In this paper a Finite strip method is developed to analyze very large deformations of thin plates and folded plates by use of the elastic Cosserat theory. The principle of virtual work is exploited to present the weak form of the governing differential equations. Through a linear mapping, a rectangular strip is transformed into a standard square computational domain in which the deformation and director fields are developed together with the general forms of the uncoupled nonlinear equations. The geometric and material tangential stiffness matrices are formed through linearization, and a step by step procedure is presented to complete the scheme. The validity and the accuracy of the method are illustrated through certain numerical examples and comparison of the results with other researches. The method is shown to be capable of handling numerical analysis of plates experiencing very large deformations.
AhmadS.IronsB.M. and ZienkiewiczO.C. (1970). “Analysis of thick and thin shell structures by curved finite elements”, International Journal for Numerical Methods in Engineering, Vol. 2, pp. 619–451.
2.
ArgyrisJ. (1982). “An excursion into large rotations”, Computer Methods in Applied Mechanics and Engineering, Vol. 32, pp. 85–155.
3.
AzhariM. and BradfordM.A. (1995). “The use of bubble functions for the post-local buckling of plate assemblies by the finite strip method”, International Journal for Numerical Methods in Engineering, Vol. 38, pp. 995–968.
4.
AzhariM.ShahidiA. R. and SaadatpourM. M. (2004). “Post-local buckling of skew and trapezoidal plates”, Advances in Structural Engineering, Vol. 7, pp. 61–70.
5.
AzizianZ.G. and DaweD.J. (1985). “Geometrically nonlinear analysis of rectangular mindlin plates using the finite strip method”, Computers & Structures, Vol. 21, No. 3, pp. 423–436.
6.
BatheK.J. (1996). Finite Element Procedures, Prentice-Hall. Englewood Cliffs. NJ.
7.
BelytschkoT.LiuW.K. and MoranB. (1987). Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons, LTD.
8.
BensonP.R. and HintonE. (1976). “A thick finite strip solution for static, free vibration and stability problems”, International Journal for Numerical Methods in Engineering, Vol. 10, pp. 665–667.
9.
BuechterN. and RammE. (1992). “Shell theory versus degeneration comparison in large rotation finite element analysis”, International Journal for Numerical Methods in Engineering, Vol. 34, pp. 39–59.
CheungY.K. and DashanZ. (1987). “Large deflection analysis of arbitrary shaped thin plate”, Computers & Structure, Vol. 26, No. 5, pp. 811–814.
12.
CheungY.K.ZhuD.S. and IuV.P. (1998). “Nonlinear vibration of thin plates with initial stress by spline finite strip method”, Thin-Walled Structure, Vol. 32, No. 4, pp. 275–287.
13.
DaweD.J. (1977a). “Static analysis of diaphragm-supported cylindrical shells using a curved finite strip”, International Journal for Numerical Methods in Engineering, Vol. 11, pp. 1347–1364.
14.
DaweD.J. (1977b). “Finite strip buckling analysis of curved plate assemblies under biaxial loading”, International Journal of Solids and Structures, Vol. 13, pp. 1141–1155.
15.
DaweD.J. (1978). “Finite strip models for vibration of mindlin plates”, Journal of Sound and Vibration, Vol. 59, No. 3, pp. 441–452.
16.
DaweD.J. and AzizianZ.G. (1986). “The performance of mindlin plate finite strips in geometrically nonlinear analysis”, Computers & Structures, Vol. 23, No. 1, pp. 1–14.
17.
DaweD. J. and LamS. S. E. (1992). “Non-linear finite strip analysis of rectangular laminates under end shortening using classical plate theory”, International Journal for Numerical Methods in Engineering, Vol. 35, pp. 1087–1110.
18.
EricksenJ.L. and TruesdellC. (1959). “Exact theory of stress and strain in rods and shells”, Archive for Rational Mechanics and Analysis, Vol. 1, pp. 295–323.
19.
SmithGraves T.R. and SridharanS. (1978). “A finite strip method for the post-locally buckled analysis of plate structures”, International Journal of Mechanical Sciences, Vol. 20, pp. 833–842.
20.
GreenA.E. and NaghdiP.M. (1965). “A general theory of a cosserat surface”, Archive for Rational Mechanics and Analysis, Vol. 20, pp. 287–308.
21.
GreenA.E.LawsN. and NaghdiP.M. (1968). “Rods, plates and shells”, Proceedings of the Cambridge Philosophical Society, Vol. 64, pp. 895–913.
22.
HughesT.J.R. (1987). The Finite Element Method, Prentice-Hall. Englewood Cliffs. NJ.
23.
HaghesT.J.R. and LiuW.K. (1981a). “Nonlinear finite element analysis of shells: Part I. three dimensional shells”, Computer Methods in Applied Mechanics and Engineering, Vol. 26, pp. 331–362.
24.
HughesT.J.R. and LiuW.K. (1981b). “Nonlinear finite element analysis of shells: Part II. two-dimensional shells”, Computer Methods in Applied Mechanics and Engineering, Vol. 27, pp. 167–181.
25.
HughesJ.R. and CarnoyE. (1983). “Nonlinear finite element shell formulation accounting for large membrane strains”, Computer Methods in Applied Mechanics and Engineering, Vol. 39, pp. 69–82.
26.
JiangL. and ChernukM.W. (1994). “A simple four-noded co-rotational shell element for arbitrarily large rotations”, Computers & Structures, Vol. 53, No. 5, pp. 1123–1132.
27.
LengyelP. and CusensA.R. (1983). “A finite strip method for the geometrically nonlinear analysis of plate structures”, International Journal for Numerical Methods in Engineering, Vol. 19, pp. 331–340.
