Elastic layers bonded to flexible reinforcements

Elastic layers bonded to reinforcing sheets are widely used in many engineering applications. While in most of the earlier applications, these layers are reinforced using steel plates, recent studies propose to replace ‘‘rigid’’ steel reinforcement with ‘‘flexible’’ fiber reinforcement to reduce both the cost and weight of the units/systems. In this study, a new formulation is presented for the analysis of elastic layers bonded to flexible reinforcements under (i) uniform compression, (ii) pure bending and (iii) pure warping. This new formulation has some distinct advantages over the others in literature. Since the displacement boundary conditions are included in the formulation, there is no need to start the formulation with some assumptions (other than those imposed by the order of the theory) on stress and/or displacement distributions in the layer or with some limitations on geometrical and material properties. Thus, the solutions derived from this formulation are valid not only for ‘‘thin’’ layers of strictly or nearly incompressible materials but also for ‘‘thick’’ layers and/or compressible materials. After presenting the formulation in its most general form, with regard to the order of the theory and shape of the layer, its applications are demonstrated by solving the governing equations for bonded layers of infinite-strip shape using zeroth and/or first order theory. For each deformation mode, closed-form expressions are obtained for displacement/stress distributions and effective layer modulus. The effects of three key parameters: (i) shape factor of the layer, (ii) Poisson’s ratio of the layer material and (iii) extensibility of the reinforcing sheets, on the layer behavior are also studied.