The Transient Dynamic Analysis of Thin Shells by the Finite Element Method

Item

Title
The Transient Dynamic Analysis of Thin Shells by the Finite Element Method
Description
A simple central difference time integration scheme along with a diagonal mass matrix is used to examine the transient dynamic response of linear elastic thin shells. The numerical stability of the explicit time integration scheme is examined and two inequalities are provided, the strongest of which defines a critical time step. Only calculations using a time step less than the critical time step are meaningful. Above the critical time step, the calculations diverge. The method is called conditionally stable. One inequality is based on membrane behavior and the other on bending behavior. Both of them are in terms of minimum mesh dimensions, shell densities and membrane and bending moduli. The diagonal mass matrix is generated from a consistent mass matrix in a rational manner. Three calculations are included to show the results of this work.
Creator
Key, Samuel W.
Beisinger, Zelma E.
Abstract
A simple central difference time integration scheme along with a diagonal mass matrix is used to examine the transient dynamic response of linear elastic thin shells. The numerical stability of the explicit time integration scheme is examined and two inequalities are provided, the strongest of which defines a critical time step. Only calculations using a time step less than the critical time step are meaningful. Above the critical time step, the calculations diverge. The method is called conditionally stable. One inequality is based on membrane behavior and the other on bending behavior. Both of them are in terms of minimum mesh dimensions, shell densities and membrane and bending moduli. The diagonal mass matrix is generated from a consistent mass matrix in a rational manner. Three calculations are included to show the results of this work.
Corporate Author
Sandia Laboratories
Report Number
AFFDL TR 71-160 p. 479-518
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 (41 pages) : ill.
Extent
41
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
AFFDLTR71-160article16.pdf

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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

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