2D closed form solution for bending of edge bonded dissimilar beams: An application of EKM

Abstract

Dissimilar material like composite laminated materials combined with metals like aluminium/steel have been extensively used to reduce the weight in automotive industries and aerospace industries. Moreover, prosthetic limbs are also designed to have varying material along the length for better suitability. At these interfaces, 3D state of stress will exist. Therefore, accurate estimation of deflection and bending stresses is very important and will lead to better design of structures. The objective of this paper is to develop a closed-form bending solution for edge-bonded beams in two dimensions (2D). Beams can be segmented along x-axis and can have any materials. Using Extended Kantorovich method, governing equations are formulated in mixed form and two sets of ordinary differential equations are obtained. Continuity of displacement and stresses are satisfied at interface of each segment. Two segmented beam having aluminium and Gr/Ep equal and unequal segment are considered. A Four segmented Al/SiC beam having gradual material variation is also analysed. The deflection and stresses are compared with the finite element solution and found in good agreement. The formulation is thoroughly verified by comparing the results with 2D FE. The present development will lead to developed solution for dissimilar plates and more complex cases.