Comparison of two linearization schemes for the nonlinear bending problem of a beam pinned at both ends

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:47

Article

Merli, R.¹  Lazaro, C.¹  Monleon, S.¹  Domingo, A.² 

[1] Univ Politecn Valencia, Dept Mecan Medios Continuos & Teoria Estructuras, Escuela Tecn Super Ingenieros Caminos Canales & P, Valencia 46022, Spain

[2] Univ Politecn Valencia, Dept Ingn Construcc, Escuela Tecn Super Ingenieros Caminos Canales & P, Valencia 46022, Spain

关键词: Multi-step transversal linearization (MTrL);    Multi-step tangential linearization (MTnL);    Locally transversal linearization (LTL);    Timoshenko beam;    Beam pinned at both ends;    Nonlinear bending problem;    Boundary value problem (BVP);    Centered finite differences;    Multi-point linear constraints;   

DOI  :  10.1016/j.ijsolstr.2009.12.001

来源: Elsevier

【 摘 要 】

The nonlinear bending problem of a constant cross-section simply supported beam pinned at both ends and subject to a uniformly distributed load q(x) is analyzed in detail. The numerical integration of the two-point boundary value problem (BVP) derived for the nonlinear Timoshenko beam is tackled through two different linearization schemes, the multi-step transversal linearization (MTrL) and the multi-step tangential linearization (MTnL), proposed by Viswanath and Roy (2007). The fundamentals of these linearization techniques are to replace the nonlinear part of the governing ODEs through a set of conditionally linearized ODE systems at the nodal grid points along the neutral axis, ensuring the intersection between the solution manifolds (transversally in the MTrL and tangentially in the MTnL). In this paper, the solution values are determined at grid points by means of a centered finite differences method with multipoint linear constraints (Keller, 1969), and a simple iterative strategy. The analytical solution for this kind of bending problem, including the extensional effects, can be worked out by integration of the governing two-point BVP equations (Monleon et al., 2008). Finally, the comparison of analytical and numerical results shows the better ability of MTnL with the proposed iterative strategy to reproduce the theoretical behavior of the beam for each load step, because the restraint of equating derivatives in MTnL leads to further closeness between solution paths of the governing ODEs and the linearized ones, in comparison with MTrL This result is opposed to the conclusion reached in Viswanath and Roy (2007), where the relative errors produced by MTrL are said to be smaller than the MTnL ones for the simply supported beam and the tip-loaded cantilever beam problems. (C) 2009 Elsevier Ltd. All rights reserved.

【 授权许可】

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