Γ-convergence for incompressible elastic plates
Γ-convergence for incompressible elastic plates
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DOI：
10.1007/s00526-008-0194-1
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发表时间：
2009-04
影响因子：
2.1
通讯作者：
S. Conti;G. Dolzmann
中科院分区：
文献类型：
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作者：
S. Conti;G. Dolzmann
我们推导了弹性板的二维模型，作为不可压缩约束下三维非线性弹性的Γ-limit。所得模型描述了板的弯曲，并由三维问题的等时弹性模量确定。在没有不可压缩性约束的情况下，freesecke等人首先推导出了平板理论（Comm Pure applied Math 55:1461-1506, 2002）。我们将他们的结果推广到p_在无穷远处生长的情况，以及不可压缩材料的情况。其主要难点在于如何构造满足非线性点向约束的恢复序列。其中一个主要成分是w2,2等距中的光滑等距密度，这是Pakzad （J Differ Geom 66:47-69, 2004）对凸域和Hornung （Comptes Rendus Mathematique 346:189 - 192,2008）对分段ec1域获得的。
We derive a two-dimensional model for elastic plates as a Γ-limit of three-dimensional nonlinear elasticity with the constraint of incompressibility. The resulting model describes plate bending, and is determined from the isochoric elastic moduli of the three-dimensional problem. Without the constraint of incompressibility, a plate theory was first derived by Friesecke et al. (Comm Pure Appl Math 55:1461–1506, 2002). We extend their result to the case ofpgrowth at infinity withpϵ [1, 2), and to the case of incompressible materials. The main difficulty is the construction of a recovery sequence which satisfies the nonlinear constraint pointwise. One main ingredient is the density of smooth isometries inW2,2isometries, which was obtained by Pakzad (J Differ Geom 66:47–69, 2004) for convex domains and by Hornung (Comptes Rendus Mathematique 346:189–192, 2008) for piecewiseC1domains.