Failure Probability Evaluation of an Anisotropic Brittle Structure Derived from a Thermal Stress Solution

  • J. Margetson


A method is presented which will allow the failure probability of a brittle structure to be evaluated from a thermal stress solution. It is based on a statistical approach, a generalisation of the simple Weibull distribution, and takes into account material variability, component size and anistropic strength. The principal stress values at the nodes of a finite element mesh are assumed to be known for the structure. The stress distribution within each element is then expressed in terms of these nodal values through suitably derived shape functions. Certain stress volume integrals are evaluated and the failure probability of each element, and hence that of the whole structure, is calculated. The accuracy of the method is assessed for various types of finite elements by analysing a simple structure.


Finite Element Analysis Principal Stress Failure Probability Finite Element Mesh Triangular Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Margetson,,“A statistical theory of brittle failure for an anisotropic structure subjected to a multiaxial stress state”, RPE Tech. Report No. 48 (1976).Google Scholar
  2. 2.
    W. J. Weibull, J. App. Mech., 1951, 18 (3).Google Scholar
  3. 3.
    E. J. Whittaker, “A course of modern analysis”, Cambridge, C.U.P., 1963.zbMATHGoogle Scholar
  4. 4.
    P. Stanley, H. Fessler and A. D. Sivell, “An engineers approach to the prediction of failure probability of brittle components”, Proc. Brit. Ceram. Soc., 1973, 22.Google Scholar
  5. 5.
    O. C. Zienkiewicz, “The finite element method in engineering science”, N.Y., McGraw-Hill, 1971.zbMATHGoogle Scholar
  6. 6.
    E. G. Phillips, “A course of analysis”, Cambridge, C.U.P., 1960.Google Scholar
  7. 7.
    F. Scheid, “Numerical analysis. Schaum’s outline series”, N.Y., McGraw-Hill, 1968.Google Scholar
  8. 8.
    S. Timoshenko, “Theory of elasticity”, N.Y., McGraw-Hill, 1934.zbMATHGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • J. Margetson
    • 1
  1. 1.Research DivisionPropellants, Explosives and Rocket Motor EstablishmentAylesbury, BucksUK

Personalised recommendations