A novel topology framework for simultaneous topology, size and shape optimization of trusses under static, free vibration and transient behavior
A novel topology framework for simultaneous topology, size and shape optimization of trusses under static, free vibration and transient behavior
复制标题
DOI：
10.1007/s00366-022-01599-5
复制
发表时间：
2022-01
影响因子：
8.7
通讯作者：
Qui X. Lieu
中科院分区：
文献类型：
--
作者：
Qui X. Lieu
本文首次提出了一种新的拓扑框架，用于在静态、自由振动和瞬态响应下同时优化具有多约束的桁架结构的拓扑、尺寸和形状。为了达到这一目的，新提出的拓扑伪面积变量的成员是离散分配给或1，分别代表一个成员的缺席或存在。该建议的目的是避免有限元分析中求解平衡方程时由于整体刚度矩阵奇异而导致的数值不稳定性，同时由于保持了有限元模型结构的完整性而节省了计算工作量。本研究的目标函数是最小化结构重量。桁架杆件的横截面积采用离散/连续设计变量，节点坐标按连续设计变量处理。此外，运动稳定性，位移，应力，欧拉屈曲载荷，固有频率和瞬态行为处理的约束。利用无导数自适应混合进化萤火虫算法作为优化器来解决包括连续-离散混合变量的优化问题。大量的基准测试的例子来验证所提出的范式的有效性。所获得的结果表明，目前的方法是有效的和强大的搜索更好的高质量的最优解对许多现有的算法在文献中。
This article proposes a novel topology framework for simultaneously optimizing topology, size and shape of truss structures with multiple constraints under static, free vibration and transient responses for the first time. To achieve such a purpose, the topology pseudo-area variable of members is newly proposed discretely assigning to eitheror 1 to respectively represent the absence or presence of a member. This suggestion aims at not only evading the numerical instability due to the singularity of global stiffness matrix when solving equilibrium equations in finite element analyses but also saving the computational effort owing to the intact preserve of FE model structure. The objective function of this study is to minimize the structural weight. The cross-sectional area of truss members is taken discrete/continuous design variables into account, whilst nodal coordinates are treated as continuous ones. In addition, kinematic stability, displacement, stress, Euler buckling loading, natural frequency and transient behavior are dealt with as constraints. The derivative-free adaptive hybrid evolutionary firefly algorithm is utilized as an optimizer to resolve such optimization problems including mixed continuous-discrete variables. A large number of benchmark examples are tested to verify the validity of the presented paradigm. Obtained outcomes indicate that the present methodology is effective and robust in searching better high-quality optimal solutions against many existing algorithms in the literature.