Research Initiation: Structural Design Optimization as a Linear Programming Problem

研究人员将调查在何种条件下， 结构设计优化图中存在的问题， 近似，线性规划（LP）问题，并创建 利用这些特殊属性的算法。 传统的方法是把这些问题当作 非线性规划（NLP） 对于大型系统，精确解 由此产生的NLP问题往往是棘手的。已经 证明了一类结构设计问题的求解 更高效地该方法需要解一个LP， 一个线性方程组。 LP的解决方案确定了一个 具有相同位移场的正则结构 最佳结构。 此位移字段呈现 平衡方程作为未知区域的线性系统， 可以解决，以产生最佳设计。 因此，在这方面， 现在可以解决对公民和 航天工程师的数量级比 以前想象的。 本研究的目标是将LP方法扩展到 包含更一般的结构设计优化类别 问题 初步的数值证据表明，该方法是 可扩展到位移和频率限制。 此外 在这些约束条件下，屈曲和多重载荷将 考虑，研究人员将定义扩展的 连续体有限元离散结构的方法。 如果成功地解决了这类更广泛的问题，LP方法 将大大减少求解所需的计算工作量 这些优化问题，作为需要解决的结果， 是LP而不是NLP。如此显著的增强 效率将使优化更有吸引力的结构 设计师

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.