Solutions of the interfacial shear and normal stresses in plate flexural-strengthened beams based on different complementary strain energy assumptions

Abstract

A series of solutions based on five different complementary strain energy assumptions (named as Assumptions A, B, C, D, E) are developed for the prediction of interfacial shear and normal stresses in plate flexural–strengthened beams. Basic differences between the Assumptions are that in the formulating of the energy, Assumption A includes the transverse normal and shear stress fields in the beam and in the plate, Assumption B includes the normal stresses but exclude the shear stresses, Assumption C includes the shear stresses but excludes the normal stresses, Assumptions D excludes the normal stresses and the shear stresses in the beam but include the shear stresses in the plate, and Assumption E excludes the normal and shear stresses in the beam and in the plate. The energy expressions of the five Assumptions are developed based on derived statically admissible stress fields and an a generalized 2D-Hooke’s law constitutive model. Through an energy variation principle, compatibility equations and boundary conditions of the interfacial stresses are obtained. Closed form and numerical solutions are then developed for the compatibility equations. By comparing against the interfacial stresses of 2D- and 3D- finite element analyses (FEA), it is observed that Assumptions A and B significantly underpredict the interfacial stresses, Assumption C excellently predicts the interfacial normal stresses, Assumptions D and E excellently predict both the interfacial shear and normal stresses, and Assumptions (C, D, E) excellently capture the FEA stress fields (those are strongly varied across the adhesive thickness). The present study is applicable to plate-strengthened beams with general force boundary conditions but it is limited to linearly elastic orthotropic/isotropic materials.