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

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