Optimization process in tall beams

Some principles presented in previous papers and some procedures to be followed to optimize structural components are briefly reviewed. They all deal with the removal of material from load-free inside boundaries to simultaneously decrease the weight and increase the strength. Some of the problems that may be found when the designer tries to optimize structural components by removing material from inside the stressed field as opposed to removing material from free boundaries are studied here. Some solutions for the case of tall beams are presented. Emphasis is put on the transformation of the solutions and of the associated stress distributions—all of which are improvements of the original design, and every one of which could be considered optimum for particular design constraints. The approach followed can be used just as well for photoelasticity as for numerical methods. It is claimed, however, that in cases similar to the ones analyzed, photoelasticity permits one to obtain a faster, less expensive and more reliable solution than numerical methods. Some of the redesigned shapes show 38 percent less weight than the original design, without increase in the maximum tensile stress.     

Photothermoelastic analysis of bonded propellant grains

A two-dimensional model of the transversal cross section of a bonded rocket propellant grain was subjected to uniform and steady thermal loading and, alternatively, to mechanically applied uniform radial displacements on the outer boundary. The optimization of perforation contours (attained in previous research programs by applying uniform pressure on the outer boundary of the grain model) was confirmed for both types of thermal loading. The concentration factor at the fillets of the inner contour was determined. An attempt was made to predict the maximum strain in the actual propellant subjected to the same thermal conditions. The material used for the model was a urethane rubber. The thermoelastic properties of the model material were determined.