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Selected Problems of Statics

  • Tomasz Lewiński
  • Tomasz Sokół
  • Cezary Graczykowski
Chapter

Abstract

In its original formulation, Michell’s (Philosophical Magazine, Series 6 8(47):589–597, 1904) problem reads as follows: find the framework of least volume in which state of stress \(\varvec{\sigma }\) satisfies the conditions \(-\sigma _C \le \min \lambda _i(\varvec{\sigma })\le \max \lambda _i (\varvec{\sigma }) \le \sigma _T\) and which a given load transmits to a given segment of the boundary of the design domain; \(\lambda _i (\varvec{A})\) represents ith eigenvalue of a symmetric matrix \(\varvec{A}\). The solution to this problem depends essentially on the ratio \(\kappa =\frac{\sigma _T}{\sigma _C}\) but does not depend on other material data. Therefore, this problem belongs to the class called the plastic optimum design.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Tomasz Lewiński
    • 1
  • Tomasz Sokół
    • 2
  • Cezary Graczykowski
    • 3
  1. 1.Faculty of Civil EngineeringWarsaw University of TechnologyWarsawPoland
  2. 2.Faculty of Civil EngineeringWarsaw University of TechnologyWarsawPoland
  3. 3.Institute of Fundamental Technological ResearchPolish Academy of SciencesWarsawPoland

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