In discrete topology optimization, state of the material is either solid or void and the intermediate state of the material does not affect the topology certainty. The existence of corners in the topology leads to unsmooth boundaries in topology solutions. The unsmooth boundaries are the major problem in any topology solution. These corners cannot be exterminated completely, but can be extenuated using corner handling strategy. The approach of mitigating the 90-degree corners to 135-degree corners is technically termed as “corner handling strategy.” The subdivision of design domain causes corners in the topology solutions, which cannot be eliminated completely. A subdivision approach is acquainted in this research to eliminate the unsmooth corners. As corners are unavoidable in topology solutions obtained by subdividing the design domain using regular triangles, a subdivision approach of triangles with curved hypotenuse are used. The complete design area is divided into quadrilateral design entities and each of these quadrilateral design entities are subdivided into triangular analysis elements with curved flanks. All boundaries and connections are smooth by using the triangular analysis cells with a curved hypotenuse. The unsmooth corners are eradicated by the introduction of a subdivision model in this research of discrete topology optimization of structures. Two structural discrete topology optimization examples are used to demonstrate this subdivision model and the conclusions for these examples are drawn using topology optimization formulation and an optimization algorithm. The optimization algorithm used is Genetic Algorithm.
January 22, 2016
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