Variational-structural method in creep problems for shallow shells of complex shape (Q2759538)

The author considers a thin isotropic shallow shell of arbitrary shape in plane under the action of transverse load. The tensor of velocities of total strain consists of tensors of elastic strain velocities and of creep strain velocities: \(\dot{\varepsilon}_{ij}= \dot{\varepsilon}_{ij}^e +\dot{p}_{ij}\) \((i,j =1,2)\). Constitutive relations for creep strain \(\dot{p}_{ij}\) are taken in incremental form, and the linearized creep problem is reduced to the problem of minimization of a functional on the set of all kinematically possible velocities of displacement. The problem is solved in two stages. At the first stage, the problem of instantaneous deformation is solved, and initial conditions for unknown functions are determined. At the second stage, the creep problem is solved. Approximate solution of the problem is found by the method of \(R\)-functions, by Ritz method, and by Runge-Kutta method. A numerical example is considered, and the transverse displacement and stresses are presented graphically.