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

Item

Title
On Derivation of Stiffness Matrices With C° Rotation Fields for Plates And Shells
Description
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.
Creator
Utku, Senol
Abstract
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.
Corporate Author
Duke University
Report Number
AFFDL TR 71-160 p. 255-274
Report Availability
Full text available
Publisher
Wright-Patterson Air Force Base, OH : Air Force Flight Dynamics Laboratory, Air Force Systems Command and Air Force Institute of Technology, Air University
Date
1973
Type
article
Date Issued
1973-12
Provenance
Bombardier/Aero
Distribution Classification
1
Distribution Conflict
No
DTIC Record Exists
No
Format
1 online resource (20 pages) : ill.
Extent
20
Identifier
AD0785968
Is Part Of
Proceedings of the Third Conference on Matrix Methods in Structural Mechanics: Proceedings of the Conference held at Wright-Patterson Air Force Base, Ohio 19-21 October 1971
Media
AFFDLTR71-160article09.pdf

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Items with "Has Part: On Derivation of Stiffness Matrices With C° Rotation Fields for Plates And Shells"
Title Class
Proceedings of the Third Conference on Matrix Methods in Structural Mechanics: Proceedings of the Conference held at Wright-Patterson Air Force Base, Ohio 19-21 October 1971