The Transient Dynamic Analysis of Thin Shells by the Finite Element Method
Report Number: AFFDL TR 71-160 p. 479-518
Author(s): Key, Samuel W., Beisinger, Zelma E.
Corporate Author(s): Sandia Laboratories
Date of Publication: 1973-12
Pages: 41
DoD Task:
Identifier: This paper is part of a conference proceedings. See AD0785968
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.
Provenance: Bombardier/Aero
Author(s): Key, Samuel W., Beisinger, Zelma E.
Corporate Author(s): Sandia Laboratories
Date of Publication: 1973-12
Pages: 41
DoD Task:
Identifier: This paper is part of a conference proceedings. See AD0785968
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.
Provenance: Bombardier/Aero
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