Expressions for membrane stress resultants are derived from a nonlinear membrane theory which eliminates the undesirable infinities in one of the two displacements and the rotation of the normal to the middle surface as predicted by linear membrane theory. The advantages of these results are that they remain meaningful for very small pressures and that no further manipulation is necessary to obtain stress resultants for all pressures and circular torus configurations. A variational equation is derived for the determination of the modes and natural frequencies of vibration of a torus whose walls have no bending stiffness and which are prestressed by internal pressure. Author
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