SOLUTION OF THREE-DIMENSIONAL DEFORMATION PROBLEMS FOR HETEROGENEOUS AREAS USING THE VARIABLE SEPARATION METHOD BASED ON A VARIATIONAL FORMULATION
The paper deals with the three-dimensional deformation modeling for heterogeneous bodies. The modeling based on the variational principle of virtual velocities and stresses. It is proposed that the deforming domain consists of sub-domains with different mechanical properties, and that the material of each sub-domain is isotropic. Conjugation conditions at the boundaries between the sub-domains are specified. The calculation of deformation process parameters on the finite time interval is fulfilled using the Lagrangian coordinates. The isochronous variational problem is solved for an arbitrary time moment. As a result the system of ordinary differential equations is obtained for the determining of time-dependent parameters. The system is solved numerically for given initial conditions. As an example, the calculations of the layered perform setting. The displacement representation used allows to simulate the barreling in the process of deformation. The conjugation conditions proposed results in the decreasing the order of differential equation system.