Analytical modelling and shape optimization of composite girder with adhesive bondline

Abstract

The paper presents a beam theory for composite girders consisting of two beams joined together with an adhesive layer. The height of the bottom beam is considered variable. The governing equations are suitable for formulation of a shape optimization problem in terms of control theory. The use of Pontryagin's maximum principle enables finding an optimal solution satisfying necessary optimality conditions. The presented optimization approach allows for including issues which cannot be accounted for by commercial topology optimization software. The introduced theory provides an estimated solution, which is then validated by an analysis of a 3D finite element model.