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Model of stressed-strained State of Multilayer Masses with regard for Non-Ideal Contact of Layers
(1997)

Thus, mathematical model stressed- strained of a condition of layered masses is constructed. The model has high accuracy. It allows to simulate slippery contact of layers without friction. Thus not the order of permitting system of the equations is increased, and at its realization the method of fenite elements does not increase quantity of required degrees freedom. The differential operators included in system the equations are similar known in the classical theory of shells. It facilitates construction of a finite element. Presence in system of the differential equations of derivative of external forces allows to use her for the decision of contact problems with a stain of contact commensurable with thickness of a masses.

There was suggested a phenomenological modified quadratic condition of the beginning of plasticity for plastic and quasifragile orthotropic materials. Limiting surface in the shape of a paraboloid with an axis bend over hydrostatic axis corresponds to the condition. The equations of theory of current with the isotropic and anisotropic hardenings, associated with the suggested yield condition, modified into the version of determining equations of strain theory of plasticity are received. These defining equations formed the basis of highlyprecise non-classic continual (along thickness) theory of non-linear deformation of thick sandwich plates and sloping shells. In the approximations along the cross coordinate the specificity of flexural and non-flexural deformations is taken into account. The necessity of introducing the approximations of higher order, as well as accounting for the cross compression while decreasing of the relatively cross normal and shear layer rigidness is shown. The specifications, obtained in comparison with the known physically nonlinear specified model of the bending of plates with orthotropic layers are distinguished. An effective procedure of linearization of the solving equations and getting the solutions in frames of the discrete-continual scheme of the finite-element method is suggested. The approximations of higher order let to model the appearance of the cracs of layers being split by the introducing of slightly hard thin layers into the finite element, not violating the idea of continuality of theory. Calculation of a threelayer plate with rigid face diaphragms on the contour is considered