具有约束支撑的张拉整体结构初始找形方法
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摘要
提出了一种适用于有约束支撑的张拉整体结构初始自应力确定方法.结构的几何拓扑关系和单元类型是本找形方法所需的唯一条件.为了找到合适的节点坐标和力密度,分别采用特征值分解和奇异值分解对结构的力密度矩阵和平衡矩阵进行循环迭代分析,直至满足对应矩阵最小秩缺失的必要条件.通过几个典型算例证明了利用本方法可以快速确定具有约束支撑的张拉整体结构的初始自应力,同时为设计和施工实际工程的张拉整体结构提供理论指导.
A novel method is presented for form-finding of tensegrity structures with constrained supports.The topology and the types of members are the only information required of this form-finding process.To find the feasible sets of nodal coordinates and force densities,the eigenvalue decomposition of force density matrix and the singular value decomposition of the equilibrium matrix were performed iteratively until the necessary minimum rank deficiency conditions satisfy.Several illustrative examples are presented to demonstrate the efficiency and robustness in finding self-equilibrium configurations of tensegrity structures,and a theoretical guide is provided to design and construct actual tensegrities.
A novel method is presented for form-finding of tensegrity structures with constrained supports.The topology and the types of members are the only information required of this form-finding process.To find the feasible sets of nodal coordinates and force densities,the eigenvalue decomposition of force density matrix and the singular value decomposition of the equilibrium matrix were performed iteratively until the necessary minimum rank deficiency conditions satisfy.Several illustrative examples are presented to demonstrate the efficiency and robustness in finding self-equilibrium configurations of tensegrity structures,and a theoretical guide is provided to design and construct actual tensegrities.
引文
[1]FENG X,GUO S.Geometrical nonlinear elasto-plastic analysis of tensegrity systems via the co-rotational method[J].Mechanics Research Communications,2017,79:32-42.
[2]TIBERT G.Deployable tensegrity structures for space applications[D].Stockholm:Royal Institute of Technology,2002.
[3]纪红娜.张拉整体移动机器人动力学及运动性能分析[D].西安:西安电子科技大学,2011.
[4]LEE J H,SHOFNER M L.Tensegrity-inspired polymer nanocomposites[J].Polymer,2017,111:9-19.
[5]INGBER D E.Tensegrity I.Cell structure and hierarchical systems biology[J].Journal of cell science,2003,116(7):1157-1173.
[6]SCHEK H J.The force density method for form finding and computation of general networks[J].Computer Methods in Applied Mechanics and Engineering,1974,3(2):115-134.
[7]MOTRO R.Tensegrity systems and geodesic domes[J].International journal of Space Structures,1990,5:341-351.
[8]BELKACEM S.Recherche de forme par relaxation dynamique des structures reticuleesspatialesautocontraintes[D].Toulouse:University Paul Sabatier de Toulouse,1987.
[9]CONNELLY R.Handbook of convex geometry[M].Amsterdam:North-Holland,1993.
[10]陈联盟,袁行飞,董石麟.索杆张力结构自应力模态分析及预应力优化[J].土木工程学报,2006,39(2):11-15.
[11]FENG X.The optimal initial self-stress design for tensegrity grid structures[J].Computers&Structures,2017,193:21-30.
[12]XU X,LUO Y.Form-finding of nonregulartensegrities using a genetic algorithm[J].Mechanics Research Communications,2010,37(1):85-91.
[13]TRAN H C,LEE J.Form-finding of tensegrity structures with multiple states of self-stress[J].Acta Mechanica,2011,222(1-2):131-147.
[14]CAI J,WANG X,DENG X,et al.Form-finding method for multi-mode tensegrity structures using extended force density method by grouping elements[J].Composite Structures,2018,187:1-9.
[15]ZHANG L Y,LI Y,CAO Y P,FENG X Q.Stiffness matrix based form-finding method of tensegrity structures[J].Engineering Structures,2014,58(7):36-48.
[16]MOTRO R.Tensegrity:Structural systems for the future[M].Kogan Page,London,2003.
