A toolbox for partial differential equation based optimization with an application to optimizing materials processing

BEAM has identified an opportunity for the development of systematic design procedures for multi-step forging. These procedures will be marketable to the forging industry in the form of robust and open computer codes capable of dealing with multi-stage forming processes and capable of designing shape as well as internal states such as stress and micro-structure. The proposed development will impact the affordability of Air Force systems, both the affordability of acquiring new systems and the affordabilaity of maintaining existing systems. This will come in the form of areduction in the costs of forging, through a reduction in the efforts of trial and error die and process development, and in the development of new precision forging capabilities that may replace machining. The propsoed development will impact performance of Air Force systems through optimal design of forgings. We can expect a reduction in the weight of piecesd and an increase in their strength and an abilaity to forge new materials that now cannot be practically forged. The technical objectives of this work are as follows: create a mathematical framework based on PDE sensitivity capable of dealing with multi-step forming processes; populate the framework with the correct physical models capable of generating results of significance to the forging industry; package the mathematical and mechanical knowledge developed in this effort in an open robust software tool that can be further developed into a commercial software paroduct and complete that development in Phase II; and develop an out reach program and dialogue with forgers performing work for the Air Force.