工程科学与技术2025，Vol.57Issue(6)：152-162,11.DOI:10.12454/j.jsuese.202301058
多自应力模态张拉整体结构质量优化研究
Study on Mass Optimization of Multi Self-stress Modes Tensegrity Structure
摘要
Abstract
Objective Considering economic costs,structural applications,and convenient transportation,the lightweight design of tensegrities with multi-self-stress modes is increasingly popular.Existing approaches primarily concentrate on mass optimization of tensegrity structures with multi self-stress modes under specific loads,without addressing the initial forming conditions that ensure structural geometrical stability.Neglecting these conditions can increase the risk of collapse once the structural stiffness diminishes due to unpredictable variations in external loads.In addition,in the case of complex tensegrities with multi-self-stress modes,the influence of prestress distribution on structural mass has been largely ignored,as current methods fail to establish the relationship between structural mass and self-stress modes.Therefore,conducting research on the mass op-timization of tensegrity structures with multi-self-stress modes based on heuristic optimization algorithms is of great significance. Methods A multi-stage mass optimization method was proposed to achieve lightweight design of complex tensegrity structures with multi-self-stress modes.In the first stage,based on the form-finding theory of tensegrities,the L2 norm was applied to characterize the geometric symmetry of the structures,and the integrity-feasible prestressing was obtained.In the second stage,the Similar Transforming Strategy(STS)was utilized to expand the population search range once the judgment on similar prestress distribution was completed.Then,the constrained optimization model of structural mass minimization was established by setting the objective function as the minimum structural mass under full stress,and the con-straint conditions,such as cable yield,bar yield,and yield buckling of bars,were considered.The effects of the Quantum Beetle Search Algorithm(QBSA),Quantum Evolution Algorithm(QEA),and Beetle Antennae Search Algorithm(BASA)were compared concerning the search of the combination coefficient for optimal multi-self-stress modes,and therefore,the objective of lightweight design of the structural system was achieved.The maximum node displacement of all comparison objects was adjusted to the same value through the insertion of the Adjusting Pre-stress Level(APL)strategy to accurately compare the impact of various prestress distributions on optimal structural mass.The performance of three different heuristic optimization algorithms in the process of mass optimization of the spatial four-way tensegrity plate before and after the implementation of the APL strategy was compared.In addition,the optimal algorithm for subsequent research was selected.The influence of vari-ous geometric parameters on the lightweight design of the tensegrity torus structure was analyzed.Comparative studies were conducted using the following three schemes:Scheme 1(simultaneously implementing APL and STS),Scheme 2(implementing APL without executing STS),and Scheme 3(implementing STS without executing APL). Results and Discussions The effectiveness of this method was comprehensively examined through three illustrative examples,and the following noteworthy results were obtained:1)For the four-way tensegrity plate without the APL strategy,the elite individuals of QBSA,QEA,and BASA were 35,33,and 6,with structural masses of 4 534,4 808,and 5 039 kg,and optimization rates of 8.05%,5.85%,and 3.24%.With the implemen-tation of the APL strategy,the number of elite individuals in QBSA,QEA,and BASA was 36,30,and 5,with structural masses of 3 790,4 280,and 4 889 kg,and optimization rates of 58.95%,51.21%,and 48.73%.QBSA has the highest number of elite individuals,which results in the lightest optimized mass and the greatest optimization rate,demonstrating its superior optimization performance.In addition,implementing the APL strat-egy effectively ensures the consistency of the maximum nodal displacement,while the structures optimized by all three algorithms achieve lighter masses and better results.2)Changes in prestress distribution affect the loading conditions of tensegrity structures.As the structural mass reduces,the maximum nodal displacement exhibits fluctuations,and changes in prestress distribution also influence the nodal position with maximum dis-placement,while it remains unchanged after adjusting the prestress level.3)The analysis of the tensegrity torus shows that when kn is deter-mined,the optimized mass decreases with the increase of nx at first,and then rises when nx exceeds 4;when nx is determined,the optimized mass improves with the increase of kn.In addition,compared to Scheme 2 and Scheme 3,Scheme 1 achieves a lighter structural mass and a higher optimization rate.4)The optimization results of the triangular prism tensegrity plate show that the variation of prestress distribution has a minor impact on structural mass optimization for plate B with Free Prestress(FP),while it has a significant impact on plate A with FP.In addition,the research results on plate A and plate B(with FP or Splicing Prestress(SP)applied)indicated that the connection bar plays an important role in structural lightweight design.In addition,the final optimized mass of plate A with FP and plate B is lower than the optimized mass corresponding to SP. Conclusions:The establishment of multi-stage objective functions facilitates effective lightweight design while ensuring the integral feasible pre-stress of tensegrity structures.QBSA demonstrates superior local and global optimization capabilities,and by incorporating APL and STS strate-gies,the optimization outcomes are effectively enhanced.In addition,for complex assembled prestressed members,this method achieves a more favorable prestress distribution compared to that obtained through the conventional SP approach.关键词
张拉整体/轻量化设计/多自应力模态/预应力水平/预应力分布Key words
tensegrity structures/lightweight design/multi-self-stress modes/prestress level/prestress distribution分类
土木建筑引用本文复制引用
冯晓东,娄晓峰,郑亦汶,吕辉,陆金钰..多自应力模态张拉整体结构质量优化研究[J].工程科学与技术,2025,57(6):152-162,11.基金项目
国家自然科学基金面上项目(52478189) （52478189）
