一类超静定变截面压杆临界荷载的优化算法

发布时间：2018-12-07 07:20

【摘要】：目的研究一端固定,一端链杆约束的一类超静定变截面梁临界载荷的优化算法原理,探讨超静定压杆临界载荷数值方法.方法基于差分原理和优化基本原理,运用差分方法将平衡状态下非线性微分方程离散化.以杆件每个离散点挠度,临界荷载和多余约束力为设计变量,以临界载荷所满足差分方程与边界条件构建目标函数,在Fortran-Power Station环境下,编制优化程序,进行常截面梁与变截面梁具体算例分析对比.结果提出了一类超静定变截面压杆的临界载荷的无约束优化算法,并验证了方法的正确性和有效性.结论算法能够有效解决工程中变截面超静定梁结构临界载荷的计算问题,为工程设计与分析提供支持.
[Abstract]:Aim to study the optimization algorithm principle of critical load of a class of statically indeterminate beams with fixed end and one end chain bar constraint, and to discuss the numerical method of critical load for statically indeterminate bars. Methods based on the difference principle and optimization principle, the nonlinear differential equation in equilibrium state is discretized by the difference method. Taking deflection, critical load and superfluous binding force of every discrete point of member as design variables, the objective function is constructed by using the difference equation and boundary condition satisfied by critical load, and the optimization program is compiled under the environment of Fortran-Power Station. The concrete examples of constant section beam and variable section beam are analyzed and compared. Results an unconstrained optimization algorithm for critical load of a class of statically indeterminate pressure bars with variable cross section is proposed and the correctness and validity of the method are verified. Conclusion the algorithm can effectively solve the problem of calculating the critical load of the statically indeterminate beam structure with variable cross section and provide support for engineering design and analysis.
【作者单位】：沈阳建筑大学机械工程学院;沈阳建筑大学土木工程学院;
【基金】：国家自然科学基金项目(51578346) 辽宁省自然科学基金项目(2015020129)
【分类号】：O302

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