鉴史驭法 撰写专著评《结构拓扑优化ICM方法新进展》

Writing a Monograph by Referencing History and Mastering MethodologiesReview of New Progress in ICM Method for Structural Topology Optimization

  • 摘要: 本文评介隋允康和彭细荣教授的专著《结构拓扑优化ICM方法新进展——概念深化及理论拓展》,其中ICM (Independent Continuous and Mapping) 意思是独立、连续和映射,该方法是结构拓扑优化的主流研究方法之一。该书借助于鉴史(力学史)和驭法(方法论),总结了自2014年以ICM方法的发展成果:深入阐述了ICM方法的阶跃函数的离散本质及对其光滑逼近的近似连续本质、逼近的快慢特性和多种映射策略;介绍了ICM方法的数学基础、求解算法和本体理论等方面的拓展性研究成果,包括可分离凸规划转换为求解对偶显式模型 DP-EM解法、互逆规划理论及其优化应用等;探讨了该领域忽视的结构拓扑优化合理化建模问题;发展了包含疲劳寿命性能的局部性能约束的结构拓扑优化解法;归纳了破损-安全设计理论的演化,给出了位移、应力及频率约束的破损-安全拓扑优化问题的建模及求解;移植ICM方法至国际上广泛应用的变密度方法中。该书可供结构优化领域内从事科研的师生和技术人员借鉴和参考。

     

    Abstract: A review of Prof. Sui Yunkang and Peng Xiirong's monograph "New Progress of ICM Methods for Structural Topological Optimization: Conceptual Deepening and Theoretical Expansion" is presented. Here, ICM means independent, continuous, and mapping. The ICM method is one of the mainstream research approaches for structural topology optimization. The book summarizes the achievements of the ICM method since 2014 by referencing histories of mechanics and mastering methodologies. The book delves into the discrete nature of the step function and the smoothed and continuous nature of its approximation function, as well as the characteristics of the speed of approximation and various mapping strategies. The book also introduces pioneering achievements in the mathematical foundation, solution algorithms, and theories of the ICM method, including the transformation of separable convex programming into the DP-EM (Dual Programming and Explicit Model) method, reciprocal programming theory, and its optimization applications. The issue of rational modeling for structural topology optimization, which has been neglected in the field, is discussed. A solution of structural topology optimization with local performance constraints, such as fatigue life, has been developed. The evolution of the fail-safe design principles has been summarized, and the modeling and solution of the fail-safe topology optimization with displacement, stress, and frequency constraints have been presented. The ICM method has been transplanted into the widely used variable density method. The book is a rare reference for researchers and technical personnel in the field of structural optimization.

     

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