A lower bound on snap-through instability of curved beams under thermomechanical loads

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• 作者：Ilinca Stanciulescu^a ; ^{ilinca@rice.edu} ; Toby Mitchell^b ; Yenny Chandra^a ; Thomas Eason^c ; Michael Spottswood^c
• 关键词：Snap-through ; Finite element ; Curved beam ; Solid (continuum) elements ; Thermomechanical loads
• 刊名：International Journal of Non-Linear Mechanics
• 出版年：2012
• 期刊代码：87_00207462
• 类别：et
• 出版时间：June, 2012
• 卷：47
• 期：5
• 页码：561-575
• 文件大小：1576 K

摘要

A non-linear finite element formulation (three dimensional continuum elements) is implemented and used for modeling dynamic snap-through in beams with initial curvature. We identify a non-trivial (non-flat) configuration of the beam at a critical temperature value below which the beam will no longer experience snap-through under any magnitude of applied quasi-static load for beams with various curvatures. The critical temperature is shown to successfully eliminate snap-through in dynamic simulations at quasistatic loading rates. Thermomechanical coupling is included in order to model a physically minimal amount of damping in the system, and the resulting post-snap vibrations are shown to be thermoelastically damped. We propose a test to determine the critical snap-free temperature for members of general geometry and loading pattern; the analogy between mechanical prestress and thermal strain that holds between the static and dynamic simulations is used to suggest a simple method for reducing the vulnerability of thin-walled structural members to dynamic snap-through in members of large initial curvature via the introduction of initial pretension.