How to cite this paper
Lee, J & Lee, B. (2018). Elastica and buckling loads of nonlinear elastic tapered cantilever columns.Engineering Solid Mechanics, 6(1), 39-50.
Refrences
Berkey, D. D., & Freedman, M. I. (1978). A perturbation method applied to the buckling of a compressed elastica. Journal of Computational and Applied Mathematics, 4(3), 213-221.
Borboni, A., & De Santis, D. (2014). Large deflection of a non-linear, elastic, asymmetric Ludwick cantilever beam subjected to horizontal force, vertical force and bending torque at the free end. Meccanica, 49(6), 1327-1336.
Brojan, M., Puksic, A., & Kosel, F. (2007). Buckling and post‐buckling of a nonlinearly elastic column. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 87(7), 518-527.
Brojan, M., Videnic, T., & Kosel, F. (2009). Large deflections of nonlinearly elastic non-prismatic cantilever beams made from materials obeying the generalized Ludwick constitutive law. Meccanica, 44(6), 733-739.
Brojan, M., Sitar, M., & Kosel, F. (2012). On static stability of nonlinearly elastic Euler's columns obeying the modified Ludwick's law. International Journal of Structural Stability and Dynamics, 12(06), 1250077.
Carnahan, B., Luther, H. A., & Wilkes, J. O. (1969). Applied Numerical. Methods, 405-415.
Eren, I. (2008). Determining large deflections in rectangular combined loaded cantilever beams made of non-linear Ludwick type material by means of different arc length assumptions. Sadhana, 33(1), 45-55.
Euler, L. (1774). Methodus inveniendi lineas curvas maxima minimive proprietate gaudentes, Additamentum I, De Curtis Elasticis, Lausanne and Geneva.
Haslach, H. W. (1985). Post-buckling behavior of columns with non-linear constitutive equations. International journal of non-linear mechanics, 20(1), 53-67.
Jung, J. H., & Kang, T. J. (2005). Large deflection analysis of fibers with nonlinear elastic properties. Textile research journal, 75(10), 715-723.
Kounadis, A. N., & Mallis, J. G. (1987). Elastica type buckling analysis of bars from non-linearly elastic material. International journal of non-linear mechanics, 22(2), 99-107.
Lee, B. K., & Oh, S. J. (2000). Elastica and buckling load of simple tapered columns with constant volume. International Journal of Solids and Structures, 37(18), 2507-2518.
Lee, J. K., & Lee, B. K. (2016). Large Deflections and Buckling Loads of Cantilever Columns with Constant Volume. International Journal of Structural Stability and Dynamics, 1750091.
Lee, J.K., & Jeong, S. (2016). Flexural and torsional free vibrations of horizontally curved beams on Pasternak foundations. Applied Mathematical Modelling, 40(3), 2242-2256.
Lee, K. (2001). Post-buckling of uniform cantilever column under a combined load. International Journal of Non-Linear Mechanics, 36(5), 813-816.
Lee, K. (2002). Large deflections of cantilever beams of non-linear elastic material under a combined loading. International Journal of Non-Linear Mechanics, 37(3), 439-443.
Lewis, G., & Monasa, F. (1981). Large deflections of cantilever beams of nonlinear materials. Computers & Structures, 14(5-6), 357-360.
Lewis, G., & Monasa, F. (1982). Large deflections of cantilever beams of non-linear materials of the Ludwick type subjected to an end moment. International Journal of Non-Linear Mechanics, 17(1), 1-6.
Rao, B. N., & Rao, G. V. (1990). Stability of tapered cantilever columns subjected to a tip-concentrated follower force with or without damping. Computers & Structures, 37(3), 333-342.
Panayotounakos, D. E., & Theocaris, P. S. (1988). Analytic solutions for nonlinear differential equations describing the elastica of straight bars: theory. Journal of the Franklin Institute, 325(5), 621-63.
