论文标题
各向同性的cosserat壳模型，其中包括$ o（h^5）$的术语。第二部分：最小化器的存在
The isotropic Cosserat shell model including terms up to $O(h^5)$. Part II: Existence of minimizers
论文作者
论文摘要
我们显示了几何非线性各向同性弹性cosserat 6参数壳模型的全局最小化器的存在。主定理的证明基于变异的直接方法，使用非线性应变和曲率测量中能量的凸度。我们首先显示了理论解决方案的存在，包括$ o（h^5）$项。能源使我们能够显示到$ o（h^5）$和能量凸的订单的条款的强制性。其次，我们仅考虑能量的那部分，包括$ O（h^3）$项。在这种情况下，获得的最小化问题与文献中先前所考虑的问题不同，因为曲面初始壳构型的影响显式地出现在能量系数的表达中，以减少二维变分问题，并存在额外的混合弯曲和曲率术语。在理论上，包括$ o（h^5）$厚度$ h $的条件是建模过程中考虑的条件，并且它们独立于本构参数，但在$ O（h^3）$中，在厚度$ h $的情况下，在一些更限制的条件下证明了强制性在某些限制性条件下证明。
We show the existence of global minimizers for a geometrically nonlinear isotropic elastic Cosserat 6-parameter shell model. The proof of the main theorem is based on the direct methods of the calculus of variations using essentially the convexity of the energy in the nonlinear strain and curvature measures. We first show the existence of the solution for the theory including $O(h^5)$ terms. The energy allows us to show the coercivity for terms up to order $O(h^5)$ and the convexity of the energy. Secondly, we consider only that part of the energy including $O(h^3)$ terms. In this case the obtained minimization problem is not the same as those previously considered in the literature, since the influence of the curved initial shell configuration appears explicitly in the expression of the coefficients of the energies for the reduced two-dimensional variational problem and additional mixed bending-curvature and curvature terms are present. While in the theory including $O(h^5)$ the conditions on the thickness $h$ are those considered in the modelling process and they are independent of the constitutive parameter, in the $O(h^3)$-case the coercivity is proven on some more restrictive conditions under the thickness $h$.
