Viscoelastic bending of beams of variable curvature radius and stiffness

E. P. Popov method of analysis of elastic beams flat bending with large displacements was generalized to the case of viscoelastic beams of variable curvature radius and stiffness using an example of bending of flat springs of variable thickness symmetrical profile. The problem is reduced to the solution of a number of boundary creep problems with link conditions on section joints by means of partitioning the original beam into sections with a constant curvature radius and stiffness. The solutions are based on exact non-linearized equation of curved sections motion (so-called nonlinear pendulum vibration equation) taking into account the changes in the magnitude of the bending moment under creep. Values of curvature radius and displacement of beams subjected to creep deformation were determined. Viscoelastic bending problem of flat polymeric spring of variable curvature radius and stiffness was solved analytically as an example.