EQUATIONS OF THE TWO-DIMENSIONAL PROBLEM OF THE VARYING-STRENGTH OF VARYING-MODULI THEORY OF ELASTICITY,

Abstract

Assumption is made of a material having constant but different moduli of elasticity in tension and compression. Likewise the Poisson ratios are different in tension and compression. For materials with such properties all the elasticity equations, the equations of compatibility, equations of equilibrium, and the generalized Hooke's law are derived and compared with the classical theory equations. For the two-dimensional case, besides the rectangular coordinates, the author uses also polar coordinates. It is shown that the Castigliano theorem is valid for the two-moduli theory as well.

Document Details

Document Type
Technical Report
Publication Date
Jan 17, 1969
Accession Number
AD0687633

Entities

People

  • S. A. Ambartsumyan

Organizations

  • National Air and Space Intelligence Center

Tags

DTIC Thesaurus Topics

  • Cartesian Coordinates
  • Compression
  • Elastic Properties
  • Equations
  • Materials
  • Mathematics
  • Physical Properties
  • Poisson Ratio
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Powder metallurgy of Titanium alloys.