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Mathematical Problems in Engineering
Volume 2014, Article ID 640983, 15 pages
http://dx.doi.org/10.1155/2014/640983
Research Article

Adaptive, Small-Rotation-Based, Corotational Technique for Analysis of 2D Nonlinear Elastic Frames

Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand

Received 30 October 2013; Revised 22 January 2014; Accepted 3 February 2014; Published 3 April 2014

Academic Editor: Paulo Batista Gonçalves

Copyright © 2014 Jaroon Rungamornrat et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents an efficient and accurate numerical technique for analysis of two-dimensional frames accounted for both geometric nonlinearity and nonlinear elastic material behavior. An adaptive remeshing scheme is utilized to optimally discretize a structure into a set of elements where the total displacement can be decomposed into the rigid body movement and one possessing small rotations. This, therefore, allows the force-deformation relationship for the latter part to be established based on small-rotation-based kinematics. Nonlinear elastic material model is integrated into such relation via the prescribed nonlinear moment-curvature relationship. The global force-displacement relation for each element can be derived subsequently using corotational formulations. A final system of nonlinear algebraic equations along with its associated gradient matrix for the whole structure is obtained by a standard assembly procedure and then solved numerically by Newton-Raphson algorithm. A selected set of results is then reported to demonstrate and discuss the computational performance including the accuracy and convergence of the proposed technique.