Real-world structural optimisation problems involve multiple loading conditions and design constraints, with responses typically depending on states of discretised governing equations. Generally, one uses gradient-based nested analysis and design approaches to solve these problems. Herein, solving both physical and adjoint problems dominates the overall computational effort. Although not commonly detected, real-world problems can contain linear dependencies between encountered physical and adjoint loads. Manually keeping track of such dependencies becomes tedious as design problems become increasingly involved. To detect and exploit such dependencies, this work proposes the use of a Linear Dependency Aware Solver (LDAS), which is able to efficiently detect linear dependencies between all loads to avoid unnecessary solves entirely and automatically. Illustrative examples are provided that demonstrate the need and benefits of using an LDAS, including a run-time experiment.

翻译：现实世界的结构优化问题涉及多重装载条件和设计限制,反应通常取决于离散的治理方程式状态。一般而言,人们使用基于梯度的嵌套分析和设计办法来解决这些问题。在这里,解决物理和连锁问题是整个计算工作的主因。虽然不常见,但现实世界的问题可能包含遇到的物理和连锁负荷之间的线性依赖性。随着设计问题越来越多地涉及,人工跟踪这种依赖性变得乏味。为了发现和利用这种依赖性,这项工作提议使用线性依赖感解答器(LDAS),它能够有效检测所有载荷之间的线性依赖性,以避免完全和自动的不必要解决。提供了说明使用LDAS的必要性和好处的例子,包括运行时间试验。