论文标题
使用线性依赖性求解器（LDA）的状态和敏感性有效计算复合结构优化问题
Efficient computation of states and sensitivities for compound structural optimisation problems using a Linear Dependency Aware Solver (LDAS)
论文作者
论文摘要
现实世界的结构优化问题涉及多个加载条件和设计约束，响应通常取决于离散的管理方程式。通常，人们使用基于梯度的嵌套分析和设计方法来解决这些问题。在此，解决了物理和伴随问题，主要是整体计算工作。尽管未检测到，但实际问题可能包含遇到的物理和伴随负载之间的线性依赖性。随着设计问题越来越涉及，手动跟踪此类依赖性变得乏味。为了检测和利用此类依赖关系，这项工作提出了使用线性依赖性意识求解器（LDA）的使用，该求解器（LDA）能够有效地检测所有负载之间的线性依赖性，以避免完全自动求解。提供了说明性示例，这些例子证明了使用LDA的需求和好处，包括运行时实验。
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.
