STABILITY OF A COMPOSITE THICK PLATE WITH INHOMOGENEOUS FIELD OF INITIAL STRESSES

Using methods of spatial nonlinear elasticity we consider the static stability of a rectangular two-layered plate. This problem has a peculiarity which relates to the appearance of nonhomogeneous initial stresses. Each layer of the plate was obtained as a result of straightening of the sector of a cylindrical shell. As a result we have the self-equilibrated initial stresses. The main aim of the paper is the analysis of these initial stresses on the pl ate buckling. The stability was analyzed with linearization method. The method consists of the determination of such critical parameters of deformations for which the linearized boundary-value problem has nonzero or nontrivial solutions. We use the Treloar model as a constitutive relation. This model describes properly deformations of incompressible elastomers up to hundreds percent. Within the linearization approach we derive the linearized boundary-value problem. Using Fourier technique we obtain its nontrivial solutions. To this end we use the representation of solutions in series of sine and cosine functions. On the principal stretches plane we show the stability region. It is demonstrated that the initial stresses may significantly deform this region. In particular, instability can be a result of initial stresses only, that is without action of external loadings. Considered problems can be used for modelling of elements of so-called stretchable electronics, which use multi-layered structures manufactured by deposition of metallic films on an elastic flexible substrate. The internal stresses may result in wrinkling of the elements and to the increase of their flexibility.