Exact determinant for infinite order FEM representation of a Timoshenko beam-column via improved transcendental member stiffness matrices

International Journal for Numerical Methods in Engineering

Volumn 59, Issue 10, 2004, Pages 1355-1371

  Williams, F W ^a   Kennedy, D ^b   Djoudi, M S ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Buckling; Eigenproblem; Member stiffness determinant; Structures; Transcendental; Vibration; Wittrick Williams algorithm

Indexed keywords

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; LOAD TESTING; NATURAL FREQUENCIES; RIGIDITY; SHEAR STRESS; STRUCTURAL MEMBERS;

SHEAR RIGIDITY;

STIFFNESS MATRIX;

EIGENVALUE;

EID: 1542749187     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.919     Document Type: Article

References (8)

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2. Wittrick WH, Williams FW. A general algorithm for computing natural frequencies of elastic structures. Quarterly Journal of Mechanics and Applied Mathematics 1971; 24:263-284.
3. Wittrick WH, Williams FW. An algorithm for computing critical buckling loads of elastic structures. Journal of Structural Mechanics 1973; 1:497-518.
4. Williams FW, Kennedy D, Djoudi MS. The member stiffness determinant and its uses for the transcendental eigenproblems of structural engineering and other disciplines. Proceedings of the Royal Society: Mathematical, Physical and Engineering Sciences 2003; 459:1001-1019.
5. Howson WP, Williams FW. Natural frequencies of frames with axially loaded Timoshenko members. Journal of Sound and Vibration 1973; 26:503-515.
6. Howson WP, Banerjee JR, Williams FW. Concise equations and program for exact eigensolutions of plane frames including member shear. Advances in Engineering Software 1983; 5:137-141.
7. Anderson ID. Dynamic Stability Functions for Continuous Structures. Heriot-Watt University: Edinburgh, 1968.
8. Williams FW, Kennedy D. Reliable use of determinants to solve non-linear structural eigenvalue problems efficiently. International Journal for Numerical Methods in Engineering 1988; 26:1825-1841.