The objective of this research is to expand and improve the mathematical description and quantitative understanding of incremental compounding and bending and processes used in the manufacture of compound-curved metal plates from flat sheet stock. The method is based on differential geometry and finite-element methods. It will provide lofting of accurate boundary curves to be cut from the flat material, as well as quantitative compounding instructions and potential feedback control, such that plates can be formed which are applicable and/or fully conformed to specific preplanned portions of a designed surface, with minimal or zero field trim. Three specific areas are addressed: (1) discovery of more efficient and accurate numerical methods for solution of the nonlinear finite-element equations; (2) formulations and solution of a finite-element characterization of bending, the extrinsic geometry of the plate; and (3) finite-element analysis of residual membrane stresses introduced during compounding, and quantification of their effects on the compounding process.
