Reverse adaptivity?a new evolutionary tool for structural optimization

This paper presents a new method, Reverse Adaptivity, for automatically generating solutions to initial design and redesign problems. The method is based on a combination of existing adaptive finite element methods and evolutionary structural optimization methods. The usual difficulties inherent in structural optimization problems, and the shortcomings of the evolutionary methods in tackling these difficulties, are reviewed as a prelude to discussing Reverse Adaptivity. Once the initial finite element problem is defined, the method proceeds with reverse adaptive analysis, which refines low stress regions of the finite element mesh by element subdivision. Following this, any low stress subdivided elements are removed and the process is repeated. With successive decrements of adapted element size, the process satisfies many of the shortcomings of existing evolutionary optimization methods, yet is simple to understand and can be readily implemented. The results produced by the method are superior to those produced by existing methods, yet can be obtained with highly practicable computational resources. As a demonstration, solutions to a number of well- known classical problems are presented, and highlight the method's ability to distinguish new classes of solutions for some problems. Full implementation and parameter details are also presented.