引用本文: 邹君, 姚卫星. 基于变分方法的工字型悬臂梁尺寸优化[J]. 力学与实践, 2014, 36(3): 294-297,307.
ZOU Jun, YAO Weixing. SIZE OPTIMIZATION FOR CANTILEVER I-BEAM BASED ON VARIATIONAL METHOD[J]. MECHANICS IN ENGINEERING, 2014, 36(3): 294-297,307.
 Citation: ZOU Jun, YAO Weixing. SIZE OPTIMIZATION FOR CANTILEVER I-BEAM BASED ON VARIATIONAL METHOD[J]. MECHANICS IN ENGINEERING, 2014, 36(3): 294-297,307.

## SIZE OPTIMIZATION FOR CANTILEVER I-BEAM BASED ON VARIATIONAL METHOD

• 摘要: 以变分方法为工具，研究了分布载荷下工字型悬臂梁的尺寸优化问题，给出了在强度和位移约束下梁缘条沿展向的宽度函数，并简要介绍了优化准则法和多岛遗传算法. 以平直机翼为工程实例，将之简化为一个工字型悬臂梁，分别采用该3 种方法进行优化设计. 结果表明变分法不仅效率高，而且给出了尺寸分布的函数，这对飞行器概念设计阶段的机翼结构设计具有较大的指导意义.

Abstract: The size optimization for a cantilever I-beam under distributed loads is based on the variational method, and the width distribution of an edge strip under the strength and stiffness constraints is used as an example to demonstrate the use of the variational method. The optimization criterion method and the MIGA (multi-island genetic algorithm) with the FEM (finite element method) are discussed. An engineering cantilever I-beam model of the wing structure is presented to illustrate the three methods. It is shown that the variational method can greatly improve the effciency compared with the other two methods, and also the exact solutions of the optimal size distribution can be obtained, which can be used in the wing structure design during the preliminary design phase.

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