Effects of transverse shear deformation on thermomechanical instabilities in patched structures with edge damage

Abstract

The problem of a patched structure under uniform thermal loading is studied, where geometric nonlinearity and shear deformation are considered. The formulation is based on the calculus of variations with propagating boundaries, and yields the governing equations, boundary conditions, matching conditions and transversality condition. Closed form analytical solutions are obtained in terms of an (unknown) membrane force parameter, the angle of rotation due to bending and the transverse displacement. Results of numerical simulations based on those solutions are presented and critical phenomena of the composite structure are unveiled. Results of the current work are compared with previously published results where transverse shear deformation was neglected. It is seen that shear deformation plays an important role in certain situations. In particular, the effects of shear deformation on the phenomena of "slingshot buckling" and "buckle trapping" are demonstrated and discussed. The influence of the relative size of the detached region and of the difference between the material properties of the base plate and of the patch (in particular, shear moduli) on the thermomechanical instabilities are elucidated.

The phenomenon of sling-shot buckling in stacked piezoelectric structures

“…Bottega (2012, 2014) showed sling-shot buckling in damaged structures, unveiled the phenomenon of ''buckle trapping'' and discussed the interaction of damage propagation with sling-shot buckling and buckle trapping. Ge and Bottega (2014) studied the effect of transverse shear on sling-shot buckling and buckle trapping in damaged structures. Pavlou (2014) extended sling-shot buckling to piezoelectric structures subjected to an increasing electric field.…”