Control equation of feasible pre-stresses and feasibility of new types of rotating surface cable domes

Abstract The study proposes the control equation of feasible pre-stresses and the corresponding solving algorithm, and verifies three new types of rotating surface cable domes. First, the study takes that the structural displacements are zero as the control equation of feasible pre-stresses, and proposes a novel solving algorithm based on that target values of structural displacements are zero. Second, the study develops three new types of cable domes with different rotating surfaces, which have different Gaussian curvature. And then their feasibility in nature are verified through determining their feasible pre-stresses using the solving algorithm. Last, their ultimate bearing capacity under full and half-span vertical loads are investigated. The results indicate that the solving algorithm can determine the feasible pre-stresses efficiently and accurately, and three new cable domes proposed in the study are feasible in nature, and they have sufficient stiffness to bear external loads. The appearance of the three new rotating surface cable domes extends the cable domes from the traditional positive Gaussian curvature to the zero Gaussian and negative Gaussian curvature.

[1]  M. Mojdis,et al.  Adaptive Cable Dome , 2015 .

[2]  Xingfei Yuan,et al.  Prestress design of cable domes with new forms , 2007 .

[3]  Xingfei Yuan,et al.  Simple approach for force finding analysis of circular Geiger domes with consideration of self-weight , 2010 .

[4]  M. Ohsaki,et al.  Step-by-step unbalanced force iteration method for cable-strut structure with irregular shape , 2018, Engineering Structures.

[5]  Hojjat Adeli,et al.  A unified approach for analysis of cable and tensegrity structures using memoryless quasi-newton minimization of total strain energy , 2019 .

[6]  L. Gardner,et al.  Prestressed stayed beam-columns: Sensitivity to prestressing levels, pre-cambering and imperfections , 2021 .

[7]  S. Pellegrino,et al.  A Class of Tensegrity Domes , 1992 .

[8]  Tuanjie Li,et al.  Mathematical relationship between mean cable tensions and structural parameters of deployable reflectors , 2016 .

[9]  Hojjat Adeli,et al.  Form-finding and analysis of hyperelastic tensegrity structures using unconstrained nonlinear programming , 2019, Engineering Structures.

[10]  Jean-Michel Muller,et al.  Choosing starting values for certain Newton-Raphson iterations , 2006, Theor. Comput. Sci..

[11]  Minger Wu,et al.  Structural behaviors of an arch stiffened by cables , 2007 .

[12]  R. Fuller,et al.  Synergetics: Explorations in the Geometry of Thinking , 1975 .

[13]  Ian F. C. Smith,et al.  Deployment of a Tensegrity Footbridge , 2015 .

[14]  Jian Feng,et al.  Feasible Prestress Modes for Cable-Strut Structures with Multiple Self-Stress States Using Particle Swarm Optimization , 2020, J. Comput. Civ. Eng..

[15]  Xi-Qiao Feng,et al.  Stiffness matrix based form-finding method of tensegrity structures , 2014 .

[16]  Dai Zhou,et al.  Pretension simulation and experiment of a negative Gaussian curvature cable dome , 2016 .

[17]  S. Pellegrino.  Structural computations with the singular value decomposition of the equilibrium matrix , 1993 .

[18]  S. Pellegrino,et al.  Matrix analysis of statically and kinematically indeterminate frameworks , 1986 .

[19]  Weigang Chen,et al.  Cable fracture simulation and experiment of a negative Gaussian curvature cable dome , 2018, Aerospace Science and Technology.

[20]  George A. Lesieutre,et al.  Deployment of n-Strut Cylindrical Tensegrity Booms , 2020 .

[21]  Yaozhi Luo,et al.  Force Finding of Tensegrity Systems Using Simulated Annealing Algorithm , 2010 .

[22]  Yaozhi Luo,et al.  Form-finding of tensegrity structures via rank minimization of force density matrix , 2021 .

[23]  Xingfei Yuan,et al.  Nonlinear analysis and optimum design of cable domes , 2002 .

[24]  Ariel Hanaor,et al.  Prestressed pin-jointed structures—Flexibility analysis and prestress design , 1988 .

[25]  Stanislav Kmet,et al.  Time-dependent analysis of cable domes using a modified dynamic relaxation method and creep theory , 2013 .

[26]  K. Bathe.  Finite Element Procedures , 1995 .

[27]  Jian Feng,et al.  Prestress design for cable-strut structures by grouping elements , 2021 .

[28]  M. Ohsaki,et al.  Multi-objective optimization for prestress design of cable-strut structures , 2019, International Journal of Solids and Structures.

[29]  Jian Feng,et al.  Efficient Symmetry Method for Calculating Integral Prestress Modes of Statically Indeterminate Cable-Strut Structures , 2015 .

[30]  Charis J. Gantes,et al.  Nonlinear dynamic behavior of saddle-form cable nets under uniform harmonic load , 2011 .

[31]  Tuanjie Li,et al.  Nonlinear dynamic analysis of parametrically excited space cable-beam structures due to thermal loads , 2015 .

[32]  Jian Feng,et al.  Form-finding of tensegrity structures using an optimization method , 2015 .

[33]  S. Pellegrino,et al.  First-order infinitesimal mechanisms , 1991 .

[34]  Baojun Zhao,et al.  A New Tensegrity Module — “Torus” , 2008 .

[35]  Ana M. Ruiz-Teran,et al.  Inverse form-finding for tensegrity structures , 2019 .

[36]  Kenneth Snelson,et al.  The Art of Tensegrity , 2012 .

[37]  Jiamin Guo,et al.  An algorithm for calculating the feasible pre-stress of cable-struts structure , 2016 .

[38]  S. Krishnan.  Structural design and behavior of prestressed cable domes , 2020 .

[39]  Mingliang Zhu,et al.  Negative Gaussian Curvature Cable Dome and Its Feasible Prestress Design , 2016 .

[40]  Jiamin Guo,et al.  A Simple Approach for Force Finding Analysis of Suspended-Domes Based on the Superposition Principle , 2014 .

[41]  Nicolò Pollini,et al.  Gradient-based prestress and size optimization for the design of cable domes , 2021, International Journal of Solids and Structures.

[42]  Jian Feng,et al.  Initial prestress design and optimization of tensegrity systems based on symmetry and stiffness , 2017 .