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A method of symmetrizing functions and its application to certain problems in elasticity theory for non-uniform bodies. (English. Russian original) Zbl 0724.73046
J. Appl. Math. Mech. 52, No. 3, 377-382 (1988); translation from Prikl. Mat. Mekh. 52, No. 3, 486-492 (1988).
A symmetrization operation is introduced for functions defined in bounded domains and vanishing on the boundary. The properties of the operation introduced are studied and its connection with Schwarz symmetrization is analyzed. Examples are considered of the application of the apparatus developed for constructing isoperimetric estimates in problems of torsion and longitudinal vibrations of an inhomogeneous rod. The stiffness estimate obtained in the problem of the torsion of a nonuniform rod is a generalization of the Polya isoperimetric inequality known in the theory of elasticity for the stiffness of a uniform rod under torsion.

MSC:
74B99 Elastic materials
74H45 Vibrations in dynamical problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
49Q20 Variational problems in a geometric measure-theoretic setting
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References:
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