Shearing form of stability loss for a three-layer circular ring under the action of uniform external pressure

Abstract

1. The state-of-the-art in laminated-plate and shell mechanics was covered in review [1]. The current status of the stability theory for three-layer plates and shells was presented in [2]. In [2], the stages of the theory’s development and lines of further inquiry were analyzed and a proposal was put forth on the classification of stability-loss forms according to Euler. In the case of three-layer plates and shells under the action of a static load, for different forms of the stressed-strained state in both supporting layers and the filler, we should distinguish the following: (1) Skew-symmetric (equiphase) and symmetric (antiphase) stability-loss forms. These forms are realized in certain structures for equal values of subcritical forces in supporting layers and zero values of subcritical transverse tangent shear stresses in a filler. (2) A mixed flexural stability-loss form. This is realized for unequal values of subcritical forces in supporting layers and zero values of subcritical transverse tangent shear stresses in a filler. (3) A pure shearing stability-loss form. This is realized for zero values of subcritical forces in supporting layers and nonzero values of subcritical transverse tangent shear stresses in a filler. (4) A flexural-shearing stability-loss form. This is realized in the case of nonzero subcritical tangential stresses in supporting layers and transverse shear stresses in a filler. (5) A shearing stability-loss form in tangential directions. This is realized for low values of the shear modulus of a supporting-layer material in the tangential plane under conditions of pure shear. (6) An arbitrary stability-loss form. This is a combination of the above forms for a subcritical stressedstrained state of an arbitrary form. 2. We consider a circular three-layer ring with a symmetric structure along the thickness, which is under the action of a uniform external pressure p. Let 2t and