论文标题
弹性板的能量和来自二克拉力弹性的壳的能量
Energies for elastic plates and shells from quadratic-stretch elasticity
论文作者
论文摘要
我们得出各向同性弹性板和壳的拉伸能量。通过在生物菌株中散装弹性能量二次的尺寸降低，我们在弯曲度量中获得了二维弯曲能量的二维能量，这些弯曲度量具有拉伸和几何曲率的双线性耦合。对于板，弯曲度量在空间扩张下是不变的，并且自然会延伸直杆的原始弯曲应变。对于壳或自然弯曲的杆，该度量不是扩张不变的，并且与以前的\ emph {Ad hoc}假定的形式形成对比。相应的场方程和边界条件在弯曲度量中具有线性矩，以及伸展和弯曲的脱钩，使得纯度矩的应用导致独特的中性表面的等轴测变形，原始行为与经典线性响应一致，但未通过常用的分析模型显示。我们简要评论了我们的能量之间的关系，源自新蜂巢的散装能量以及常用的平膜模型。尽管派生需要考虑拉伸和旋转场，但所得的能量和场方程可以完全用变形和参考表面的度量和曲率成分表示。
We derive stretching and bending energies for isotropic elastic plates and shells. Through the dimensional reduction of a bulk elastic energy quadratic in Biot strains, we obtain two-dimensional bending energies quadratic in bending measures featuring a bilinear coupling of stretches and geometric curvatures. For plates, the bending measure is invariant under spatial dilations and naturally extends primitive bending strains for straight rods. For shells or naturally-curved rods, the measure is not dilation invariant, and contrasts with previous \emph{ad hoc} postulated forms. The corresponding field equations and boundary conditions feature moments linear in the bending measures, and a decoupling of stretching and bending such that application of a pure moment results in isometric deformation of a unique neutral surface, primitive behaviors in agreement with classical linear response but not displayed by commonly used analytical models. We briefly comment on relations between our energies, those derived from a neo-Hookean bulk energy, and a commonly used discrete model for flat membranes. Although the derivation requires consideration of stretch and rotation fields, the resulting energy and field equations can be expressed entirely in terms of metric and curvature components of deformed and reference surfaces.
