A displacement finite volume formulation for the static and dynamic analysis of shear deformable circular curved beams

Document Type : Article

Authors

Department of Civil Engineering, University of Guilan, Rasht, Iran

Abstract

In this paper, a finite volume formulation is proposed for static and in-plane vibration analysis of curved beams in which the axis extensibility, shear deformation and rotary inertia are considered. A curved cell with three degrees of freedom is used in discretization. The unknowns and their derivatives on cell faces are approximated either by assuming a linear variation of unknowns between the two consecutive computational points or by using the moving least squares technique (MLS). The proposed method is validated through a series of benchmark comparisons where its capability in accurate predictions without shear and membrane locking deficiencies is revealed.

Keywords

Main Subjects


References

1. Stolarski, H. and Belytschko, T. \Membrane locking
and reduced integration for curved elements", J. Appl.
Mech., 49(1), pp. 172-176 (1982).
2. Reddy, B.D. and Volpi, M.B. \Mixed nite element
methods for the circular arch problem. Comput Methods",
Appl. Mech. Eng., 97(1), pp. 125-145 (1992).
3. Raveendranath, P., Singh, G., and Pradhan, B. \A
two-noded locking-free shear
exible curved beam
element", Int. J. Numer. Meth. Eng., 44(2), pp. 265-
280 (1999).
4. Litewka, P. and Rakowski, J. \The exact thick arc
nite element. Comput Methods", Appl. Mech. Eng.,
68, pp. 369-379 (1998).
5. Sa ari, H. and Tabatabaei, R. \A nite circular
arch element based on trigonometric shape functions",
Math Probl. Eng., Article ID. 78507, 19 pages (2007).
DOI: 10.1155/2007/78507
6. Koschnick, F. and Bischo , M. \The discrete strain
gap method and membrane locking", Comput. Methods
Appl. Mech. Eng., 194, pp. 2444-2463 (2005).
7. Zhang, C. and Di, S. \New accurate two-noded shear-

