Shape design for thin-walled beam cross sections using rational B splines

Abstract

Shape optimization of thin-walled beams is discussed. The cross-sectional shape of the beam is described by nonuniform rational B-spline curves. The optimization problem is defined in terms of cross-sectional properties and stresses. Design variables are the control parameters of the rational B-spline curves and the wall thickness of the beam. Cross-sectional properties and stresses are obtained from the elasticity solution for the beam. Consideration of torsion and pure shear requires the solution of Laplace equations which is accomplished using finite elements. A design sensitivity analysis is given for the cross-sectional properties and stresses. A sample problem is presented to illustrate the formulations.