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首页> 外文期刊>Meccanica: Journal of the Italian Association of Theoretical and Applied Mechanics >The constrained buckling problem of geometrically imperfect beams: a mathematical approach for the determination of the critical instability points
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The constrained buckling problem of geometrically imperfect beams: a mathematical approach for the determination of the critical instability points

机译：几何不完美梁的约束屈曲问题：确定临界失稳点的数学方法

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摘要

The constrained buckling problem of geometrically imperfect beams with intermediate unilateral supports is studied in the present paper. The proposed methodology offers the ability to calculate analytically the critical loads and the buckling shape of beams with arbitrary initial geometric imperfections, for a variety of different initial contact conditions in the framework of elastic stability theory. The proposed mathematical approach is based on the formulation of the equilibrium equations in the deformed position, in which the function of the unilateral constraints is appropriately taken into account. The analytical solution is obtained after the splitting of the initial constrained non-homogeneous boundary value problem (BVP) into constrained subproblems and the utilization of a classical mathematical theorem from the field of ordinary non-homogeneous BVPs. The implementation of the presented technique is demonstrated through characteristic examples. In order to validate the proposed mathematical method, the obtained results are compared with the respective numerical ones. The latter are obtained through the utilization of geometric nonlinear finite element analysis. The paper ends with the presentation of an investigation on the variation of the critical load with respect to different positions of the unilateral constraints.
机译：研究了具有单边中间支撑的几何缺陷梁的约束屈曲问题。在弹性稳定性理论的框架下，针对各种不同的初始接触条件，所提出的方法提供了分析任意临界初始几何缺陷的梁的临界载荷和屈曲形状的能力。所提出的数学方法是基于变形位置上的平衡方程的公式化，其中适当考虑了单边约束的功能。通过将初始约束非齐次边值问题（BVP）分解为约束子问题并利用普通非齐次BVP领域的经典数学定理，可以得到解析解。通过特征示例演示了所提出技术的实现。为了验证所提出的数学方法，将获得的结果与相应的数值进行比较。后者是通过利用几何非线性有限元分析获得的。本文以关于单边约束的不同位置的临界载荷变化的研究报告为结尾。

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