Research Initiation: Structural Design Optimization as a Linear Programming Problem

研究启动：结构设计优化作为线性规划问题

• 批准号: 9009597
• 负责人: Omar Ghattas
• 金额: $ 7万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9009597&HistoricalAwards=false
• 关键词: Research; Initiation; Structural; Design; Optimization

The researcher will investigate conditions under which problems in structural design optimization map, without approximation, to linear programming (LP) problems, and to create algorithms which exploit these special properties. The conventional approach is to treat such problems as ones in nonlinear programming (NLP). For large systems, exact solution of the resulting NLP problem is often intractable. It has been shown that a class of structural design problems can be solved much more efficiently. The method requires solution of an LP followed by a system of linear equations. Solution of the LP identifies a canonical structure which possesses the same displacement field as the optimal structure. This displacement field renders the equilibrium equations as a linear system in unknown areas, which can be solved to yield the optimum design. As a consequence, problems can now be solved of practical interest to civil and aerospace engineers several orders of magnitude larger than previously imagined. The goal of this research is to extend the LP methodology to encompass a more general class of structural design optimization problems. Initial numerical evidence indicates that the method is extendable to displacement and frequency constraints. In addition to these constraints, buckling and multiple loads will be considered, and the researchers will define extensions of the method to structures discretized by continuum finite elements. If successful for this broader class of problem, the LP method will greatly reduce the computational effort required for solving these optimization problems, as a consequence of the need to solve an LP rather than a NLP. Such a significant enhancement of efficiency will make optimization more attractive to structural designers.

研究人员将研究在什么情况下结构设计优化问题在没有近似的情况下映射到线性规划(LP)问题，并创造利用这些特殊性质的算法。传统的方法是将这类问题归结为非线性规划问题。对于大系统，所产生的NLP问题的精确解通常是难以解决的。结果表明，该方法能更有效地解决一类结构设计问题。该方法需要解一个线性规划，然后是一个线性方程组。线性规划的解识别出与最优结构具有相同位移场的正则结构。这种位移场使平衡方程在未知区域表现为线性系统，可以求解以产生最优设计。因此，土木工程和航空航天工程师现在可以解决比之前想象的大几个数量级的实际感兴趣的问题。这项研究的目标是扩展线性规划方法，以涵盖更一般的结构设计优化问题。初步的数值结果表明，该方法可以推广到位移和频率约束。除了这些约束外，还将考虑屈曲和多重载荷，研究人员将定义该方法的扩展到由连续体有限元离散的结构。如果成功地解决了这类更广泛的问题，由于需要求解LP而不是NLP，LP方法将极大地减少求解这些优化问题所需的计算工作量。这种效率的显著提高将使优化对结构设计者更具吸引力。