A new high-precision triangular plate element

• Autorzy: Manna M. C.
• Języki publikacji: EN

Abstrakty

EN

This paper deals with the development of a new triangular finite element for bending analysis of isotropic rectangular plates by an explicit stiffness matrix. The first order shear deformation theory (FOSDT) is used to include the effect of transverse shear deformation. The element has eighteen nodes on the sides and six internal nodes. The geometry of the element is expressed by three linear shape functions of area coordinates. The formulation is displacement type and the use of area coordinates makes the shape functions for field variables to be expressed explicitly. No numerical integration is required to get the element stiffness matrix. The element has fifty-one degrees of freedom, which can be reduced to thirty-nine degrees of freedom by a standard static condensation of the degrees of freedom associated with the internal nodes. An interesting feature of the element is that it is not prone to shear locking. Numerical examples are presented to show the accuracy and convergence characteristics of the element.

Słowa kluczowe

EN

explicit stiffness matrix; FOSDT; static condensation; shear locking; convergence characteristic

PL

kondensacja; ścinanie; zbieżność

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2004
• Tom: Vol. 9, no 2
• Strony: 361--382
• Opis fizyczny: Bibliogr. 32 poz., rys., tab., wykr.

Twórcy

autor

Manna M. C.

• Bengal Engineering College (Deemed University) P.O. - Botanic Garden, Howrah - 711 103, West Bengal, INDIA

