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CROSS-SECTIONAL ANALYSIS OF PRE-TWISTED THICK BEAMS USING VARIATIONAL ASYMPTOTIC METHOD

Ameen, Maqsood M and Harursampath, Dineshkumar (2014) CROSS-SECTIONAL ANALYSIS OF PRE-TWISTED THICK BEAMS USING VARIATIONAL ASYMPTOTIC METHOD. In: 11th World Congress on Computational Mechanics (WCCM) / 5th European Conference on Computational Mechanics (ECCM) / 6th European Conference on Computational Fluid Dynamics (ECFD), JUL 20-25, 2014, Barcelona, SPAIN, pp. 100-107.

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Abstract

An asymptotically-exact methodology is presented for obtaining the cross-sectional stiffness matrix of a pre-twisted moderately-thick beam having rectangular cross sections and made of transversely isotropic materials. The anisotropic beam is modeled from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy of the beam is computed making use of the constitutive law and the kinematical relations derived with the inclusion of geometrical nonlinearities and initial twist. Large displacements and rotations are allowed, but small strain is assumed. The Variational Asymptotic Method is used to minimize the energy functional, thereby reducing the cross section to a point on the reference line with appropriate properties, yielding a 1-D constitutive law. In this method as applied herein, the 2-D cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged as orders of the small parameters. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that renders the 1-D strain measures well-defined. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.

Item Type: Conference Proceedings
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Additional Information: Copy right for this article belongs to the INT CENTER NUMERICAL METHODS ENGINEERING, GRAN CAPITAN, S-N, CAMPUS NORTE UPC, MODULO C1, 08034 BARCELONA, SPAIN
Keywords: Moderately-thick beams; VAM; Composite Mechanics; Advanced Beam Theory
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering)
Date Deposited: 15 Jun 2015 10:13
Last Modified: 23 Jul 2015 09:37
URI: http://eprints.iisc.ernet.in/id/eprint/51678

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