Shell theories arising as low energy Γ-limit of 3d nonlinear elasticity

A Riemannian Approach to Reduced Plate, Shell, and Rod Theories

We derive a dimensionally-reduced limit theory for an $n$-dimensional nonlinear elastic body that is slender along $k$ dimensions. The starting point is to view an elastic body as an $n$-dimensional Riemannian manifold together with a not necessarily isometric $W^{1,2}$-immersion in $n$-dimensional Euclidean space. The equilibrium configuration is the immersion that minimizes the average discrepancy between the induced and intrinsic metrics. The dimensionally reduced limit theory views the elastic body as a $k$-dimensional Riemannian manifold along with an isometric $W^{2,2}$-immersion in $n$-…

Von Kármán 薄弹性壳在压力作用下的理论

Von Kármán theories for thin elastic shells subject to pressure

本文在恒定压力载荷下，从三维非线性弹性变分推导二维 von Kármán 壳能量，将压力板分析推广至弯曲壳，并引入非线性压力力补充经典推导。