混合数据驱动计算力学中接触问题的建模与启发式求解
Formulating and Heuristic Solving of Contact Problems in Hybrid Data-Driven Computational Mechanics
AI总结：
本研究针对混合数据驱动计算力学框架，引入几何不等式约束构建带互补约束的接触问题数学规划，提出最多求解4个非线性优化问题的启发式快速解法，通过3组难度递增的实验验证了方法的潜力与局限。
摘要：
本研究针对混合数据驱动计算力学（DDCM，Data-Driven Computational Mechanics）方法展开，该方法通过重构光滑本构流形得到性态良好的非线性优化问题（NLP），而非直接DDCM方法中难度高得多的离散-连续非线性优化问题（DCNLP）。研究核心是在混合DDCM公式体系中加入几何不等式约束：此时所需的约束力会导出一类带互补约束的数学规划（MPCC）形式的接触问题，该类问题的复杂度仍低于DCNLP。针对该MPCC，本文提出一种启发式快速求解方法，最多通过求解4个NLP即可生成可验证的解。研究针对3个难度递增的不同接触问题开展了多组数值实验，以验证该方法的潜力与局限性。
英文摘要：
In this work we consider the hybrid Data-Driven Computational Mechanics (DDCM) approach, in which a smooth constitutive manifold is reconstructed to obtain a well-behaved nonlinear optimization problem (NLP) rather than the much harder discrete-continous NLP (DCNLP) of the direct DDCM approach. The key focus is on the addition of geometric inequality constraints to the hybrid DDCM formulation. Therein, the required constraint force leads to a contact problem in the form of a mathematical program with complementarity constraints (MPCC), a problem class that is still less complex than the DCNLP. For this MPCC we propose a heuristic quick-shot solution approach, which can produce verifiable solutions by solving up to four NLPs. We perform various numerical experiments on three different contact problems of increasing difficulty to demonstrate the potential and limitations of this approach.
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