Magnetostatic deformation experiment: Bending of a thin plate

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The Euler buckling formula is a simple deduction from the Bernoulli-Euler theory of bending. Perhaps a correct magnetoelastic buckling formula with be obtained as a simple deduction from a correct theory of magnetoelastic bending. The present investigation is a first step toward creating such a theory. Thin rectangular plates of solft steel were rigidly fixed at one end and caused to bend into a cylindrical shape by applying a uniform magnetic field whose direction made a small angle (five degrees) with the normal to the undeformed plate surface. Strain measurements and field measurements were made along top and bottom surfaces of the plate. A bending-moment diagram was calculated from the strain measurements and a bending-moment diagram was calculated from field measurements, using the integrand of the first Maxwell stress formula to calculate the force distribution acting on the plate. To get agreement between the two diagrams it was necessary to add a concentrated couple and transverse force (not revealed by the field measurements) at the free end of the plate. The postulated couple and force alone accounted for approximately 30 percent of the bending moment values calculated from strains. We conclude that if the external magnetic field at the surface of a magnetic body cann be calculated correctly, the integrand of the Maxwell formula will corretly give the force distribution over the surface, and classical elasticity theory will then given correctly the elalstic deformation. © 1989 Society for Experimental Mechanics, Inc.

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Experimental Mechanics