Sage Journals: Discover world-class research

Abstract

This paper presents an exact solution for large deflection behavior of nonprismatic cantilever beams of nonlinear bimodulus type material and subjected to tip concentrated moment. The highly nonlinear simultaneous first-order differential equations were solved analytically using the power series approach. Several numerical examples are carried out to investigate the effect of bimodulus properties, material parameter, n, and the applied tip moment on the large deflection behavior of nonprismatic cantilever beams. The numerical results show that the interaction (i.e., coupling) between the bimodulus material properties, the material constant, n, and the applied tip moment, plays a significant role on the large deflection behavior of cantilever beams. A comparative study with ADINA has been made to verify the accuracy of the presented analytical solution, and excellent agreement has been obtained.

Keywords

ADINA bimodulus material cantilever beam large deflection nonlinear elastic material.

Get full access to this article

View all access options for this article.

References

Oden, J.T. and Childs, S.B. (1970). Finite Deflections of a Nonlinearly Elastic Bar , Journal of Applied Mechanics, 69: 48—52.

Parathep, G. and Varadan, T.K. (1976). The Inelastic Large Deformation of Beams, Journal of Applied Mechanics, 43: 689—690.

Lo, C.C. and Gupta, S.D. (1978). Bending of a Nonlinear Rectangular Beam in Large Deflection, Journal of Applied Mechanics, 45: 213—215.

Monasa, F. (1979). The Effect of Material Nonlinearity on the Bending of the Elastica, Proceedings of the 3rd Engineering Mechanical Specialty Conference ASCE, 638—641.

Kounadis, A.N. and Mallis, J.G. (1987). Elastic Type Buckling Analysis of Bars from Nonlinearly Elastic Material, International Journal of Nonlinear Mechanics, 22(2): 99—107.

Lewis, G. and Monasa, F. (1981). Large Deflection of Cantilever Beams of Nonlinear Materials, International Journal of Computers and Structures , 14(5—6): 357—360.

Lewis, G. and Monasa, F. (1982). Large Deflection of Cantilever Beams of Nonlinear Materials of the Ludwick Type Subjected to an End Moment, International Journal of Nonlinear Mechanics, 17(1): 1—6.

Haslach, H.W. (1985). Post-buckling Behavior of Columns with Non-linear Constitutive Equations, International Journal of Non-linear Mechanics, 20(1): 53—67.

Coulter, B.A. and Miller, R.E. (1988). Numerical Analysis of a Generalized Plane ``Elastica'' with Nonlinear Material Behavior, International Journal of Numerical Methods in Engineering, 26: 617—630.

10.

Fertis, D.G. and Lee, C.T. (1991). Inelastic Analysis of Flexible Bars using Simplified Nonlinear Equivalent Systems, Comput. Struct., 41: 947—958.

11.

Fertis, D.G. (1999). Nonlinear Mechanics, 2nd Edition, CRC Press, Boca Raton, FL.

12.

Lee, K. (2002). Large Deflections of Cantilever Beams of Nonlinear Elastic Material under a Combined Loading, International Journal of Nonlinear Mechanics, 37: 439—443.

13.

Virgin, L.N. and Plaut, R.H. (2004). Post-buckling and Vibration of Linearly Elastic and Softening Columns under Self-weight, Int. J. of Solids and Struct., 41: 4989—5001.

14.

Adina (2000). ADINA User Interface (AUI) Users Guide, ADINA R and D, Inc., Watertown, MA.

15.

Kreyszig Erwin (1993). Advanced Engineering Mathematics . 7th edition, John Wiley & Sons, Inc., New York.

Exact Large Deflection Analysis of Nonprismatic Cantilever Beams of Nonlinear Bimodulus Material Subjected to Tip Moment

Abstract

Keywords

Get full access to this article

References