The numerical anaysis of stressed state of multilayered coverings with defects on an rigid foundation
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 80, Issue 4
Abstract
Multilayered coverings can be considered as thick plates resting on a rigid substrate. For research of stress-strain state (SSS) of multilayered plates on an rigid foundation the refined structural-continual model of momentless symmetrical SSS is offered. The layers of the plate are both isotropic and transversely isotropic, with any but constant thickness with rigid interlaminar contact. The design diagram of a transversely loaded plate is formed by supplementing it with a symmetric one relatively the contact surface of the foundation. The load on a double thickness plate is applied bilaterally, being symmetrical to its median surface. The SSS of a plate becomes symmetrical (unflexural). Such a diagram models shear without friction on the contact surface of a plate with the foundation. The rigid contact of the initial plate with the foundation is modelled by introducing an additional thin practically nondeformable layer. Numerically model is realized by the variational-difference method (VDM). To obtain the desing system of algebraic equations of VDM the Lagrange integration variational functional on a half step of digitization with simultaneous application of left and forward differences for the first derivative of functions of displacement, is applied. Calculations confirm the efficiency of such approach, which allows to obtain solutions qualitatively and quantitatively close to three-dimensional ones. The positive influence on SSS of two-layered plate by presence of a thin layer slippage in the hard layer plate is presented. The problems with a discrete change in rigidity of the plate in its plane through the occurrence of longitudinal planar defects and under different conditions of contact of the plate with foundation is solved. On the border of the defect and change of the contact condition of the plate with foundation coupling conditions of displacements are applied on the upper surface of the plate in two neighboring grid nodes by using the undetermined Lagrange multipliers.
Authors and Affiliations
Sergiy Tynchuk
Keywords
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