Mathematical Sciences: Duality Theory in Finite Deformation Nonsmooth Mechanics and Numerical Approaches

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Gao 9400565 Based on the complementarity theory developed by Gao- Strang in 1988-89, the objective of this proposed research is to offer a comprehensive study on the duality theory in nonsmooth mechanics and the related numerical methods for finite deformation systems. Topics will include: (1) Nonsmooth plastic flow and structural limit analysis; (2) Nonlinear buckling analysis for plates and shells; (3) Control problems and optimal design of smart materials and structures; (4) Complementary finite element method for nonsmooth optimization. Finite deformation nonsmooth mechanics has been found more and more important applications in smart structural analysis, civil and aerospace engineering. Direct method for solving nonlinear and nonsmooth systems has always presented serious difficulties for mathematicians and engineers. The dual approach andcomplementary finite element method, however, possess a great of advantages. We can expect that the results of this proposed research will provide new insight to the nonsmooth mechanics, variational methods, finite deformation theory, nonlinear optimization theory and numerical methods.