On Derivation of Stiffness Matrices With C° Rotation Fields for Plates And Shells

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Report Number: AFFDL TR 71-160 p. 255-274
Author(s): Utku, Senol
Corporate Author(s): Duke University
Date of Publication: 1973-12
Pages: 20
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Identifier: This paper is part of a conference proceedings. See AD0785968

The use of C° deflection (displacements and rotations) fields over triangular meshes in the middle plane of a plate for the total potential energy functional always requires the retention of the transverse shear strain energy in order to have the stiffness matrix of the supported structure non-singular when the degrees of freedom in the transverse direction are not suppressed. This situation is similar to the case of sandwich plates and shells where the transverse shear strain energy is retained because of its importance. Since the transverse shear strain energy is a function of transverse shear moduli, rather than in-plane shear modulus, it should be computed directly from the deflection fields, but not from the corresponding stress couple fields. This paper shows the method of computation of transverse shear strain energy directly from the deflection fields. Applying the method to C° deflection fields, a mathematical foundation is laid for a widely used plate and shell element by Martin, Melosh and Utku.

Provenance: Bombardier/Aero

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