Vol 72, No 5 (2017)

Some minimal prior constraints are imposed on the two material functions used in the Rabotnov nonlinear constitutive relation. The asymptotic dependence of creep curves on the characteristics of these material functions and on the parameters of loading programs is analytically studied in the case of stepped loadings. Some conditions are obtained for the case when these curves tend to the creep curve under instantaneous loading as t→∞. The importance of the limit value of the creep function derivative at infinity is analyzed for the plastic strain accumulation. A number of distinctions and additional possibilities are found compared to the linear integral relation of viscoelasticity.

For an adequate description of free and controlled motions of one-dimensional elastic systems with distributed parameters, we consider a suitable model expressed by a linear problem with Robin boundary conditions. It is assumed that the control action is used additively in the equation of motion and in the boundary conditions. The coefficients used in the equation of state and in the boundary conditions may depend on the spectral parameter (frequency), which allows one to take into account the inertial and/or force load at one or both ends of the boundary as well as the elastic properties (the Rayleigh correction) and other imperfections.

An analytical formula is obtained, which allows us to find the maximum pressure within a multilayer spherical vessel in the case of a linear decrease of pressure between the layers.