自由曲面薄壳结构数值逆吊找形方法研究

数值逆吊找形法是一种生成零弯矩型自由曲面薄壳结构的高效方法。为了解决基于非线性有限元数值逆吊找形法在求解弱刚度结构时收敛性不佳的问题，通过引入向量式有限元法，提出了一种改进的数值逆吊找形方法。该方法采用向量式有限元法求解逆吊结构的平衡构形，并通过局部线性化方法调整柔性索单元的弹性模量，实现对逆吊结构形状的控制。在此基础上，进一步提出了可实现多点精确控制的分步刚化法，解决了复杂形状逆吊结构的找形问题。应用所提方法对Isler设计的某逆吊石膏模型进行数值找形，并将数值找形结果与实际模型扫描结果进行对比，验证了所提方法的正确性和有效性。

Study on numerical inverse hanging method for freeform shell structure

Numerical inverse hanging method is a kind of efficient form-finding method which can generate shell structures free of bending moments under certain external loads. This paper proposes an improved numerical inverse hanging method based on the vector form intrinsic finite element (VFIFE), for improving the poor convergence performance of the existing method based on the nonlinear finite element method. By using VFIFE to find the equilibrium form of inverted structures and using the local linearization method to adjust the Young’s modulus of cable elements, the form-control problem of inverted structures is solved. Moreover, a step rigidization method is proposed, which can realize the form-control of complex structures with multiple target points. Finally, the accuracy and efficiency of the numerical method is verified by observing one Isler’s plaster model and comparing its physical shape with the numerical simulating result.