Upper and Lower Bounds in Finite Element Analysis of Aerospace Structures

The proposed research is intended to develop a new analysis for stresses and displacements in aerospace structures based on the combined conventional Displacement (Stiffness) Method and on a new formulation of the Force Method developed by the principal investigator. Since some of the elements used currently in the Displacement Method violate equations of stress equilibrium, an additional analysis by the Force Method in which element stresses do not violate the equations of equilibrium will provide bracketing on the solution (i.e. upper and lower bounds on stresses and displacements) thereby ensuring greater confidence in numerical results. Since the Force Method stresses are derived directly from internal forces they are more accurate than the stresses in the Displacement Method which requires differentiation of the displacement field within the element. The method will be illustrated on a typical multispar wing structure. The current project at this time will address only the overall concept of modifying existing computer codes; however, the actual modification of a specific commercial code or codes and subsequent commercialization will be addressed as a follow-on project after the completion of Phase I.