28.
LiuC.S. and HongH.K. (2001). “Using comparison theorem to compare co-rotational stress rates in the model of perfect elastoplasticity”, International Journal of Solids and Structures, Vol. 38, pp. 2969–2987.
29.
MizusawaT.KajitaT. and NaruokaM. (1980). “Buckling of skew plate structures using B-spline functions”, International Journal for Numerical Methods in Engineering, Vol. 15, pp. 87–96.
30.
MoitaG.F. and CrisfieldM.A. (1996). “A finite element formulation for 3-D continua using the co-rotational technique”, International Journal for Numerical Methods in Engineering, Vol. 39, pp. 3775–3792.
31.
NaghdiP. M. (1972). The Theory of Shells and Plates, in TruesdellC., Handbuch der Physik, Vol. Via/2.
32.
OnateE. and SuaresB. (1983). “A comparison of the linear quadratic and cubic mindlin strip elements for the analysis of thick and thin plates”, Computers & Structures, Vol. 17, No. 3, pp. 427–439.
33.
ParischH. (1991). “An investigation of a finite rotation four node assumed strain shell element”, International Journal for Numerical Methods in Engineering, Vol. 31, pp. 127–150.
34.
PengX. and CrisfieldM.A. (1992). “A consistent co-rotational formulation for shells using the constant stress/constant moment triangle”, International Journal for Numerical Methods in Engineering, Vol. 35, pp. 1829–1847.
35.
PlankR.J. and WittrickW.H. (1974). “Buckling under combined loading of thin-walled structures by a complex finite strip method”, International Journal for Numerical Methods in Engineering, Vol. 8, pp. 323–339.
36.
RoufaeilO.L. and DaweD.J. (1985). “Vibration analysis of rectangular mindlin plates by the finite strip method”, Computers & Structures, Vol. 12, pp. 833–842.
37.
SandersJ.L. (1962). “Nonlinear theories for thin shells”, Archive for Rational Mechanics and Analysis, Vol. 21, pp. 21–36.
38.
SansourC. and BuflerH. (1992). “An exact finite rotation shell theory, its mixed variational formulation and its finite element implementation”, International Journal for Numerical Methods in Engineering, Vol. 34, pp. 73–115.
39.
SheikhA.H. and MukhopadhyayM. (2000). “Geometric nonlinear analysis of stiffened plates by the spline finite strip method”, Computers & Structures, Vol. 76, pp. 765–785.
40.
SimoJ.C. and FoxD.D. (1982). “On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parameterization”, Computer Methods in Applied Mechanics and Engineering, Vol. 72, pp. 267–304.
41.
SimoJ.C.FoxD.D. and RifaiM.S. (1989). “On a stress resultant geometrically exact shell model. Part II: The linear theory: Computational aspects”, Computer Methods in Applied Mechanics and Engineering, Vol. 73, pp. 53–92.
42.
SimoJ.C.FoxD.D. and RifaiM.S. (1990a). “On a stress resultant geometrically exact shell model. Part III: Computational aspects of the nonlinear theory”, Computer Methods in Applied Mechanics and Engineering, Vol. 79, pp. 21–70
43.
SimoJ.C.RifaiM.S. and FoxD.D. (1990b). “On a stress resultant geometrically exact shell model. Part IV: Variable thickness shells with through-the-thickness stretching”, Computer Methods in Applied Mechanics and Engineering, Vol. 81, pp. 91–126.
44.
SimoJ.C.RifaiM.S. and FoxD.D. (1990c). “On a stress resultant geometrically exact shell model Part VI: Nonlinear dynamics and conserving algorithms”, International Journal for Numerical Methods in Engineering, Vol. 34, pp. 117–164.
45.
SimoJ.C. and KennedyJ.G. (1992). “On a stress resultant geometrically exact shell model. Part V: Nonlinear plasticity formulation and integration algorithms”, Computer Methods in Applied Mechanics and Engineering, Vol. 96, pp. 133–171.
46.
SimoJ.C. (1993). “On a stress resultant geometrically exact shell model. Part VII: Shell intersections with 5/6-DOF finite element formulations”, Computer Methods in Applied Mechanics and Engineering, Vol. 108, pp. 319–339.
47.
TimoshenkoS.P. and GereJ.M. (1961). Theory of Elastic Stability, McGraw Hill, New York. USA.
48.
WangnerW. (1990). “A finite element model for non-linear shells of revolution with finite rotations”, International Journal for Numerical Methods in Engineering, Vol. 29, pp. 1455–1471.
49.
WempnerG. (1987). “Finite elements, finite rotations and small strains of flexible shells”, International Journal of Solids and Structures, Vol. 5, pp. 117–153.
50.
WittrickW.H. (1968). “General sinusoidal stiffness matrices for buckling and vibration analysis of thin-walled structures”, International Journal of Mechanical Sciences, Vol. 10, pp. 949–966.
51.
WittrickW.H. and CurzonP.L.V. (1968). “Stability of thin flat-walled structures with the walls in combined shear and compression”, Aeronautical Quarterly, Vol. 19, pp. 327–351.
52.
YamakiN. (1959). “Post-buckling behavior of rectangular plates with small initial curvature loaded in end compression”, Journal of Applied Mechanics, ASME, Vol. 26, pp. 407–414.
53.
YangH.Y. and ChongK.P. (1984). “Finite strip method with X-spline functions”, Computers & Structures, Vol. 18, No. 1, pp. 127–132.
54.
ZhuD.S. and CheungY.K. (1996). “Post-buckling analysis of circular cylindrical shell under combined loads”, Computers & Structures, Vol. 58, No. 1, pp. 21–26.
