الفهرس | Only 14 pages are availabe for public view |
Abstract Most of the research works dedicated to the size optimization of trusses subject to dynamic loading have been devoted to the maximization of the fundamental frequency of the truss (i.e. increasing rigidity and/or reducing its mass). Much less work considered the dynamic stresses resulting from actual dynamic loading. In practice, most truss designers are interested in the mass minimization of the truss while constraining the stresses to a certain limit to safely sustain the loads. This does not necessarily correspond to the maximization of the fundamental frequency of the truss. In the present work, the sizing optimization problem of undamped trusses subjected to dynamic loading is investigated, aiming to minimize the truss mass while maintaining the dynamic stresses to certain appropriate safe limits. The Finite Element Method is utilized for modelling the mechanical behaviour of trusses. The investigation aim is achieved by comparing three optimization models which are proposed and examined by two simple examples. The first model is the minimization of the truss mass while maintaining the dynamic stresses within specific limits. The second is the minimization of the absolute value of the dynamic compliance while its mass is constrained to the mass of the optimal truss obtained in the solution of the first model. The third is the minimization of the maximum overall dynamic strain energy while its mass is constrained to the mass of the optimal truss obtained in the solution of the first model. The results have shown that the first model achieves the objective in relatively long time due to the large number of constraints which is equal to twice the number of the truss bars. Based on this outcome, an optimization procedure, aiming to minimizing the truss mass is proposed. This procedure starts with finding an improved initial solution either by the second or the third model, and then the first model is used. The proposed optimization procedure is applied by numerical examples involving plane and space trusses up to 582 bars. Numerical examples revealed that the truss mass is minimized with remarkable reduction in the computational costs by implementing the proposed procedure. Also in this work, a mathematical model for sizing optimization of undamped trusses subjected to varying load leading to fatigue is proposed. The combined effect of static and dynamic loading is considered. An optimization model is developed to maximize of the safety factor by changing the configuration of the truss bars cross-sectional areas. A new quantity ‘Equivalent Fatigue Strain Energy’ combining the effects of static and dynamic stresses is proposed. This quantity is used as a global measure of how far fatigue failure is. This assumption is verified through two simple examples. The predictions of the presented Finite Element model are verified experimentally through measurements on a real simple truss. The truss is subjected to different static loads and the deflections are measured and compared to those predicted by the Finite Element model. Results show a fair agreement between the experiments and the model and deviations are justifiable. Maintaining the same stress levels for the given dynamic loads within the safe limits, the proposed optimization model is used to optimize the design of the tower of a wind turbine as a case study for structures subjected to dynamic loading. The resulting optimized structure is almost 60% less in mass than tubular towers. |