OPTIMAL LOCATIONS OF INTERNAL RESTRAINTS IN BEAMS AND PLATES AGAINST BUCKLING OR VIBRATION

Abstract

In this thesis, a class of structural optimization problems - restraint location optimization is studied. More specifically, the study considers the optimization of internal restraint locations in beams and plates for maximum buckling load or maximum fundamental frequency. These restraint location optimization problems are somewhat difficult to solve if discretion techniques (such as the finite difference method, finite element method, collocation method) were to be employed for the buckling or vibration analyses. This is because the positions of the discretization nodes must be changed continually so as to coincide with the restraint locations during the optimization iterations. However, if a continuum method, such as the Rayleigh-Ritz method, was adopted instead for the analyses, then this requirement of node coincidence with the restraint locations can be avoided. By incorporating a computerized version of the Rayleigh-Ritz method as the buckling and vibration analysis subroutine in the main optimization program, the restraint location optimization problems considered may be solved readily. Until now, both the internally restrained beam and plate problems considered herein have not been investigated. In the beam problem, the restraints treated are either rigid braces or internal roller supports which prevent either lateral or twists displacements or both at the restraint points. The elastic lateral buckling load of transversely loaded beams is to be maximized with respect to the restraint locations along the beam length. In the plate problems, the considered restraint takes the form of either a line support or a ring (circular or elliptical shape) support which imposes a zero transverse displacement along the restraint length. The buckling load of loaded plates or the fundamental frequency of unloaded plates 1s to be maximized with respect to the parameter defining the location and shape of these restraints. In view of a simple and efficient numerical method based on the Rayleigh - Ritz method for analysis and the Hooke and Jeeves pattern search method for optimization, extensive sets of optimal solution for internal restrained beams and plates are obtained. These new optimal results are either presented in tabulated or in graphical form. Such optimal solutions are useful to designers and researchers because they provide a basis for measuring the efficiency of any other design and show the direction to be taken towards maximizing the structural performance. Sensitivity studies are also carried out to investigate the effect of restraint location (and shape as in the case of ring supports) on the buckling loads or fundamental frequency. For these studies, beams and plates with restraints at specified locations are analysed and compared with the optimal ones. In general, the buckling load or fundamental frequency is significantly affected by the location (and size) of the supports and departure from the optimal solution may result in a great reduction in the buckling load or fundamental frequency.