利用植物根系形态形成机理的加筋薄壳结构拓扑优化设计

Topology Design Optimization of Stiffened Thin-wall Shell Structures Based on Growth Mechanism of Root System

将自然界植物根系的形态形成机理应用于加筋薄壳结构加强筋分布设计方法的研究。将加筋薄壳结构加强筋的分布看成一个逐渐形成的过程,则此过程应能自适应于一定的工作条件,使结构逐步趋向具有最佳力学性能的最优结构,这样的过程和自然界中植物根系的形态形成过程具有一定的相似性。在对植物根系形态形成机理进行探讨的基础上,建立基于形态形成机理的加筋薄壳结构加强筋设计准则,即为了得到最小柔顺度结构,结构上的加强筋应沿着结构的应变能相对于加强筋断面积的设计灵敏度大的方向成长,且成长速度也与设计灵敏度成比例。以加筋薄壁圆柱壳结构为例进行加强筋的分布设计,用有限元法对设计结果进行验证。结果表明,提出的利用植物根系形态形成机理的结构拓扑优化设计方法比现有的方法简单高效,并且由于其设计结果是符合工程习惯的清晰加强筋分布,而不是模糊的密度分布,更有利于结构拓扑优化技术的实际应用。设计结果可作为进一步详细设计的初始优化模型。

The growth mechanism of root system in nature is applied to the research of the topology design optimization technique for stiffened thin-wall shell structures. The process of the stiffener generation on a thin-wall shell structure can be regarded as a gradual growth process to achieve a global optimum by adapting to the local working condition, which is similar to the growth process of root system of plants. The design criterion of the stiffener layout on thin-wall shell structures is suggested on the basis of the growth mechanism of root system morphology, i.e., the growth direction and velocity of a stiffener are decided by its design sensitivity, which is the derivation of the strain energy with respect to its cross-sectional area in the case of the minimum compliance design problem. The numerical results of stiffened thin-wall cylindrical shell are illustrated, and validated by the finite element analysis. The suggested design method is simpler and more effective than the conventional methods, and it is more applicable to the practical pro blem because the result is legible distribution of the stiffeners rather than the vague density distribution. The design results can be used to the initial optimum models in the further detail design process.