An improved dog-leg method for form-finding of tensegrity structures
An improved dog-leg method for form-finding of tensegrity structures
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DOI：
10.1016/j.compstruc.2023.107237
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发表时间：
2024-02
期刊：
影响因子：
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通讯作者：
Yan Zhou;Yafeng Wang;Shu Li;Chao Yang;Y. Luo
中科院分区：
文献类型：
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作者：
Yan Zhou;Yafeng Wang;Shu Li;Chao Yang;Y. Luo
本文提出了一种新颖高效的张拉整体结构找形方法。该方法将以节点坐标向量为变量的非线性平衡方程转化为非线性最小二乘问题。随后，应用狗腿法对这些转化后的问题进行求解。此外，将Dog-Leg法与MBFGS(ModifiedBroyden-Fletcher-Goldfarb-Shanno)法相结合，克服了刚度矩阵的奇异性问题。由此产生的改进的Dog-Leg方法，即DL-MBFGS方法，不仅可以有效地处理自应力和非自应力张拉整体结构的找形问题，而且可以有效地解决受外荷载作用的张拉整体结构以及包括机构和大位移问题在内的其他情况下的找形问题，显示了该方法的通用性和鲁棒性。数值算例验证了该方法的准确性和有效性。
This paper presents a novel and highly efficient form-finding method for tensegrity structures. The method is based on converting the nonlinear equilibrium equations with the nodal coordinates vector as the variables into nonlinear least-squares problems. Subsequently, the Dog-Leg method is applied to solve these transformed problems. Furthermore, the Dog-Leg method is combined with the MBFGS (Modified Broyden-Fletcher-Goldfarb-Shanno) method to overcome the singularity problem of the stiffness matrix. The resulting improved Dog-Leg method, i.e., DL-MBFGS method, can effectively address form-finding problems not only in self-stressed and non-self-stressed tensegrity structures, but also for tensegrities subjected to external loads and other scenarios including mechanisms and large displacements problems, which shows its great versatility and robustness. Several numerical examples are presented to validate the accuracy and effectiveness of the proposed method.