基于Python优化的任意钢-混组合截面应力与承载力分析研究

Study on calculation of bearing capacity of arbitrary steel-concrete combined section based on the optimization of Python

近年来,Python编程语言以其简洁、易学、易读、易维护性以及可扩展性已经发展成为最受欢迎的程序设计语言之一,并在各个领域得到广泛应用。随着土木工程结构的创新与发展,工程中经常会采用由不同材料及非常规几何形状截面组合而成的复杂截面。该截面在外部作用下的应力及极限承载能力的计算已超出了设计规范计算公式的范围,而目前主要的计算方法中存在网格划分不便、收敛性差、精度低、适用性不高等问题。尝试将Python编程语言应用于土木工程结构设计,基于Meshpy库对任意形状及任意材料组成的截面进行自适应三角网格划分,再根据材料本构关系及网格几何特性进行积分得到全截面内力并将内、外力差值的平方和作为目标函数建立优化模型,混合使用Scipy库中2种优化算法进行求解,实现了对任意钢-混组合截面在轴力及双弯矩作用下的截面应力及极限承载力的计算。与相关文献中的经典算例对比分析表明:本文所述计算分析方法计算速度快、收敛稳定且精度高,具有极强的实用性。

In recent years, Python programming language has become one of the most popular programming languages with its simplicity, ease of learning, ease of reading, ease of maintenance and scalability, and has been widely used in various fields. With the innovation and development of civil engineering structure, complex sections composed of different materials and unconventional geometric shapes are often used in engineering. The calculation of stress and ultimate bearing capacity of sections has exceeded the calculation formula range of design specification. The paper attempted to apply Python programming language to civil engineering structure design. Based on the Python framework’s Meshpy package, self-adaptive triangular meshing generation was performed on arbitrary cross section and materials, and integrals were obtained according to the constitutive relationship of the material and the geometric characteristics of the mesh to calculate the internal force of the full cross-section. Thus, an optimized model of internal and external force balance can be established. Based on the optimization library of Python, the hybrid optimization method was used to solve the optimization model, and the calculation of the section stress and the load-carrying capacity of arbitrarily shaped composite section subjected to biaxial bending was realized. Numerical examples demonstrate that the method is efficient, accurate and highly practical.