Michell trusses in two dimensions as a $$Gamma $$Γ-limit of optimal design problems in linear elasticity
Michell trusses in two dimensions as a $$Gamma $$Γ-limit of optimal design problems in linear elasticity
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二维米歇尔桁架作为线弹性最优设计问题的 $$Gamma $$Γ 极限
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发表时间：
2017
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通讯作者：
H. Olbermann
中科院分区：
文献类型：
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作者：
H. Olbermann
我们重新考虑了给定重量下具有牵引边界条件的二维弹性体柔度的最小化问题。如何将这个优化设计问题改写为一个非线性变分问题是众所周知的。在变分公式中，我们通过将合适的拉格朗日乘子赋于无穷来求权值消失的极限。我们证明，在$$Gamma $$ Γ-convergence意义上，极限是一个特定的米歇尔桁架问题。这证明了Kohn和Allaire的一个猜想。
We reconsider the minimization of the compliance of a two dimensional elastic body with traction boundary conditions for a given weight. It is well known how to rewrite this optimal design problem as a nonlinear variational problem. We take the limit of vanishing weight by sending a suitable Lagrange multiplier to infinity in the variational formulation. We show that the limit, in the sense of $$Gamma $$Γ-convergence, is a certain Michell truss problem. This proves a conjecture by Kohn and Allaire.