Mathematical models of deformation of underground pipelines interacting with the ground under spatial-variable loading

The paper formulates a statement of the problem and develops mathematical models deformation underground pipelines under spatially variable loading, taking into account accumulation damageability materials. Based on theory small elasto-plastic deformations Hamilton-Ostrogradsky variational principle, differential equations motion (equilibrium) system alternating loading with appropriate boundary initial conditions has been obtained for first time. finite difference method matrix runs solve repeated static loading. Numerical results calculation displacement vector pipeline - rod, clamped at ends cyclic are given.