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首页> 外文期刊>International Journal of Solids and Structures >Column buckling with shear deformations - A hyperelastic formulation
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Column buckling with shear deformations - A hyperelastic formulation

机译：具有剪切变形的柱屈曲-超弹性公式

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摘要

Column constitutive relationships and buckling equations are derived using a consistent hyperelastic neo-Hookean formulation. It is shown that the Mandel stress tensor provides the most concise representation for stress components. The analogous definitions for uniaxial beam plane stress and plane strain for large deformations are established by examining the virtual work equations. Anticlastic transverse curvature of the beam cross-section is incorporated when plane stress or thick beam dimensions are assumed. Column buckling equations which allow for shear and axial deformations are derived using the positive definiteness of the second order work. The buckling equations agree with the equation derived by Haringx and are extended to incorporate anticlastic transverse curvature which is important for low slenderness, high buckling modes and with increasing width to thickness ratio. The work in this paper does not support the existence of a shear buckling mode for straight prismatic columns made of an isotropic material.
机译：列本构关系和屈曲方程式是使用一致的超弹性新霍克公式得出的。结果表明，Mandel应力张量为应力分量提供了最简洁的表示。通过检查虚拟功方程，建立大变形的单轴梁平面应力和平面应变的类似定义。当假定为平面应力或较厚的梁尺寸时，将合并梁横截面的抗弹性横向曲率。利用二阶功的正定性推导了允许剪切和轴向变形的柱屈曲方程。屈曲方程与Haringx推导的方程相吻合，并扩展到包含抗剪横向曲率，这对于低细长度，高屈曲模式和宽度与厚度之比的增加很重要。本文的工作不支持由各向同性材料制成的直棱柱的剪切屈曲模式的存在。

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