General solutions of weakened equations in terms of stresses in the theory of elasticity

The general solutions of some weakened systems of equations in terms of stresses in isotropic elasticity are analyzed. These systems which are not equivalent to the classic one, involve (besides the equilibrium equations) only three of six compatibility equations, namely either diagonal or off-diagonal ones. An equivalence of the formulations of quasistatic boundary-value problems in elasticity in terms of stresses based on such systems is discussed.