Solving a one mixed problem in elasticity theory for half-space with a cylindrical cavity by the generalized Fourier method

Designing and constructing underground structures for various purposes, such as tunnels, mines, mine workings, necessitate the development of procedures calculating their strength reliability. The physical model objects worth considering is a homogeneous isotropic half-space that contains an infinitely long hollow cylinder, located parallel to its border. One can explore problems related mechanics deformable solids multiply connected body. This paper reports proofs addition theorems basic solutions Lamé equation regarding cylinder recorded, respectively, in Cartesian cylindrical coordinate systems. result important from theoretical point view order substantiate numerical-analytical method ? generalized Fourier method. makes it possible solve spatial boundary theory elasticity thermo-elasticity transversal-isotropic bodies. Similar classical method, general equilibrium equations have been used here but several systems rather than one. From practical view, this has made investigate combined problem multiply-connected body described above. analysis stressed-strained state elastic draw conclusions on determining those regions are most vulnerable destruction. highest values accepted by normal stresses region between boundaries cylinder. Changing ?y component along Ox axis corresponds displacements assigned half-space. ?xy contributes less distribution ?x ?y. applied aspect using reported results possibility apply them when designing