SUMMARYThis 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 "nite element methods and evolutionary structural optimization methods. The usual di$culties inherent in structural optimization problems, and the shortcomings of the evolutionary methods in tackling these di$culties, are reviewed as a prelude to discussing Reverse Adaptivity. Once the initial "nite element problem is de"ned, the method proceeds with reverse adaptive analysis, which re"nes low stress regions of the "nite 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 satis"es 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 wellknown 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.

Demonstrates the simple but effective application of a standard finite element program (PAFEC), and the associated geometric modelling code (PIGS), to the improvement of the design of an engineering component. The technique adopted involves augmenting material around zones of high stress and removing material in zones of low stress. This evolutionary procedure is related to the behaviour of bones in animals. The essentially two‐step procedure involves; finite element analysis of the preliminary component design using PAFEC; and, definition of a new geometry using PIGS, with selected stress contours giving an indication of the new shape. The technique, which proceeds iteratively, was first tested successfully on some classical academic optimisation problems. Its subsequent application to the industrial problem of a twin chamber pressurised extruded aluminium section, the primary component of an air drying system, resulted in material savings of up to 50 per cent and an associated drop in the maximum von Mises stress of 45 per cent. While this method does not determine the optimal structural form, it does generate substantial improvements in terms of material usage and reduced maximum stresses. It has the advantage that it can be used by any competent engineer with a working knowledge of the strength of materials, finite elements and structural form.

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