Analytical solutions of problems of the adiabatic compression of thick-walled spherical and cylindrical shells made of incompressible viscoplastic material

Exact solutions of the one-dimensional non-stationary problems of the adiabatic compression of thin-walled spherical and cylindrical shells made of incompressible viscoplastic material are obtained, assuming that, at the initial instant of time, the radial velocity distributions satisfy the conditions of incompressibility of the shell material. From these solutions it is also easy to obtain the solutions for cases of expansion of the shells.