Minimum weight design of beams with inequality constraints on stress and equality constraints on deflection

Minimum weight design of beams with inequality constraints on stress (shear and bending) and an equality constraint on deflection has been studied in this thesis. Analytical solutions are obtained for a cantilever beam loaded first with a concentrated moment and then with a concentrated load at its free end for a given tip deflection. These two problems and a simply supported beam loaded with a concentrated load for a given mid point deflection are then solved numerically using the Convex Programming Algorithm and the Flexible Tolerance Method. The results obtained by the analytical and the two numerical methods for several values of the specified deflection for each example problem have been tabulated at the end of Chapter V for comparison.