超静定变截面梁极限载荷的优化算法

An Optimum Algorithm for Limit Load Calculation of Statically Indeterminate Beam with Varying Sections

目的针对超静定变截面梁结构的极限载荷求解问题,提出一种新的无约束优化算法.方法以待求极限载荷、多余约束力和截面最大弯矩处的对应坐标为设计变量,以不同坐标位置的工作弯矩与对应极限弯矩关系和剪力需要满足的条件构建目标函数,采用多维Powell的无约束优化原理,并将设计变量无量纲转化,应用Fortran-Power Station语言编制优化算法程序,进行算例分析求解,并对数值解和程序计算对比分析.结果运用优化程序计算分析,在给定收敛精度条件下,获得超静定变截面梁的极限载荷大小,梁上产生极限弯矩的坐标以及梁的多余约束力的大小.结论提出的极限载荷的优化算法有效地解决了复杂变截面梁极限载荷的精确计算问题,具有实用性和可行性.为复杂工程变截面结构问题的极限载荷求解提供依据.

A new unconstrained optimization algorithm for solving problems of statically indeterminate beam with varying sections was proposed in this paper. Taking the unknow n limit load,the coordinates of the extra bending moment and the cross-section where the maximum bending moment occurs as the design variables,shear conditions and the function relationship betw een the working moment and the ultimate moment as the objective functions,based on the Power ＇s unconstrained optimization principle,an optimization algorithm program was built with the computer language Fortran-Power Station. The obtained results by authors were compared with the know n numerical results. It indicates that under the given convergence accuracy conditions,the limit load,the coordinates of the ultimate moment and the redundant constraint forces can be calculated. Conclusion is that the proposed algorithm can accurately and effectually calculate the limit load of statically inde-terminate beam with varying sections. It means that the algorithm is practical and feasible and can provide references for calculating extreme loads of the beam with complex cross-sectional shapes.