MATHEMATICAL MODELING OF THE DYNAMICS OF AN ELASTIC HALF-MEDIUM WITH A CYLINDRICAL CAVITY REINFORCED BY A SHELL UNDER AXISYMMETRIC LOADS

Purpose. The development of a mathematical model an elastic semi-medium with cylindrical cavity reinforced by shell and plate that reinforces the surface based on finite-element approach. non-stationary dynamic stress-strain state this mechanical system under axisymmetric loads, which depends time as unit Heaviside function was analyzed. solution corresponding static problem obtained. Based obtained results, coefficient considered calculated.
 Research methods. finite element method Wilson - were used for solving matrix equation correspondingly. last one allows reducing differential to iterative sequence quasi-static problems. To obtain approximate systems linear algebraic equations take place in process quasi-statistical problems, conjugate gradients used.
 Results. A developed. stress-deformed action loads results has been obtained, determined.
 Scientific novelty. developed approach into account mutual influence applied plate.
 Practical value. models can be design underground structures, particular mine shafts.