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ON LINEAR EQUATIONS OF ISOTROPIC ELASTIC PLATES AND SHELLS.
Scientific rept. no. 2,
POLYTECHNIC INST OF BROOKLYN N Y
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A generalized Hamiltons principle and the associated variational equation of motion for nonlinear elasticity theory were given in a previous paper. Presented in this paper is a modified linearized version, from which the corresponding variational principle for an isotropic shell of arbitrary thickness is deduced by means of the series expansion method. The complete system of shell equations are obtained as the Euler equations. These reduce to Mindlins result for isotropic plates as a special case. When the infinite series is truncated, the first-order approximation yields for the shell the stress equations of motion of the usual type, the strain-displacement relations given previously by Sanders, and, with the exception of those for transverse shearing stresses and strains, the stress-strain relations that are reducible to those given by Reissner. Author
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