Analytic trapezoidal Fourier p-element for vibrating plane problems

Journal of Sound and Vibration

Volumn 271, Issue 1-2, 2004, Pages 67-81

  Leung, A Y T ^a   Zhu, Bin ^a   Zheng, Jianjin ^a   Yang, Hao ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DEGREES OF FREEDOM (MECHANICS); ELASTICITY; FINITE ELEMENT METHOD; FOURIER TRANSFORMS; MATRIX ALGEBRA; NATURAL FREQUENCIES; POLYNOMIALS;

ELASTIC SOLIDS; TRIGNOMETRIC FUNCTIONS; VIBRATING PLANE PROBLEMS;

VIBRATIONS (MECHANICAL);

EID: 1542788619     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-460X(03)00263-3     Document Type: Article

References (26)

1. D.V. Griffiths, G.G.W. Mustoe, Selective reduced integration of four-node plane element in closed form, Journal of Engineering Mechanics 121 (1995) 725-729.
2. L. Videla, M. Cerrolaza, N. Aparicio, Explicit integration of the stiffness matrix of a four-noded plane elasticity finite element, Communications in Numerical Methods in Engineering 12 (1996) 731-743.
3. K.E. Barrett, Explicit eight-noded quadrilateral elements, Finite Elements in Analysis and Design 31 (1999) 209-222.
4. T.H.H. Pian, Derivation of element stiffness matrices by assumed stress distributions, American Institute of Aeronautics and Astronautics Journal 2 (1964) 1333-1336.
5. Y.K. Cheung, W. Chen, Refined hybrid method for plane isoparametric element using an orthogonal approach, Computers and Structures 42 (1992) 638-694.
6. W. Chen, Y.K. Cheung, A robust refined quadrilateral plane element, International Journal for Numerical Methods in Engineering 38 (1995) 649-666.
7. S.T. Yeo, B.G. Lee, New stress assumption for hybrid stress elements and refined four-node plane and eight-node brick elements, International Journal for Numerical Methods in Engineering 40 (1997) 2933-2952.
8. T.J.R. Hughes, Generalization of selective integration procedures to anisotropic and nonlinear media, International Journal for Numerical Methods in Engineering 15 (1980) 1413-1418.
9. J.C. Simo, M.S. Rifai, A class of mixed assumed strain methods and the method of incompatible medes, International Journal for Numerical Methods in Engineering 29 (1990) 1595-1638.
10. O.C. Zienkiewicz, R.L. Taylor, The Finite Method, Vol. 1, 4th Edition, McGraw-Hill, New York, 1989.
11. Q. Nie, Q. Niu, p-Version large strain finite element formulation and application in elastic-plastic deformation, Computers and Structures 65 (1997) 761-765.
12. A. Houmat, Hierarchical finite element analysis of the vibration of membranes, Journal of Sound and Vibration 201 (1997) 465-472.
13. N.S. Bardell, J.N. Dunsdon, R.S. Langley, Free vibration of coplanar sandwich panels, Composite Structures 38 (1997) 463-475.
14. A. Houmat, A triangular Fourier p-element for the analysis of membrane vibrations, Journal of Sound and Vibration 230 (2000) 31-43.
15. A. Houmat, A sector Fourier p-element for free vibration analysis of sectorial membranes, Computers and Structures 79 (2001) 1147-1152.
16. A.Y.T. Leung, J.K.W. Chan, Fourier p-element for the analysis of beams and plates, Journal of Sound and Vibration 212 (1998) 179-185.
17. R.D. Cook, Improved two-dimensional finite element, Journal of the Structure Division American Society of Civil Engineers 100 (1974) 1851-1863.
18. A.Y.T. Leung, Dynamic Stiffness and Substructures, Springer, London, 1993.
19. R.W. Clough, J. Penzien, Dynamic of Structures, McGraw-Hill, New York, 1975.
20. K.K. Gupta, Development of a finite dynamic element for free vibration analysis of two-dimensional structures, International Journal for Numerical Methods in Engineering 12 (1978) 1311-1327.
21. C. Zhao, P. Steven, Asymptotic solutions for predicted natural frequencies of two-dimensional elastic solid vibration problems in finite element analysis, International Journal for Numerical Methods in Engineering 39 (1996) 2821-2835.
22. R.D. Cook, D.S. Malkus, M.E. Plesha, Concepts and Applications of Finite Element Analysis, 4th Edition, Wiley, New York, 1989.
23. M. Petyt, Introduction to Finite Element Vibration Analysis, Cambridge University Press, Cambridge, UK, 1990.
24. Y.K. Cheung, Y.X. Zhang, W.J. Chen, A refined nonconforming plane quadrilateral element, Computers and Structures 78 (2000) 699-709.
25. J.B. Carr, The effect of shear flexibility and rotatory inertia on the natural frequencies of uniform beams, The Aeronautical Quarterly 21 (1970) 79-90.
26. R.W. Clough, A.K. Chopra, Earthquake stress analysis in earth dams, Journal of Engineering Mechanics American Society of Civil Engineers 93 (1966) 197-211.