ENERGY FUNCTIONAL DERIVATIVE OF THE LENGTH OF A CURVILINEAR OBLIQUE CUT IN THE PROBLEM OF EQUILIBRIUM OF A TIMOSHENKO PLATE
N. P. Lazarev1,2
1Scientific Research Institute of Mathematics, Yakutsk, 677000 Russia
nyurgun@ngs.ru
2Lavrent'ev Institute of Hydrodynamics, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: наклонная трещина, вариационное неравенство, пластина Тимошенко, условие непроникания, производная функционала энергии, oblique crack, variational inequality, Timoshenko plate, nonpenetration condition, energy functional derivative
Abstract
This paper describes the dependence of the solution of the problem of equilibrium of a Timoshenko plate and the total energy functional of the plate on the surface perturbation, which is an oblique crack. The nonlinearity of the problem is caused by the boundary conditions in the form of inequalities (conditions such as the Signorini conditions), which simulate mutual nonpenetration of the opposite crack faces. The continuous dependence of the solution of the problem on the perturbation of the crack length is established. A formula for the energy functional derivative of the perturbation of the crack length is obtained.
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