Load Diffusion in Linear and Nonlinear Solid Mechanics

Abstract

Abstract : The asymptotic behavior of solutions in solid mechanics is a broad topic of considerable mathematical and technological interest. Safe efficient operation of aircraft structures and components requires accurate assessment of the rate of diffusion of end effects, particularly for anisotropic and composite materials. This requires study of the spatial decay of solutions of elliptic partial differential equations (or systems of equations). In this research. we have investigated a sequence of boundary-value problems for second-order and fourth-order elliptic partial differential equations. Both linear and nonlinear, isotropic and anisotropic problems have been considered. The results of such investigations have widespread impact on the AFOSR mission. In particular, rigorously obtained asymptotic estimates for the rate of load diffusion in solids are immediately applicable in engineering analysis and design and have been used, for example, by the Boeing Commercial Airplane Group in application to composite structures.