A layerwise plate element formulation with adhesive interface compliance and thermal loads for bonded multilayer structures

This paper presents a novel layerwise plate finite element formulation for the modelling of adhesively bonded multilayer structures subjected to thermal loading. Each structural layer is represented as a Reissner–Mindlin plate, while interlayer coupling is achieved through adhesive shear layers with defined thickness and shear stiffness. This approach enables the direct representation of adhesive compliance, which is often simplified or neglected in layerwise plate formulations. The formulation is derived via the principle of virtual work and incorporates mixed interpolation of tensorial components to prevent shear locking. Numerical examples demonstrate the accuracy and computational efficiency of the proposed element. Comparisons with three-dimensional solid finite element reference models show good agreement with the computed deflections, while requiring substantially fewer degrees of freedom. The resulting computational efficiency makes the approach particularly attractive for iterative analyses such as process simulations and parametric studies involving thermally induced deformations. Since the adhesive shear modulus enters the formulation only as a parameter, time- or temperature-dependent behaviour can be incorporated through constitutive modelling without modification of the element formulation.