Numerical approximation strategy for solutions and their derivatives for two-dimensional solids

The paper presents the approximation strategy for solutions and derivatives of solutions of boundary value problems on the example of two-dimensional solids. The effectiveness of the proposed strategy lies in the fact that it gives possibility to calculate solutions and their derivatives continuously at all points of the boundary and the domain, irrespective of the method used to solve the boundary problem and regardless of the type of the problem. The strategy has been developed in order to: (1) improve the accuracy of solutions (displacement) and their derivatives (strains, stresses) in the vicinity of the boundary, where they are affected by errors, (2) make the ability to directly obtain the derivatives of solutions (strains, stresses) on the boundary, (3) avoid computing strongly singular integrals present in the integral identity used for obtaining solutions or their derivatives (e.g. stresses in plasticity problems). The different variants of the proposed strategy have been developed and their accuracy has been verified considering examples with analytical solutions.