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首页> 外文期刊>International Journal of Solids and Structures >Drilling couples and refined constitutive equations in the resultant geometrically non-linear theory of elastic shells
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Drilling couples and refined constitutive equations in the resultant geometrically non-linear theory of elastic shells

机译：弹性壳合成几何非线性理论中的钻井偶和精细本构方程

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It is well known that distribution of displacements through the shell thickness is non-linear, in general. We introduce a modified polar decomposition of shell deformation gradient and a vector of deviation from the linear displacement distribution. When strains are assumed to be small, this allows one to propose an explicit definition of the drilling couples which is proportional to tangential components of the deviation vector. The consistent second approximation to the complementary energy density of the geometrically non-linear theory of isotropic elastic shells is constructed. From differentiation of the density we obtain the consistently refined constitutive equations for 2D surface stretch and bending measures. These equations are then inverted for 2D stress resultants and stress couples. The second-order terms in these constitutive equations take consistent account of influence of undeformed midsurface curvatures. The drilling couples are explicitly expressed by the stress couples, undeformed midsurface curvatures, and amplitudes of quadratic part of displacement distribution through the thickness. The drilling couples are shown to be much smaller than the stress couples, and their influence on the stress and strain state of the shell is negligible. However, such very small drilling couples have to be admitted in non-linear analyses of irregular multi-shell structures, e.g. shells with branches, intersections, or technological junctions. In such shell problems six 2D couple resultants are required to preserve the structure of the resultant shell theory at the junctions during entire deformation process.
机译：众所周知，通常，通过壳厚度的位移分布是非线性的。我们介绍了壳变形梯度的修正极性分解和线性位移分布的偏差向量。当假定应变很小时，这允许人们提出对钻头的明确定义，该定义与偏差矢量的切向分量成比例。构造了各向同性弹性壳几何非线性理论的互补能量密度的一致第二近似。通过密度的微分，我们获得了二维表面拉伸和弯曲度量的一致完善的本构方程。然后将这些方程式求逆，以得到2D应力合力和应力偶。这些本构方程中的二阶项始终考虑未变形的中表面曲率的影响。应力偶，未变形的中表面曲率和整个厚度范围内位移分布的二次部分的振幅明确表示了钻井偶。所示的钻井偶比应力偶小得多，并且它们对壳体应力和应变状态的影响可以忽略不计。然而，在对不规则的多壳结构进行非线性分析时，例如在钻探过程中，必须考虑到这种非常小的钻具。具有分支，交叉点或技术交叉点的壳体。在这样的壳问题中，需要六个二维耦合结果以在整个变形过程中保持结处的壳理论结构。

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