### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 3aSA10. Direct global stiffness matrix method for thin cylindrical shell
dynamics.

**Mark A. Hayner
**

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J. Robert Fricke
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*MIT, Rm. 5-435, 77 Massachusetts Ave., Cambridge, MA 02139
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This paper introduces the direct global stiffness matrix (DGSM) method for
analyzing the dynamics of cylindrical shells with axial symmetry. The dynamic
stiffness matrix of a straight, circular cross-section cylindrical element is
formulated in terms of ring forces and displacements at each end on a per
circumferential mode basis. The stiffness matrix is based on an exact wave-type
solution of the thin shell Donnell equations. More complicated shell systems are
analyzed by assembling any number of cylindrical elements. For example, a
cylinder with a gradual variation in radius may be modeled by a series of shell
elements welded together at their ends. Total system dynamics are found at any
given frequency by inverting the global system matrix formed from the individual
stiffness element matrices and summing over circumferential mode number. Results
for a test case are presented to demonstrate and verify the implementation.
[Research sponsored by ONR.] [sup a)]E-mail: hayner@mit.edu