理想塑性极限分析启发的抽象inf-sup问题及其应用
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications
摘要：
本文研究了由双线性拉格朗日量和凸约束产生的抽象inf-sup问题。我们研究的条件，保证没有差距之间的inf-sup和相关的sup-inf问题。本文中引入的关键假设推广了著名的Babuska-Brezzi条件。它是基于一个inf-sup条件定义的凸锥在函数空间。我们还采用了正则化方法方便地解决inf-sup问题，并推导出一个可计算的优势的临界（inf-sup）值，它可以用于后验误差分析的数值结果。抽象问题得到的结果适用于连续介质力学。特别是，极限载荷问题和类似的经典塑性，梯度塑性和分层中出现的例子进行了介绍。
英文摘要：
This work is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the inf-sup and related sup-inf problems. The key assumption introduced in the paper generalizes the well-known Babuska-Brezzi condition. It is based on an inf-sup condition defined for convex cones in function spaces. We also apply a regularization method convenient for solving the inf-sup problem and derive a computable majorant of the critical (inf-sup) value, which can be used in a posteriori error analysis of numerical results. Results obtained for the abstract problem are applied to continuum mechanics. In particular, examples of limit load problems and similar ones arising in classical plasticity, gradient plasticity and delamination are introduced.
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