Applications of higher order shear deformation theories on stress distribution in a five layer sandwich plate

In this paper, layerwise theory (LT) along with the first, second and third-order shear deformation theories (FSDT, SSDT and TSDT) are used to determine the stress distribution in a simply supported square sandwich plate subjected to a uniformly distributed load. Two functionally graded (FG) face sheets encapsulate an elastomeric core while two epoxy adhesive layers adhere the core to the face sheets. The sandwich plate is assumed to be symmetric with respect to its core mid-plane. First, second and third-order shear deformation theories are used to model shear distribution in the adhesive layers as well as others. Results obtained from the three theories are compared with those of finite element solution. Results indicate that finite element analysis (FEA) and LT based on the first, second and third-order shear deformation theories give almost the same estimations on planar stresses. Moreover, the out-of-plane shear stresses obtained by FEA, are slightly different from those of LT based on FSDT. The differences are decreased on using LT based on SSDT or TSDT. Additionally, SSDT and TSDT predict almost the same distribution for the two planer stress and out-of-plane shear stress components along the face sheet thickness. Furthermore, third-order shear deformation theory seems to be more appropriate for prediction of out-of-plane shear stress at lower values of a/h ratio