Optimization of geometrical parameters of gable rectangular beam

Abstract

Optimization of geometrical parameters of gable rectangular beam

Karamysheva A.A., Yazyev B.M., Chepurnenko A.S., Yazyeva S.B.

Incoming article date: 03.08.2015

We solved the problem of optimizing the gable beam by minimizing the strain energy at constant volume. The problem reduced to an integral equation for determining the optimum angle of the beam. This equation was solved numerically by the method of bisection. Integral was calculated using the method of trapezoids. Solution was made in software package Matlab. The optimum angle depends on the width of the cross section b, and the volume of the beam. It was found that with increasing of width of the cross section the optimum tilt angle decreases. Also the volume increases by increasing the width of the beam.

Keywords: optimization, gable beam, strain energy, variable rigidity, minimum volume, method of bisection