We consider the equations of linear theory of elasticity in stresses for the threedimensional space. Solutions are decomposed into sums of stationary solutions not satisfying the compatibility condition (residual stresses) and nonstationary solutions satisfying the compatibility condition and hence represented through the displacements. The construction of this decomposition is reduced to solving a series of Poisson equations.
- elasticity theory
- residual stresses
- Saint-Venant compatibility conditions
- strain tensor
- stress tensor