论文标题
压力活载荷和线性弹性的变异推导
Pressure live loads and the variational derivation of linear elasticity
论文作者
论文摘要
通过伽马连接的方式，线性弹性的严格推导是一个众所周知的结果，它已扩展到不同模型，也扩展到了弹性方案之外。但是，在这些结果中，通常认为施加的力是死载荷，也就是说，参考配置中的密度与实际变形无关。在本文中，我们开始研究在有活载荷存在下线性弹性的变异推导。我们考虑了受压力活载荷的非线性弹性体的纯牵引问题，并通过γ-连接来计算其线性化的小压力。我们允许弱强制弹性能量密度，并证明最小化器的强烈收敛性。
The rigorous derivation of linear elasticity from finite elasticity by means of Gamma-convergence is a well-known result, which has been extended to different models also beyond the elastic regime. However, in these results the applied forces are usually assumed to be dead loads, that is, their density in the reference configuration is independent of the actual deformation. In this paper we begin a study of the variational derivation of linear elasticity in the presence of live loads. We consider a pure traction problem for a nonlinearly elastic body subject to a pressure live load and we compute its linearization for small pressure by Gamma-convergence. We allow for a weakly coercive elastic energy density and we prove strong convergence of minimizers.
