Optimal stress fields and load capacity ratios of perfectly plastic bodies and structures

Reuven Segev, Lior Falach

Research output: Contribution to journalConference articlepeer-review

Abstract

A mathematical setting that applies to the analysis of strength of perfectly plastic bodies and structures is presented. Specifically, the worst case analysis under the loads in any vector subspace of the space of all loadings is performed. It is shown that there is a number C, depending only on the geometry of the body, such that the body will not collapse plastically under any applied boundary load t, as long as ∥t∥≤syC independently of the distribution of t, where sY is the yield stress of the material. We give examples for computations of C, the load capacity ratio of the body, and examples of computations of worst case loadings. The analysis also shows that perfectly plastic materials are optimal in the following sense. Without specifying a constitutive relation, let Σf denote the collection of all stress fields σ that are in equilibrium with a given loading f and consider sfopt=inf σ∈Σf{supx|σ(x)|} - the optimal maximal stress. Then, for perfectly plastic materials at the limit state, the optimum is attained where sfopt=sY. The abstract mathematical setting may be described as follows. For a norm preserving linear mapping ε:W→S, we consider the optimal solution of the under-determined equation f=ε*(σ), i.e., we look for s fopt=inf{∥σ∥|σ∈ε *1{f}}. Next, for a mapping β*:M*→W*, an expression is obtained for the worst case factor K=sup S β*(t)opt/∥t∥ t∈M*.

Original languageEnglish
Pages (from-to)368-371
Number of pages4
JournalAIP CONFERENCE PROCEEDINGS
Volume1281
DOIs
StatePublished - 1 Dec 2010
EventInternational Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010 - Rhodes, Greece
Duration: 19 Sep 201025 Sep 2010

Keywords

  • Optimal solutions
  • limit analysis
  • load capacity
  • stress analysis
  • worst case analysis

ASJC Scopus subject areas

  • General Physics and Astronomy

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