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首页> 外文期刊>International journal of non-linear mechanics >Buckling and postbuckling of extensible, shear-deformable beams: Some exact solutions and new insights
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Buckling and postbuckling of extensible, shear-deformable beams: Some exact solutions and new insights

机译：屈曲和出版物的可伸缩，剪切可变形梁：一些精确的解决方案和新的见解

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摘要

This paper presents exact solutions for the buckling loads and postbuckling states of extensible, shear deformable beams. The governing equation for the large-amplitude lateral deformation of beams in compression is expanded in Taylor series up to the cubic nonlinearity. Closed-form solutions in terms of the axial and shear stiffnesses are developed for statically determinate and statically indeterminate beams. Namely, pinned-pinned, cantilevered, clamped-clamped, and clamped-pinned beams are considered with the loaded end is a roller that is able to slide. The postbuckling response under a given axial load is exactly derived. The dependence of the buckling load on the length-to-radius of gyration is discussed. It is shown that the extensibility and the shear deformation significantly affect the buckling loads and the postbuckling response. For conventional materials with positive Poisson's ratio, the inclusion of the axial and shear deformation results in a meaningful reduction of the buckling load. It is further shown that the buckling load can be enhanced by designing artificial metamaterials materials with an effective negative Poisson's ratio.
机译：本文为可伸缩剪切可变形梁的屈曲负荷和后置型状态提供了精确的解决方案。压缩中梁的大幅度横向变形的控制方程在泰勒串中扩展到立方非线性。在轴向和剪切刚度方面的闭合溶液用于静态测定和静态不确定梁。即，与装载的端部考虑固定，悬臂，夹紧夹紧和夹紧钉梁是能够滑动的辊。在给定的轴向载荷下的后粘合响应完全导出。讨论了屈曲负荷对旋转长度的旋转半径的依赖性。结果表明，可扩展性和剪切变形显着影响屈曲负荷和后置响应。对于具有正泊松比率的常规材料，轴向和剪切变形的包含导致屈曲负荷的有意义降低。进一步表明，通过设计具有有效负泊松比的人工超材料材料，可以提高屈曲负荷。

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