Various Calculation Methods for Large Deflections of Nonlinear Elastic Material Subjected to a Moment
Large deflections were calculated for nonlinear Ludwick type cantilever beams made of Ludwick type rectangular cross-sectional material subjected to a moment at the free end, by employing approximate and numerical methods for trial functions satisfying boundary conditions. Adequately approximate results were obtained for calculations employing single and binominal constant, second and fourth degree polynomial type trial functions. Increasing number of constant term and degree of trial functions resulted in more approximate values
___
- Bisshopp, K. E. and Drucker, D.C. Large Deflections of Cantilever Beams, Q. Appl. Math.,3: 272-275. (1945).
- Scott, E. J. Carver, D. R. and Kan M. On the Linear Differential Equation for Beam Deflection, J. Appl. Mech., 22: 245-248. (1955).
- Lau, J. H. Large Deflections of Beams with Combined Loads, J. Eng. Mech., 108: 180- 185. (1982).
- Rao, B. N. and Rao, G. V. On the Large Deflection of Cantilever Beams with End Rotational Load, Z. Angew-Math. Mech., 66: 507-509. (1986).
- Baker, G. On the Large Deflections of Non- prismatic Cantilevers with a Finite Depth, Comput. Struct., 46: 365-370. (1993).
- Lee, B. K., Wilson, J.F. and Oh, S.J. Elastica of Cantilevered Beams with Variable Cross Sections, Int. J. Non-Linear Mech., 28: 579-589. (1993).
- Frisch-Fay, R. Flexible Bars, Butter Worths, London. (1962).
- Fertis, D. G. Nonlinear Mechanics, CRC Pres, New York. (1999).
- Prathap, G. and Varadan, T. K. The Inelastic Large Deformation of Beams, J. Appl. Mech., 43: 689-690. (1976).
- Varadan, T. L. and Joseph, D. Inelastic Finite Deflections of Cantilever Beams, J. Aeronaut Soc. India, 39: 39-41. (1987).
- Lewis, G. And Monosa, F. Large Deflections of Cantilever Beams of Non-linear Materials, Comput. Strct., 14: 357-360. (1981).
- Lewis, G. And Monosa, F. Large Deflections of Cantilever Beams of Non-linear Materials of the Ludwick Typr Subjected to an End Moment, Int. J. Non-Linear Mech., 17: 1-6. (1982).
- Lo, C.C. and Gupta, S.D. Bending of a Nonlinear Rectangular Beam in Large Deflection, J. Appl. Mech., 45: 213-215. (1978).
- Lee, K. Large Deflections of Cantilever Beams of Non-linear Elastic Material under a Combined Loading, Int. J. Non-Linear Mech., 37: 439-443. (2002).
- Güven, U., Baykara, C., Bayer, İ., Large deflections of a cantilever beam of nonlinear bimodulus material subjected to an end moment, J.Reinforced Plastics and Composites, Vol.24, 12:1321-1326. (2005).