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A Derivation Procedure for the Dynamic Flexibility Matrix of a Triangular Bending Element

Published online by Cambridge University Press:  04 July 2016

J. Robinson
J. Robinson*
Affiliation:
Department of Civil Engineering, University of Southampton now at Structural Mechanics and Materials Dept, Lockheed-California
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Of the two main finite element approaches, the displacement method has progressed more rapidly than the force method in the area of element representation. Many authors have contributed to the displacement method with both static and dynamic stiffness matrices for beam elements, plane stress elements and plate bending elements. The plane stress and bending elements being rectangular, triangular or quadrilateral in form. A dynamic stiffness matrix consists of a static stiffness matrix and a mass matrix. In the force method, .static flexibility matrices have been developed for beam elements and plane stress elements. However, static flexibility matrices for plate bending elements have only recently been published (Kaufman and Hall, Morley, Robinson, Przemieniecki). For the past few years, the author has been investigating the rank force method for structural vibration analysis. In ref. 6 a dynamic flexibility matrix is presented for a beam element. This matrix consists of a static flexibility matrix and an inverse mass matrix. Ref. 5 contains the derivation of a dynamic flexibility matrix for a rectangular plate element in bending, twisting and shear. The author, in collaboration with Petyt, demonstrated how a dynamic stiffness and flexibility matrix can be extended to include material damping.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 74 , Issue 712 , April 1970 , pp. 327 - 330
Copyright
Copyright © Royal Aeronautical Society 1970 

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References

1. Timoshenko, S. P. and Woinowsky-Krieger, S. Theory of Plates and Shells. McGraw-Hill Book Co Inc, New York, 1959.Google Scholar
2. Sechler, E. E. Elasticity in Engineering. John Wiley & Sons Inc, New York, 1952.Google Scholar
3. Jaeger, L. G. Elementary Theory of Elastic Plates. The MacMillan Company, New York, 1964.Google Scholar
4. Mead, D. J. The Effect of a Damping Compound on Jet-Efflux Excited Vibrations. Aircraft Engineering, March 1960.Google Scholar
5. Robinson, J. A Study of the Rank Force Method for Structural Matrix Vibration Analysis. PhD Thesis, University of Southampton, 1967.Google Scholar
6. Robinson, J. Eigenvalues of Collinear Beams Structures using Finite Element Techniques and Various Dynamic Representations for the Structural Elements. Wiss Z Hochsch Archit Bauwes, Weimar, 1967 Heft 3. Paper pre sented at the 4th International Congress on the Application of Mathematics in Engineering, Weimar, East Germany, June 1967.Google Scholar
7. Robinson, J. Static Flexibility Matrices for a Rectangular Plate Element in Bending, Twisting and Shear. Uniform and Non-Uniform Distributed Loading. Paper presented at the International Symposium on Experiences with Com putation Techniques for Bridge Erection, Research Institute of Civil Engineering, Bratislava, Czechoslovakia, October 1968. (Also, Civil Eng Dept Report No CE/15/68, University of Southampton.)Google Scholar
8. Robinson, J. Structural Matrix Analysis for the Engineer. John Wiley & Sons, Inc, New York, 1966.Google Scholar
9. Robinson, J. and Petyt, M. Finite Element Techniques in Structural Vibrations. Book in preparation.Google Scholar
10. Robinson, J. and Petyt, M. Dynamic Analysis of Real Structures using the Rank Force Method. Submitted for publication.Google Scholar
11. Kaufman, S. and Hall, D. B. Bending Elements for Plate and Shell Networks. AIAA Journal, Vol 5, No 3, March 1967.Google Scholar
12. Morley, L. S. D. A Triangular Equilibrium Element with Linearly Varying Bending Moments for Plate Bending Problems. Journal of the Royal Aeronautical Society, Vol 71, p 715, October 1967.Google Scholar
13. Morley, L. S. D. The Triangular Equilibrium Element in the Solution of Plate Bending Problems. The Aeronautical Quarterly, Vol XIX, May 1968.Google Scholar
14. Przemieniecki, J. S. Theory of Matrix Structural Analysis. McGraw-Hill Book Company, New York, 1968.Google Scholar
15. Robinson, J. Element Static Flexibility and Stiffness Matrices for the Finite Element Analysis of Beam, Plate and Shell Structures (Part I, Plane Elements). ISVR Report No 196, September 1967.Google Scholar