Complementary Potentials of Finite Elasticity

by Gerald Wempner,

Abstract: The principles of virtual displacements and forces are embodied in a functional P. The complementary potential Pc is defined by the equation; Pc = P - Pw where Pw denotes the potential. The stationarity of functional P holds for all continuous bodies whereas the extremal properties of the complementary functionals, Pw and Pc, hold for continuous elastic bodies. The extremal properties of the latter have been exploited only in the case of 'infinitesimal' deformations. Indeed, until the work of Fraeijs de Veubeke and Koiter in 1972 and 1973, respectively, a stationary theorem and the requisite complementary potential were not available for finite deformations.

Subject Headings: Elastic analysis | Deformation (mechanics) | Displacement (mechanics) | Case studies

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