Postolaki L. Solving direct and inverse elasticity problems for rectangular areas with the use of the variational approach

The analytically-numeral methods for solving 2-D direct and inverse elasticity problems for rectangular areas and piece-wise homogeneous strip with the use of the variational method of homogeneous solutions have been developed. The model of residual stresses in piece-wise homogeneous body with planar joint has been built. The joint has been modeled by a thin inhomogeneous layer with incompatible strain. Mathematical problems arising in methods for non-destructive determination of joint stress-strain state on the base of data about displacement and/or stress components distributions on a part of body's surface accessible for measurement have been formulated in the frame of the model and numerically studied. Developed mathematical tools can be applied to create new methods and facilities for non-destructive determination of residual stresses in ferromagnetic materials with the use of piezomagnetic effect. They can be applied also for monitoring of stress-strain state of heterogeneous materials joints in operational conditions using the data of measuring of elastic displacements on the body surface by optical methods.