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Complementary Potentials of Finite Elasticity

by Gerald Wempner,



Document Type: Proceeding Paper

Part of: Engineering Mechanics

Abstract:

The principles of virtual displacements and forces are embodied in a functional P. The complementary potential P_c is defined by the equation; P_c = P - P_w where P_w denotes the potential. The stationarity of functional P holds for all continuous bodies whereas the extremal properties of the complementary functionals, P_w and P_c, 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) | Mathematics | Engineering mechanics | Case studies

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