[17]ZHANG J Y,OHASKI M,KANNO Y.A direct approach to design of geometry and forces of tensegrity systems[J].International Journal of Solids&Structures,2006,43(7-8):2260-2278.
[18]PELLEGRINO S,CALLADINE C R,PELLEGRINO S,et al.Matrix analysis of statically and kinematically indeterminate frameworks[J].International Journal of Solids&Structures,1986,22(4):409-428.
[19]VASSART N,MOTRO R.Multiparametered Form-finding Method:Application to Tensegrity Systems[J].International Journal of Space Structures,1999,14(2):147-154.
[20]CONNELLY R,BACK A.Mathematics and Tensegrity:Group and representation theory make it possible to form a complete catalogue of"strut-cable"constructions with prescribed symmetries[J].American Scientist,1998,86(2):142-151.
[21]ZHANG J Y.,OHSAKI M.Adaptive force density method for form-finding problem of tensegrity structures[J].International Journal of Solids&Structures,2006,43(18-19):5658-5673.
[2]TIBERT G.Deployable tensegrity structures for space applications[D].Stockholm:Royal Institute of Technology,2002.
[3]纪红娜.张拉整体移动机器人动力学及运动性能分析[D].西安:西安电子科技大学,2011.
[4]LEE J H,SHOFNER M L.Tensegrity-inspired polymer nanocomposites[J].Polymer,2017,111:9-19.
[5]INGBER D E.Tensegrity I.Cell structure and hierarchical systems biology[J].Journal of cell science,2003,116(7):1157-1173.
[6]SCHEK H J.The force density method for form finding and computation of general networks[J].Computer Methods in Applied Mechanics and Engineering,1974,3(2):115-134.
[7]MOTRO R.Tensegrity systems and geodesic domes[J].International journal of Space Structures,1990,5:341-351.
[8]BELKACEM S.Recherche de forme par relaxation dynamique des structures reticuleesspatialesautocontraintes[D].Toulouse:University Paul Sabatier de Toulouse,1987.
[9]CONNELLY R.Handbook of convex geometry[M].Amsterdam:North-Holland,1993.
[10]陈联盟,袁行飞,董石麟.索杆张力结构自应力模态分析及预应力优化[J].土木工程学报,2006,39(2):11-15.
[11]FENG X.The optimal initial self-stress design for tensegrity grid structures[J].Computers&Structures,2017,193:21-30.
[12]XU X,LUO Y.Form-finding of nonregulartensegrities using a genetic algorithm[J].Mechanics Research Communications,2010,37(1):85-91.
[13]TRAN H C,LEE J.Form-finding of tensegrity structures with multiple states of self-stress[J].Acta Mechanica,2011,222(1-2):131-147.
[14]CAI J,WANG X,DENG X,et al.Form-finding method for multi-mode tensegrity structures using extended force density method by grouping elements[J].Composite Structures,2018,187:1-9.
[15]ZHANG L Y,LI Y,CAO Y P,FENG X Q.Stiffness matrix based form-finding method of tensegrity structures[J].Engineering Structures,2014,58(7):36-48.
[16]MOTRO R.Tensegrity:Structural systems for the future[M].Kogan Page,London,2003.
[17]ZHANG J Y,OHASKI M,KANNO Y.A direct approach to design of geometry and forces of tensegrity systems[J].International Journal of Solids&Structures,2006,43(7-8):2260-2278.
[18]PELLEGRINO S,CALLADINE C R,PELLEGRINO S,et al.Matrix analysis of statically and kinematically indeterminate frameworks[J].International Journal of Solids&Structures,1986,22(4):409-428.
[19]VASSART N,MOTRO R.Multiparametered Form-finding Method:Application to Tensegrity Systems[J].International Journal of Space Structures,1999,14(2):147-154.
[20]CONNELLY R,BACK A.Mathematics and Tensegrity:Group and representation theory make it possible to form a complete catalogue of"strut-cable"constructions with prescribed symmetries[J].American Scientist,1998,86(2):142-151.
[21]ZHANG J Y.,OHSAKI M.Adaptive force density method for form-finding problem of tensegrity structures[J].International Journal of Solids&Structures,2006,43(18-19):5658-5673.