Explicit solutions for multi-layered wide plates and beams with perfect and imperfect bonding and delaminations under thermo-mechanical loading

Abstract

Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical loading. The expressions are general and apply to plates composed of an arbitrary number of layers, of arbitrary thickness and elastic/thermal properties, and where the interfaces between the layers may be imperfect and allow relative sliding. The closed-form solutions are obtained using a multiscale homogenized model which depends on only three displacement variables and overcomes limitations of current approaches based on computationally expensive discrete-layer models. The accuracy of the expressions in predicting the highly complex and discontinuous fields, which characterize the response of thick and highly anisotropic plates with interlayer damage and delaminations, is verified using exact 2D thermo-elasticity solutions. The asymptotic limits of the model/solution correspond to the problems of an intact and a multiply delaminated plate. They are derived using a perturbation technique, which also explains the multiscale dependence of the model on the parameters.