The fixed nodal position method for form finding of high-precision lightweight truss structures

Abstract A new form-finding method, namely the Fixed Nodal Position Method (FNPM), is developed for design of geometric configuration and internal force distribution for a class of truss structures with a requirement of high shape or surface accuracy. Different from existing form-finding methods, which usually follow a stress-first-and-displacement-later procedure, the FNPM first assigns nodal coordinates for a truss structure, and then determines the internal force distribution of the structure by an optimization process. The highlight of the FNPM is that the prescribed nodal coordinates are unchanged during the form finding process. This special feature of fixed nodal positions allows the proposed method to place the nodes of a truss structure at desired locations, satisfying complicated constrains and yielding high shape/surface accuracy as required. Moreover, because the assignment of geometric configuration (nodal coordinates) and the determination of internal force distribution are undertaken separately, the computational effort in the FNPM-based form finding is much less than that by a conventional method. The proposed method is applied to two large deployable mesh reflectors of 217 nodes and 865 nodes, respectively, and show high efficiency and accuracy in form finding.

[1]  Sergio Pellegrino,et al.  Mechanics of kinematically indeterminate structures , 1986 .

[2]  John F. Abel,et al.  Initial equilibrium solution methods for cable reinforced membranes part I—formulations , 1982 .

[3]  P. Gill,et al.  Algebraic tensegrity form-finding , 2005 .

[4]  René Motro,et al.  Form-Finding of Nonregular Tensegrity Systems , 2006 .

[5]  H. Schek.  The force density method for form finding and computation of general networks , 1974 .

[6]  Bernard Maurin,et al.  Numerical form-finding of geotensoid tension truss for mesh reflector , 2012 .

[7]  Reg Connelly,et al.  Globally rigid Symmetric Tensegrities , 1995 .

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

[9]  S. Pellegrino.  Analysis of prestressed mechanisms , 1990 .

[10]  A. Tibert,et al.  Review of Form-Finding Methods for Tensegrity Structures , 2003 .

[11]  Jaehong Lee,et al.  Initial self-stress design of tensegrity grid structures , 2010 .

[12]  Xiaodong Feng.  The optimal initial self-stress design for tensegrity grid structures , 2017 .

[13]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[14]  R. Motro,et al.  Form finding numerical methods for tensegrity systems. , 1994 .

[15]  K. Miura,et al.  Concept of the tension truss antenna , 1990 .

[16]  Baiyan He,et al.  Deployment dynamics modeling and analysis for mesh reflector antennas considering the motion feasibility , 2017 .

[17]  Hao Li,et al.  Predictive Power of Machine Learning for Optimizing Solar Water Heater Performance: The Potential Application of High-Throughput Screening , 2017 .

[18]  P. Agrawal,et al.  Preliminary design of large reflectors with flat facets , 1981 .

[19]  R. Motro.  Structural Morphology Of Tensegrity Systems , 1996 .

[20]  Tuanjie Li,et al.  Pillow Distortion Analysis for a Space Mesh Reflector Antenna , 2017 .

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

[22]  Simon D. Guest,et al.  The stiffness of prestressed frameworks: A unifying approach , 2006 .

[23]  Hang Shi,et al.  New Methodology of Surface Mesh Geometry Design for Deployable Mesh Reflectors , 2017 .

[24]  M. Barnes,et al.  Form Finding and Analysis of Tension Structures by Dynamic Relaxation , 1999 .

[25]  R. Kalaba,et al.  Analytical Dynamics: A New Approach , 1996 .

[26]  M. Pagitz,et al.  Finite element based form-finding algorithm for tensegrity structures , 2009 .

[27]  Sergio Pellegrino,et al.  Deployable Tensegrity Reflectors for Small Satellites , 2002 .

[28]  Bingen Yang,et al.  The Projecting Surface Method for improvement of surface accuracy of large deployable mesh reflectors , 2018, Acta Astronautica.

[29]  John Argyris,et al.  A general method for the shape finding of lightweight tension structures , 1974 .

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

[31]  Baiyan He,et al.  Deployment analysis for space cable net structures with varying topologies and parameters , 2017 .

[32]  Houfei Fang,et al.  Form-Finding of Large Deployable Mesh Reflectors with Elastic Deformations of Supporting Structures , 2018 .

[33]  M.W. Thomson,et al.  The AstroMesh deployable reflector , 1999, IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010).

[34]  K. Linkwitz,et al.  Einige Bemerkungen zur Berechnung von vorgespannten Seilnetzkonstruktionen , 1971 .

[35]  Philippe Block,et al.  An overview and comparison of structural form finding methods for general networks , 2012 .

[36]  Kazufumi Ito,et al.  The Primal-Dual Active Set Strategy as a Semismooth Newton Method , 2002, SIAM J. Optim..

[37]  Mark W. Thomson,et al.  ASTROMESH™ DEPLOYABLE REFLECTORS FOR KU- AND KA-BAND COMMERCIAL SATELLITES , 2002 .

[38]  K. Koohestani.  Form-finding of tensegrity structures via genetic algorithm , 2012 .

[39]  Jingyao Zhang,et al.  Adaptive force density method for form-finding problem of tensegrity structures , 2006 .