthogonal directional. These are accounted for through the application of Euler-Bernoulli theory for bending and extensions and torsional values are verified by St-Venant theory. We finally obtain a 4x4 simplified matrix, which is computational much efficient and this should incorporate all non-linearity like extension-twist coupling, warping,etc.which may be dominating in thin walled beam sections found in rotor blades and turbomachinery. For initial analysis and studies, small deflections/rotation assumptions might prove enough , and classical linear theories might be applicable to obtain governing equations and closed form solutions for the one-dimensional models, but gradually as the structure gets exposed to higher loads, causing large  deflections and rotations, ad hoc assumptions found in classical approaches might prove unreliable, and non-linear may be prove vital. For this purpose, geometrically exact intrinsic beam theory derived using variational principle is adopted for the analysis. The strain energy field in terms of the 1D strain terms is developed using the warping field, and the strain energy density is integrated over the one dimensional length to obtain the strain energy per unit dimensional in the one dimensional analysis. Based on the above theory, a nonlinear mixed finite element formulation is employed for the structural analysis, where the nonlinear cross sectional constitutive law serves as the input. A complete finite element solver for the beam statics is developed considering both 1D non-linearity arising due to large deflections/rotations and cross sectional nonlinearities due to non-classical effects like extensional-twist coupling, also known as ’trapeze effect’. The solution obtained contains asymptotically exact static displacement and rotation variations of the body for arbitrary loading and stacking sequence. Out of plane stresses (interlaminar) are recovered from the global 3D equilibrium equations which can be used further for delamination and failure studies.

Presenting Author: Sandeep Suresh Babu Indian Institute of Technology Bombay

Authors:

Sandeep Suresh Babu Indian Institute of Technology Bombay
Abdel-Hamid I. Mourad United Arab Emirates University