SOME CONSIDERATIONS ON STRESS FUNCTIONS

Abstract

INVESTIGATIONS INTO STRESS PROBLEMS ARE PRESENTED: In Part I, stress functions in a three dimensional stress problem of the small displacement theory in rectangular Cartessian coordinates are discussed, and an application to a flat plate problem is shown. In Part II, stress functions in a three dimensional stress problem of the finite displacement theory in general curvilinear coordinates are shown to be derivable by the use of the vanishing conditions of Riemann-Christoffel curvature tensors and the principle of virtual work. It is obvious that the stress functions thus obtained include those of the small displacement theory as a special case. In Part III, the technique developed in Part II is applied to a shell problem of the small displacement theory, and stress functions for a thin shell are obtained. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1961
Accession Number
AD0267389

Entities

People

  • K. Washizu

Organizations

  • Massachusetts Institute of Technology

Tags

DTIC Thesaurus Topics

  • Curvature
  • Displacement
  • Geometric Forms
  • Geometry
  • Lines (Geometry)
  • Mathematics
  • Three Dimensional

Fields of Study

  • Engineering
  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Structural Dynamics.