Bibliografia

• [1] Allman D.J. (1970): Triangular finite elements for plate bending with constant and linearly varying bending moments. - Proc. IUTAM Conference on High Speed Computing of Elastic Structures, Liege, Belgium, pp. 105-136.
• [2] Batoz J.L., Bathe K.J. and Ho L.W. (1980): A study of three-node triangular plate bending elements. - Int. J. Numer. Meth. Engg., vol.15, pp.1771-1812.
• [3] Batoz J.L. (1982): An explicit formulation for an efficient triangular plate-bending element. - Int. J. Numer. Meth. Engg., vol.18, pp.1071-1089.
• [4] Batoz J.L. and Katili I. (1992): On a simple triangular Reissner/Mindlin plate element based on incompatible modes and discrete constraints. - Int. J. Numer. Meth. Engg., vol.35, pp. 1603-1632.
• [5] Bergan P.G. and Felippa C.A. (1985): A triangular membrane element with rotational degrees of freedom. - Comp. Meths. Appl. Mech. Engg., vol.50, pp.25-69.
• [6] Bhashyam G.R. and Gallagher R.H. (1984): An approach to the inclusion of transverse shear deformation in finite element plate bending analysis. - Computers and Structures, vol. 19, pp.35-40.
• [7] Batoz J.L., Zheng C.L. and Hammadi F. (2001): Formulation and evaluation of new triangular, quadrilateral pentagonal and hexagonal discrete Kirchhoff plate/shell elements. - Int. J. Numer. Meth. Engng., vol.52, pp.615-630.
• [8] Cheung Y.K. and Chen W. (1989): Hybrid quadrilateral element based on Mindlin/Reissner plate theory. - Computers and Structures, vol.32, pp.327-339.
• [9] Clough R.W. and Tocher J.L. (1965): Finite element stiffness matrices for analysis of plate bending. - Proc. 1st Conf. on Mat. Meth. in Struct. Mech., Wright-Patterson Air Force Base, Ohio, pp.515-545.
• [10] Felippa C.A. and Bergan P.G. (1987): A triangular plate bending element based on an energy-orthogonal free formulation. - Comp. Meths. Appl. Mech. Engg., vol.61, pp.129-160.
• [11] Hughes T.J.R., Taylor R. and Kanolkulchai W. (1977): A simple and efficient finite element for plate bending. - Int. J. Numer. Meth. Engng., vol. 11, pp.1529-1543.
• [12] Hughes T.J.R. and Cohen M. (1978): The heterosis finite element for plate bending. - Computers and Structures, vol.9, pp.445-450.
• [13] Hughes T.J.R. and Tezduyaf T.E. (1981): Finite elements based on Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. - J. Appl. Mech., vol.48, pp.587-596.
• [14] Hrabok M.M. and Hrudey T.M. (1984): A review and catalogue of plate bending finite elements. - Computers and Structures, vol. 19, pp.479-495.
• [15] Hong W.I., Kim Y.H. and Lee S.W. (2001a): An assumed strain triangular solid shell element with bubble function displacements for analysis of plates and shells. - Int. J. Numer. Meth. Engng., vol.52, pp.455-469.
• [16] Hong W.I., Kim J.H., Kim Y.H. and Lee S.W. (2001b): An assumed strain triangular curved solid shell element formulation for analysis of plates and shells undergoing finite rotations. - Int. J. Numer. Meth. Engng., vol.52, pp.747-761.
• [17] Kim J.H. and Kim Y.H. (2002): A three-node ANS element for geometrically non-linear structural analysis. - Comput. Methods Appl. Mech. Engrg., vol. 191, pp.4035-4059.
• [18] Liew K.M., Xiang Y. and Kitipornchai S. (1995): Research on thick plate vibration: A literature survey. - Journal of Sound and Vibration, vol. 180, No.l, pp. 163-176.
• [19] Monforton G.R. and Schmit L.A. (1968): Finite element analysis of skew plates in bending. - American Institute Aeronautics and Astronautics J., vol.6, pp. 1150-1152.
• [20] Pryor C.W., Barker R.M. and Frederick D. (1970): Finite element bending analysis of Reissner plate. - J. Eng. Mech. Div. ASCE, vol.96, pp.967-983.
• [21] Pugh E.D.L., Hinton E. and Zienkiewicz O.C. (1987): A study of quadrilateral plate bending elements with reduced integration. - Int. J. Numer. Meth. Engng., vol.12, pp.1059-1079.
• [22] Petrolito J. (1989): A modified ACM element for thick plate analysis. - Computers and Structures, vol.32, pp. 1303-1309.
• [23] Rao G.V., Venkataramana J. and Raj I.S. (1974): A high precision triangular plate bending element for the analysis of thick plates. - Nucí. Engg. Des., vol.30, pp.408-412.
• [24] Razzaque A. (1973): Programme for triangular bending elements with derivative smoothing. - Int. J. Numer. Methi Engng., vol.6, pp.333-345.
• [25] Salerno V.L. and Goldberg M.A. (1968): Effect of shear deformations on the bending of rectangular plates. - Appl, Mech., ASME, vol.27, pp.54-58.
• [26] Sengupta D. (1991): Stress analysis of flat plates with shear using explicit stiffness matrix. - Int. J. Numer. Meth. EngM vol.32, pp. 1389-1409.
• [27] Tessler A. and Hughes T.J.R. (1985): A three-node Mindlin plate element with improved transverse shear. - Comp, Meth. Appl. Mech. Eng., vol.50, pp.71-101.
• [28] Wang C.M., Reddy J.N. and Lee K.H. (2000): Shear Deformable Beams and Plates: Realationships with Classi Solutions. - Amsterdam: Elsevier Science.
• [29] Yuan F.G. and Miller R.E. (1989): A cubic triangular finite element for flat plate with shear. - Int. J. Numer. Meth Engg., vol.28, pp.109-126.
• [30] Zienkiewicz O.C. and Lefebvre D. (1988): A robust triangular plate bending element of the Reissner-Mindlin typ$% Int. J. Numer. Meth. Engng., vol.26, pp.1169-1184.
• [31] Zienkiewicz O.C. and Taylor R.L. (1988): The Finite Element Methods. - New York: McGraw Hill (two volumes).
• [32] Zhongnian Xu. (1992): A thick-thin triangular plate element. - Int. J. Numer. Meth. Eng, vol.33, pp.963-973.