论文标题
圆锥编程在非平滑力学中的应用
Applications of conic programming in non-smooth mechanics
论文作者
论文摘要
在非线性力学领域，许多具有挑战性的问题（例如可塑性，接触，砌体结构，非线性膜）被证明是圆锥程序。通常，此类问题本质上是非平滑的（可塑性条件，单方面状况等），这使其通过标准的牛顿方法的数值分辨率非常困难。他们作为圆锥计划的表述减轻了这一困难，因为由于发展专用的内点算法的发展，现在可以非常强大，有效地解决大规模的圆锥优化问题。在这项贡献中，我们回顾了各种非平滑力学问题的旧配方，包括与非线性硬化，非线性膜，最小裂纹表面和粘膜塑料流体流相关的可塑性。
In the field of nonlinear mechanics, many challenging problems (e.g. plasticity, contact, masonry structures, nonlinear membranes) turn out to be expressible as conic programs. In general, such problems are non-smooth in nature (plasticity condition, unilateral condition, etc.), which makes their numerical resolution through standard Newton methods quite difficult. Their formulation as conic programs alleviates this difficulty since large-scale conic optimization problems can now be solved in a very robust and efficient manner, thanks to the development of dedicated interior-point algorithms. In this contribution, we review old and novel formulations of various non-smooth mechanics problems including associated plasticity with nonlinear hardening, nonlinear membranes, minimal crack surfaces and visco-plastic fluid flows.
