Research On The ESO Heuristic Algorithm Based On Virtual Materials

With the rapid development of science technology and production activities, thetraditional structure design method has been unable to meet complex engineeringstructure design requirements. The development of computer technology and finiteelement theory provides a strong support for structure optimization. Because of itssimple ideas and obvious effect, easy to implement, Evolutionary StructuralOptimization(ESO) method has become the new research direction in the field ofstructural topology optimization.Although the ESO method has made a lot of research results in the aspect oftheoretical research and engineering application, but the algorithm is considered to be acompletely heuristic algorithm, the lack of rigorous mathematical theory. Differentsensitivity calculation values based on stress, stiffness and so on determine theinefficient element in the structure and then delete them in various algorithms by thetheory of ESO. To delete and return the element by the only calculated sensitivity valueslacks verification process, which can’t determine whether the deleted element to ensurethat the structure doesn’t fail to be retained element. The Tie-beam example byproposed by Rozvany, which is used to question the effectiveness of the ESO methodalso shows that original ESO method would delete element by mistake to lead thisalgorithm invalid.In terms of stress constraints, through the introduction of virtual materials,changing the elastic modulus of element determined by the sensitivity to be deleted,which simulates materials to yield and detects the material yield stress redistributionphenomenon, this paper forms the ESO heuristic algorithm based virtual material bystress constraint. By introducing virtual stiffness, stress variation caused by the changeof element stiffness matrix is measured, which provides the quantitative basis for thealgorithm. If the stress of element to be deleted reduces by the introduction of virtualmaterial, which shows occur the phenomenon of stress redistribution and transfer theinternal load, the element to be deleted is inefficient to delete, if the stress remainsunchanged, then the element can’t be deleted. By the validation of example, theheuristic algorithm of this paper can not only get the optimization results of originalESO method, but also avoid the failure of original ESO in particular operator. At thesame time, the influence of the heuristic algorithm is controlled by various parameters is lower than original ESO method obviously.According to stiffness optimization problem, through the comparison of the strainenergy of element to be deleted, which is whether greater than the threshold value todetermine the element removed or reserved, this paper constructs the heuristic algorithmbased virtual material by stiffness constraint. The algorithm not only can solve thefailure of Tie-beam example, and get a good optimization results. Through thevalidation of classical examples, it shows that the algorithm is very universality.