在具有线性组合定律的非线性三维空间系统中通过合并/发散实现屈曲消失

IF 2.8 3区 工程技术 Q2 MECHANICS
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引用次数: 0

摘要

本论文研究了屈曲消失现象,这种现象发生在具有非三维基本路径的、与参数相关的系统家族中。研究发现了两种不同的消失形式,即:(i) 发散,即临界载荷持续趋于无穷大;(ii) 合并,即两个临界载荷相互接近、聚合,然后在临界载荷的有限值处消失。研究表明,当改变一个合适的弹性几何参数时,同一机械系统也会出现这两种现象。更重要的是,研究证明,当第二个参数发生变化时,合并会不断转变为发散。我们选择了一个典型系统来说明这两种形式的屈曲,即一个三自由度球形摆,在地面受到弹性约束,由一个横向力和/或由两个纵向势能力组成的保守耦合加载。弹簧采用弹性线性,以强调发散并不一定需要引入非线性构成定律,这在文献中也有提及。这里只进行了线性分岔分析,目的是沿着非线性基本路径找到分岔点。然而,由于存在不可忽略的预应变,这种分岔问题受非线性代数方程支配,其根数无法事先预测。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Buckling disappearance via merging/divergence in a nonlinear three-d.o.f. system with linear constitutive law
The phenomenon of buckling disappearance, occurring in a parameter-dependent family of systems admitting a nontrivial fundamental path, is studied. Two different forms of disappearance are detected, namely: (i) the divergence, in which the critical load continuously tends to infinity, and (ii) the merging, in which two critical loads approach each other, coalesce, and then disappear at a finite value of the critical load. It is shown that the two phenomena can be exhibited by the same mechanical system, when a suitable elasto-geometric parameter is varied. More importantly, it is proved that merging continuously changes into divergence when a second parameter is changed. A paradigmatic system is chosen to illustrate the two forms of buckling, i.e., a three degree-of-freedom spherical pendulum, elastically constrained at the ground, loaded by a transverse force and/or a conservative couple, made of two longitudinal potential forces. The springs are taken elastically linear, to stress the fact that divergence not necessarily calls for introducing a nonlinear constitutive law, as also mentioned in literature. Only a linear bifurcation analysis is carried out here, aimed to find the bifurcation points along the nonlinear fundamental path. However, due to the presence of non-negligible prestrains, such a bifurcation problem is governed by nonlinear algebraic equations, whose number of roots cannot be predicted in advance.
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来源期刊
CiteScore
5.50
自引率
9.40%
发文量
192
审稿时长
67 days
期刊介绍: The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.
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