Saetiew, W., & Chucheepsakul, S. (2012). Post-buckling of linearly tapered column made of nonlinear elastic materials obeying the generalized Ludwick constitutive law. International Journal of Mechanical Sciences, 65(1), 83-96.
Borboni, A., & De Santis, D. (2014). Large deflection of a non-linear, elastic, asymmetric Ludwick cantilever beam subjected to horizontal force, vertical force and bending torque at the free end. Meccanica, 49(6), 1327-1336.
Brojan, M., Puksic, A., & Kosel, F. (2007). Buckling and post‐buckling of a nonlinearly elastic column. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 87(7), 518-527.
Brojan, M., Videnic, T., & Kosel, F. (2009). Large deflections of nonlinearly elastic non-prismatic cantilever beams made from materials obeying the generalized Ludwick constitutive law. Meccanica, 44(6), 733-739.
Brojan, M., Sitar, M., & Kosel, F. (2012). On static stability of nonlinearly elastic Euler's columns obeying the modified Ludwick's law. International Journal of Structural Stability and Dynamics, 12(06), 1250077.
Carnahan, B., Luther, H. A., & Wilkes, J. O. (1969). Applied Numerical. Methods, 405-415.
Eren, I. (2008). Determining large deflections in rectangular combined loaded cantilever beams made of non-linear Ludwick type material by means of different arc length assumptions. Sadhana, 33(1), 45-55.
Euler, L. (1774). Methodus inveniendi lineas curvas maxima minimive proprietate gaudentes, Additamentum I, De Curtis Elasticis, Lausanne and Geneva.
Haslach, H. W. (1985). Post-buckling behavior of columns with non-linear constitutive equations. International journal of non-linear mechanics, 20(1), 53-67.
Jung, J. H., & Kang, T. J. (2005). Large deflection analysis of fibers with nonlinear elastic properties. Textile research journal, 75(10), 715-723.
Kounadis, A. N., & Mallis, J. G. (1987). Elastica type buckling analysis of bars from non-linearly elastic material. International journal of non-linear mechanics, 22(2), 99-107.
Lee, B. K., & Oh, S. J. (2000). Elastica and buckling load of simple tapered columns with constant volume. International Journal of Solids and Structures, 37(18), 2507-2518.
Lee, J. K., & Lee, B. K. (2016). Large Deflections and Buckling Loads of Cantilever Columns with Constant Volume. International Journal of Structural Stability and Dynamics, 1750091.
Lee, J.K., & Jeong, S. (2016). Flexural and torsional free vibrations of horizontally curved beams on Pasternak foundations. Applied Mathematical Modelling, 40(3), 2242-2256.
Lee, K. (2001). Post-buckling of uniform cantilever column under a combined load. International Journal of Non-Linear Mechanics, 36(5), 813-816.
Lee, K. (2002). Large deflections of cantilever beams of non-linear elastic material under a combined loading. International Journal of Non-Linear Mechanics, 37(3), 439-443.
Lewis, G., & Monasa, F. (1981). Large deflections of cantilever beams of nonlinear materials. Computers & Structures, 14(5-6), 357-360.
Lewis, G., & Monasa, F. (1982). Large deflections of cantilever beams of non-linear materials of the Ludwick type subjected to an end moment. International Journal of Non-Linear Mechanics, 17(1), 1-6.
Rao, B. N., & Rao, G. V. (1990). Stability of tapered cantilever columns subjected to a tip-concentrated follower force with or without damping. Computers & Structures, 37(3), 333-342.
Panayotounakos, D. E., & Theocaris, P. S. (1988). Analytic solutions for nonlinear differential equations describing the elastica of straight bars: theory. Journal of the Franklin Institute, 325(5), 621-63.
Saetiew, W., & Chucheepsakul, S. (2012). Post-buckling of linearly tapered column made of nonlinear elastic materials obeying the generalized Ludwick constitutive law. International Journal of Mechanical Sciences, 65(1), 83-96.