论文标题
通过GAMMA收敛性
A geometrically nonlinear Cosserat (micropolar) curvy shell model via Gamma convergence
论文作者
论文摘要
使用$γ$ -Convergence参数，我们在从几何非线性的，物理上线性的三维各向同性Cosserat模型开始的弯曲参考配置上构建了一个非线性膜状的Cosserat壳模型。即使与经典非线性弹性中提出的膜壳模型相比，该理论是$ o o（h）$的$ o（h）$，除了公制的变化外，类似膜的cosserat壳模型仍然能够捕获横向剪切变形和{cosserat} -cosserat} -coSurvature futy futy cosserat效应。 我们通过缩放未知数，变形和微连接张量来提出极限问题，并通过相对于虚拟的扁平构型来表达父母的三维Cosserat能量。通过$γ$ -Convergence获得的模型与膜相似{（no $ O（H^3）$ flefural项，但仍取决于Cosserat-Curvature）} Cosserat壳模型通过推导方法得出的cosserat shell模型，但这两个模型不合时宜。还包括与其他外壳模型的比较。
Using $Γ$-convergence arguments, we construct a nonlinear membrane-like Cosserat shell model on a curvy reference configuration starting from a geometrically nonlinear, physically linear three-dimensional isotropic Cosserat model. Even if the theory is of order $O(h)$ in the shell thickness $h$, by comparison to the membrane shell models proposed in classical nonlinear elasticity, beside the change of metric, the membrane-like Cosserat shell model is still capable to capture the transverse shear deformation and the {Cosserat}-curvature due to remaining Cosserat effects. We formulate the limit problem by scaling both unknowns, the deformation and the microrotation tensor, and by expressing the parental three-dimensional Cosserat energy with respect to a fictitious flat configuration. The model obtained via $Γ$-convergence is similar to the membrane {(no $O(h^3)$ flexural terms, but still depending on the Cosserat-curvature)} Cosserat shell model derived via a derivation approach but these two models do not coincide. Comparisons to other shell models are also included.