exible curved beam elements", Comput. Mech., 30,
pp. 81-87 (2003).
8. Kim, J.G. and Kim, Y.Y. \A new higher order hybrid
mixed curved beam element", Int. J. Numer. Meth.
Eng., 43, pp. 925-940 (1998).
9. Wolf, J.A. \Natural frequencies of circular arches", J.
Struct. Eng.-ASCE, 97, pp. 2337-2350 (1971).
10. Irie, T., Yamada, G., and Tanaka, K. \Natural frequencies
of in-plane vibrations of arcs", J. Appl. Mech.,
50, pp. 449-452 (1983).
11. Eisenberger, M. and Efraim, E. \In-plane vibrations of
shear deformable curved beams", Int. J. Numer. Meth.
Eng., 52, pp. 1221-1234 (2001).
12. Friedman, Z. and Kosmatka, J.B. \An accurate
two-node nite element for shear deformable curved
beams", Int. J. Numer. Meth. Eng., 41, pp. 473-498
(1998).
13. Yang, F., Sedaghati, R., and Esmailzadeh, E. \Free
in-plane vibration of general curved beams using nite
element method", J. Sound. Vib., pp. 850-867 (1998).
14. Bailey, C. and Cross, M. \A nite volume procedure
to solve elastic solid mechanics problems in three
dimensions on an unstructured mesh", Int. J. Numer.
Meth. Eng., 38, pp. 1757-1776 (1995).
15. Demirdzic, I. and Martinovic, D. \Finite volume
method for thermo-elasto-plastic stress analysis",
Comput. Methods Appl. Mech. Eng., 109, pp. 331-349
(1993).
16. Wheel, M.A. \A nite volume method for analysing
the bending deformation of thick and thin plates",
Comput. Methods Appl. Mech. Eng., 147, pp. 199-208
(1997).
17. Fallah, N. \A cell vertex and cell centred nite volume
method for plate bending analysis", Comput. Methods
Appl. Mech. Eng., 193, pp. 3457-3470 (2004).
18. Fallah, N. \On the use of shape functions in the
cell centered nite volume formulation for plate bending
analysis based on Mindlin-Reissner plate theory",
Comput Struct, 84, pp. 1664-1672 (2006).
19. Slone, A.K., Bailey, C., and Cross, M. \Dynamic solid
mechanics using nite volume methods", Appl. Math.
Modelling, 27, pp. 69-87 (2003).
1014 N. Fallah and A. Ghanbari/Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 999{1014
20. Slone, A.K., Pericleous, K., Bailey, C., and Cross, M.
\Dynamic
uid structure interaction using nite volume
unstructured mesh procedures", Comput. Struct.,
80, pp. 371-390 (2002).
21. Fallah, N. and Parandeh-Shahrestany, A. \A novel
nite volume based formulation for the elasto-plastic
analysis of plates", Thin Wall Struct., 77, pp. 153-164
(2014).
22. Fallah, N. and Ebrahimnejad, M. \Finite volume
analysis of adaptive beams with piezoelectric sensors
and actuators", Appl. Math. Model., 38, pp. 722-737
(2014).
23. Fallah, N. \Finite volume method for determining
the natural characteristics of structures", J. Eng. Sci.
Tech., 8(1), pp. 93-106 (2013).
24. Fallah, N. \A method for calculation of face gradients
in two-dimensional, cell centred, nite volume formulation
for stress analysis in solid problems", Sci. Iran.,
15, pp. 286-294 (2008).
25. Lancaster, P. and Salkauskas, K. \Surfaces generated
by moving least squares methods", Math. Comput., 37,
pp. 141-158 (1981).
26. Day, R.A. and Potts, D.M. \Curved Mindlin beam and
axi-symmetric shell elements - A new approach", Int.
J. Numer. Meth. Eng., 30, pp. 1263-1274 (1990).
27. Fallah, N. and Hatami, F. \A displacement formulation
based on nite volume method for analysis
of Timoshenko beam", In: Proceedings of the 7th
International Conference in Civil Engineering, Iran,
May 8-10 (2006).
28. Liu, G.R. and GU, Y.T., An Introduction to Meshfree
Methods and Their Programming, Springer Press,
Berlin (2005).
29. Chopra, A.K., Dynamic of Structure, Theory and
Applications to Earthquake Engineering, Prentice Hall
(1995).
30. Majkut, L. \Free and forced vibration of Timoshenko
beam described by single di erence equation", J.
Theor. Appl. Mech., 47(1), pp. 193-210 (2009).
31. ANSYS, Swanson Analysis Systems Inc., Ansys Reference
Manual (version 12.1) (2009).
32. Hughes, T.J.R., Cohen, M., and Haroun, M. \Reduced
and selective integration techniques in the nite element
analysis of plates", Nucl. Eng. Des., 46, pp. 203-
222 (1978).
33. Bathe, K.J., Finite Element Procedures, Prentice-Hall
(1996).
34. Lee, P.G. and Sin, H.C. \Locking-free curved beam
element based on curvature", Int. J. Numer. Meth.
Eng., 37(6), pp. 989-1007 (1994).
35. Heyliger, P.R. and Reddy, J.N. \A higher order beam
nite element for bending and vibration problems", J.
Sound. Vib., 126(2), pp. 309-326 (1998).
36. Prathap, G. and Bhashyam, G.R. \Reduced integration
and the shear-
exible beam element", Int. J.
Numer. Meth. Eng., 18, pp. 195-210 (1982).
37. Veletsos, A. and Austin, W. \Free vibration of arches flexible in shear", J. Eng. Mech-ASCE, 99, pp. 735-753 (1973).
38. ABAQUS, 6.12.1.

Volume 25, Issue 3
Transactions on Civil Engineering (A)
May and June 2018
Pages 999-1014
  • Receive Date: 11 November 2015
  • Revise Date: 28 May 2016
  • Accept Date: 19 December 2016