含弯矩线性增长能量的降维
Dimensional reduction for energies with linear growth involving the bending moment
摘要：
一个$Γ$ -收敛性分析被用来执行三维-二维降维的线性增长的变分问题。所采用的缩放引起一个非线性膜模型，由于存在高阶外部载荷引起的弯矩，可能取决于平均在横向方向上的Cosserat向量场，以及对中平面的变形。线性增长的能量的假设导致的措施和有界变差的函数的空间中的渐近分析。
英文摘要：
A $Γ$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation.
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