Investigation On The ESO Method Based On Enumeration Algorithms

With the rapid development of society, it requires increasing higher performance for each structure in various engineering fields, which results in more and more complicated factors being taken into consideration. Thus, it is so difficult for the traditional structure design method to deal with these problems. Meanwhile, it poses much more challenges for the traditional design algorithms with the increasingly emerging of innovative structures and novel materials. In this case, modern optimization method comes out at the same time. Among these optimal design tools, evolutionary structural optimization(ESO) method is extensively used in the structural optimization for its simple concept and idea, and it is easy to implement in the FEA package.Since the initial introduction of ESO method, it has experienced rapid development and applied in a wide range of structural design problems including stress, stiffness, frequency and buckling optimization. It is considered, however, as a fully heuristic method without any rigorous mathematics proof and there is not any rational relation between its criterion function and objection function. Therefore, it is lack of rationality by taking the Von Mises stress and strain energy as its optimal criterion and the efficiency determination. Thus, it is also unreasonable to remove such inefficient elements from the design domain since these elements ‘removal cannot ensure the structure converge to the final optima. The Tie-beam example, proposed by Rozvany in order to query the rationality of ESO method, also illustrates this shortcoming.Based on the above discussion, as for the stiffness optimization problem, the enumeration algorithm is introduced into the original ESO method so that it can rectify the break-down of ESO. when there is a sharp increase in the mean compliance of the structure, the iteration of ESO then should be stopped, instead enumeration algorithms is introduced into the proposed method in order to find out the most inefficient elements at the present iteration. By selecting all the combinations of elements under the current volume constraint using enumeration algorithms, then calculating each objection function when removing one of these element components, we can finally determine which elements combination are the most inefficient at the current iteration and remove these elements. After that, we can return to the original ESO procedure. A wide range of problems can be obtained optimal topologies as same as ESO’s solutions by the proposed method combining with enumeration algorithms. This illustrates that the proposed method can be completely void the failure of ESO in Tie-beam example result from the wrong elements removal. Noticeable, it has little influence on the initial optimal parameters and the mesh size.In terms of the low efficiency of the proposed method, this dissertation has introduced one improve strategy into the implementation of enumeration algorithms. Through defining an amplification coefficient λ of inefficient elements based on the original ESO method, then we can use enumeration in this local area. By selecting all the combinations of elements in this local inefficient area using enumeration algorithms, then calculating each objection function when removing one of these element components, we can finally determine which elements combination are the most inefficient in the inefficient area and remove these elements. This improvement in the way of implementation of enumeration makes the proposed method work smoothly. It is shown that all the traditional stiffness optimization problems can be solved by this proposed simple method and the final topologies have smaller weights than the existing solutions obtained by ESO method. Therefore, the proposed method has a strong ability to find out optimal topologies and can be used extensively.