Optimum structure to carry a uniform load between pinned supports

Since the time of Huygens in the 17th century it has been believed that, if the weight of the structural members themselves are negligible in comparison to the applied load, the optimum structure to carry a uniformly distributed load between pinned supports will take the form of a parabolic arch rib (or, equivalently, a suspended cable). In this study, numerical layout optimization techniques are used to demonstrate that when a standard material with equal tension and compressive strength is involved, a simple parabolic arch rib is not the true optimum structure. Instead, a considerably more complex structural form, comprising a central parabolic section and networks of truss bars in the haunch regions, is found to possess a lower structural volume.

[1]  G.I.N.Rozvany Wang,et al.  Prager-structures: Archgrids and cable networks of optimal layout , 1982 .

[2]  E. H. Lockwood,et al.  A Book of Curves , 1963, The Mathematical Gazette.

[3]  M. Gilbert,et al.  Layout optimization of large‐scale pin‐jointed frames , 2003 .

[4]  Moshe B. Fuchs,et al.  Optimal structural topologies with transmissible loads , 2000 .

[5]  W. S. Hemp.  MICHELL FRAMEWORK FOR UNIFORM LOAD BETWEEN FIXED SUPPORTS , 1974 .

[6]  George I. N. Rozvany,et al.  A critical review of established methods of structural topology optimization , 2009 .

[7]  John Benjamin Brynmor Owen,et al.  The analysis and design of light structures , 1965 .

[8]  George I. N. Rozvany,et al.  On plane Prager-structures—I☆ , 1983 .

[9]  G. Chiandussi,et al.  Computers and Mathematics with Applications Topology Optimization with Optimality Criteria and Transmissible Loads , 2022 .

[10]  J. Bernoulli,et al.  Die Werke von Jakob Bernoulli , 1969 .

[11]  Harvey J. Greenberg,et al.  Automatic design of optimal structures , 1964 .

[12]  Edith Dudley Sylla.  Die Werke von Jakob Bernoulli. Vol. 5, Differentialgeometrie: Edited by André Weil and Martin Mattmüller. Basel/Boston/Berlin (Birkhäuser Verlag). 1999. xxv + 445 pp. EUR 211 , 2003 .

[13]  Richard E. McConnel.  Least-Weight Frameworks for Loads Across Span , 1974 .

[14]  Y. Xie,et al.  Evolutionary methods for topology optimisation of continuous structures with design dependent loads , 2005 .

[15]  H. Chan,et al.  Symmetric Plane Frameworks of Least Weight , 1975 .

[16]  W. Prager,et al.  A new class of structural optimization problems: Optimal archgrids , 1979 .

[17]  Paul Shepherd,et al.  Application of Large-scale Layout Optimization Techniques in Structural Engineering Practice , 2005 .

[18]  Donald E. Knuth,et al.  The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .