以结构的传力路径作为设计变量,通过在传力路径上对结构内力进行积分,得到相应的结构承载因子。由于结构的外形和内力都会变化,因此该承载因子是结构传力路径的泛函。用变分法导出了对应结构最短传力路径的微分方程,并用里兹法求解该微分方程,得出结构的最短传力路径。通过变分法优化得到结构的最短传力路径,然后应用结构尺寸优化方法,得到结构的最小质量。以平面悬臂梁结构的传力路径优化为例,分析了悬臂梁结构在不同外形下对应的最短传力路径,并和用Michell桁架理论得到的结果进行比较。最佳结构基于理论分析得到,整个过程不需要进行有限元分析,不存在拓扑优化中的数值不稳定性问题。另一方面,通过采用板杆结构模拟传力形式,将目前拓扑优化研究中通常采用的杆、板等单一单元结构推广到单元的组合结构。%In this paper,the force transfer path of structure（FTP） is taken as the design variables to obtain the load-carrying factor（LCF） by the integraion of internal force on the force transfer path.As the structure will change,so the LCF is the functional of structural FTP.Then differential equation of the shortest FTP is derived by variational method,and the equation is solved using the Ritz method to obtain the shortest PFT.Compared with the Michell truss theory and continuum structural topology optimization,the proposed method used two-step strategy： first the shortest FTP is obtained by variational method,and then the structural size optimization is conducted to get the minimum quality of the structure.Then a cantilever beam structure is takes the as an example to analyze the shortest FTP of structure under different shapes,and compared with the results obtained by the Michell theory,it proves the validity of the proposed model.In the present study,the optimal structure is obtained by the theoretical analysis without finite element modeling;therefore there is no numerical instability problem.On the other hand,as board-truss structure is used to simulate power transmission form,the current topology optimization research is generalized from a single unit structure to combination units.The present study also makes up the shortage of Michell criteria that it can only optimize the truss structure.
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