Analytical Solution of two Traction-Value Problems in Second-Order Elasticity with Live Loads

We present a generalization of Signorini's method to the case of live loads which allows us to derive approximate solutions to some pure traction-value prob-lems in nite elastostatics. The boundary value problems and the corresponding compatibility conditions are formulated in order to determine the displacement of the system up to the second-order approximation. In particular, we consider the case of homogeneous and isotropic elastic bodies and we solve the following two pure traction-value problems with live loads: (i) a sphere subjected to the action of a uni-form pressure eld; (ii) a hollow circular cylinder whose inner and outer surfaces are subjected to uniform pressures. Then, starting from these solutions, we sug-gest experiments to determine the second-order constitutive constants of the elastic body. Expressions of the second-order material constants in terms of displacements and Lamé coefcients are determined. Acknowledgments In the rst place, I wish to express my sincere gratitude to my Advisor Dr. Romesh C. Batra for his patient and careful guidance. Then, I thank Dr. Edmund G. Henneke and Dr. Surot Thangjitham for serv-ing on my committee and taking the time to read my thesis. I would like to exten