A variational principle in calculating the long-term strength of structures

A variational principle of mixed type is proposed to determine the stress-strain state of a non-linear viscoelastic body, on the assumption that the processes of creep and damage are interrelated and taking geometrical non-linearity into account. A special feature of the functional is its formulation in terms of accelerations, which enables the system of Euler equations to be expanded by adding, besides the equilibrium equations, an equation of vulnerability to damage. The functional has been tested in connection with the problem of the long-term strength of a cylindrical shell under internal pressure.