几何非线性弹性结构和柔顺机构拓扑optimization中的不精确牛顿组合逼近
Inexact Newton combined approximations in the topology optimization of geometrically nonlinear elastic structures and compliant mechanisms
摘要：
本文将不精确牛顿法与迭代组合逼近法（ICA）相结合，在几何非线性假设下求解拓扑最优化问题。使用顺序分段线性规划（SPLP）算法解决基于密度的问题配方。已提出五种不同的策略来控制非线性平衡方程的雅可比矩阵因式分解的频率。为了在保持近似解精度的同时加快整个迭代方案的速度，其中三种策略还将ICA方案用于与灵敏度分析相关的伴随线性系。所提出的再分析策略的鲁棒性通过四个基准问题的数值实验得到证实-两个结构和两个符合机制。除了评估考虑固定迭代预算的策略的性能外，还分析了理论上支持的SPLP算法停止准则的影响。
英文摘要：
This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a sequential piecewise linear programming (SPLP) algorithm. Five distinct strategies have been proposed to control the frequency of the factorizations of the Jacobian matrices of the nonlinear equilibrium equations. Aiming at speeding up the overall iterative scheme while keeping the accuracy of the approximate solutions, three of the strategies also use an ICA scheme for the adjoint linear system associated with the sensitivity analysis. The robustness of the proposed reanalysis strategies is corroborated by means of numerical experiments with four benchmark problems -- two structures and two compliant mechanisms. Besides assessing the performance of the strategies considering a fixed budget of iterations, the impact of a theoretically supported stopping criterion for the SPLP algorithm was analyzed as well.
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