Advanced search
Publication Cover
Inverse Problems in Science and Engineering Volume 19, 2011 - Issue 8
Submit an article Journal homepage
430
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Shape functions associated with super-convergent mass matrix

S. FaroughiSchool of Mechanical Engineering, Urmia University of Technology, Band Street, Urmia, IRAN
,
H. AhmadianSchool of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 16844, IRAN
&
A. GhareghaniSchool of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 16844, IRAN
Pages 1087-1095 | Received 27 Nov 2010, Accepted 09 May 2011, Published online: 14 Jun 2011

References

  • Faroughi, S, and Ahmadian, H, 2010. Shape functions associated with the inverse element formulations, J. Mech. Eng. Sci. 225 (2010), pp. 304–311.
  • Zienkiwicz, OC, and Taylor, RL, 1989. The Finite Element Method, . Vol. 1. New York: McGraw-Hill; 1989.
  • Houmat, A, 2009. A sector elliptic p-element applied to membrane vibrations, Thin Wall. Struct. 47 (2009), pp. 172–177.
  • Argris, JS, Hasse, M, and Mlejnek, HP, 1980. On an unconventional but natural formulation of stiffness matrix, Comput. Meth. Appl. Mech. Eng. 22 (1980), pp. 1–22.
  • Bergan, PG, and Nygard, MK, 1984. Finite element with increased freedom in choosing shape function matrix, Int. J. Numer. Meth. Eng. 20 (1984), pp. 643–663.
  • Simo, C, and Rifai, MS, 1990. A class of mixed assumed strain methods and the method of incompatible modes, Int. J. Numer. Meth. Eng. 29 (1990), pp. 1595–1638.
  • MacNeal- Schwendler Crop, NASTRAN Theoretical Manual, Los Angeles, CA, 1972.
  • Kim, KI, 1993. A review of mass matrices for eigenproblems, Comp. Struct. 46 (1993), pp. 1041–1048.
  • Hansson, P-A, and Sandberg, G, 1997. Mass matrices by minimization of modal errors, Int. J. Numer. Meth. Eng. 40 (1997), pp. 4259–4271.
  • Fried, I, and Chavez, M, 2004. Superaccurate finite element eigenvalue computation, J. Sound Vibr. 275 (2004), pp. 415–422.
  • Fried, I, and Leong, K, 2005. Super accurate finite element eigenvalue via a Rayleigh quotient correction, J. Sound Vibr. 288 (2005), pp. 375–386.
  • Stavrindis, C, Clinckemailliet, J, and Dubois, J, 1989. New concepts for finite element mass matrix formulations, AIAA J. 27 (1989), pp. 1249–1255.
  • Ahmadian, H, Friswell, MI, and Mottershead, JE, 1998. Minimization of the discretization error in mass and stiffness formulation by inverse method, Int. J. Numer. Meth. Eng. 41 (1998), pp. 371–387.
  • Ahmadian, H, and Faroughi, S, 2010. Super-convergent eigenvalue bending plate element, Inverse Prob. Sci. Eng. 18 (2010), pp. 1–18.
  • Heppler, GR, and Hansen, JS, 1988. Timoshenko beam finite elements using trigonometric basis functions, AIAA J. 11 (1988), pp. 1378–1386.
  • Milsted, MG, and Hutchinson, JR, 1974. Use of trigonometric terms in the finite element method with application to vibration membranes, J. Sound Vibr. 32 (1974), pp. 327–346.
  • Shavezipur, M, and Hashemi, SM, 2009. Free vibration of triply coupled centrifugally stiffened non-uniform beams using a refined dynamic finite element method, Aerospace Sci. Technol. 13 (2009), pp. 59–70.
  • Christian, M, 2009. Explicit local buckling analysis of stiffened composite plates accounting for periodic boundary conditions and stiffener-plate interaction, Composite struct. 91 (2009), pp. 249–265.
  • Hutton, DV, 2004. Fundamentals of Finite Element Analysis. Singapore: McGraw Hill; 2004.
  • Rao, SS, 2004. The Finite Element Method in Engineering. Burlington, MA: Elsevier Science & Technology Books; 2004.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.