EQUILIBRIUM BIFURCATION OF MULTILAYER MICROPOLAR PLATES WITH INTERNAL STRESSES

The problem of equilibrium stability for deformable bodies is of considerable interest, both from theoretical and practical perspectives, because the exhaustion of load-bearing capacity and collapse of buildings and engineering structures quite often occurs due to buckling under external loads. Due to the development of modern technologies and the emergence of new materials, the stability analysis of various composite nonlinear elastic bodies with a complex microstructure and internal stresses is becoming quite relevant. In the present paper, within the framework of the general theory of stability for three-dimensional bodies, we have studied the problem of equilibrium bifurcation for a rectangular multilayer plate under biaxial compressionextension. It was assumed that the plate layers could be preliminary deformed and contain initial (residual) stresses. The model of a micropolar medium (Cosserat continuum) was applied to describe the behavior of the considered plate. This allowed us to take into account in detail the effect of microstructure on buckling. Using representations of constitutive relations for different reference configurations, in the case of a physically linear micropolar material model, linearized equilibrium equations were derived that describe the behavior of composite plates with prestressed parts in a perturbed state. Using a special substitution, the stability analysis of a rectangular N-layer micropolar plate was reduced to solving linear homogeneous boundary value problem for a system of 6N ordinary differential equations. Given the material parameters of the layers, their thickness, and initial strains, this boundary value problem can be easily solved numerically using the finite-difference method.

nonlinear elasticity, stability of deformable bodies, micropolar medium, Cosserat continuum, multilayer plate, internal stresses