Abstract
Expressions for the physical tangential and bending strains of nonlinear thin elastic shell theory in nonorthogonal coordinates are derived in a new, relatively compact form. The geometric and physical significance of the results is interpreted, where possible. In addition, the quantities describing the differential geometry of a deformed surface are also given. All results obtained are exact in the sense that no restrictions are imposed on the magnitude of strains in the derivations. The expressions for the nonlinear case are compared with the corresponding formulas of the linear theory. The results obtained together with further results to be published on the strains of the parallel surface, the statics of shells, and constitutive relations find direct application in the analysis of the nonlinear behavior of thin shells.
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