EQUATIONS OF THE TWO-DIMENSIONAL PROBLEM OF THE VARYING-STRENGTH OF VARYING-MODULI THEORY OF ELASTICITY,
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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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 Hookes 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.