Optimal thickness distribution of stepped nonlinear Gao beam

Abstract We present an optimal shape design problem of a transversely and axially loaded nonlinear stepped elastic beam with piecewise constant thickness distribution. The nonlinear beam model proposed by D.Y. Gao in 1996 is considered for modelling the state problem. The objective of the optimization is to find the thickness distribution to maximize the stiffness of the beam subjected to geometrical constraints, namely the preservation of volume is imposed. The stiffness is characterised by the compliance cost functional. The existence of solutions of the optimization problem and convergence properties of discretization using finite element approach is analysed. The theory is illustrated by numerical results.