Abstract
This paper furnishes a simple constructive proof of the equivalence of integral laws of motion for continua to the Principle of Virtual Work. The approach used is designed to avoid the artificiality of introducing the classical equations of motion in an intermediate step. The hypotheses employed are virtually the weakest possible that are consistent with the requirement that the integrals appearing in these formulations make sense as Lebesgue integrals. Particular attention is devoted to the treatment of boundary conditions, which may assume a very general form.
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Antman, S.S., Osborn, J.E. The principle of virtual work and integral laws of motion. Arch. Rational Mech. Anal. 69, 231–262 (1979). https://doi.org/10.1007/BF00248135
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DOI: https://doi.org/10.1007/BF00248135