Methods of solving spatial problems of the mechanics of a deformable solid in terms of stresses (Q2266600)

The formulation in \textit{B. E. Pobedrya}'s book on Numerical methods in the theory of elasticity and plasticity (1981) of a quasistatic problem of mechanics of a deformable solid in terms of stresses is discussed, including also the variational formulation, which consists of solving six equations in six symmetric stress tensor components when six boundary conditions are satisfied. Methods of successive approximation are proposed for solving this problem and theorems on the convergence of these methods, including a ''rapidly converging'' method, whose rate of convergence is substantially higher than a geometric progression, are proved.