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Large deflections of point loaded cantilevers with nonlinear behaviour. (English) Zbl 0503.73026


MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
65D30 Numerical integration
74S30 Other numerical methods in solid mechanics (MSC2010)
34A34 Nonlinear ordinary differential equations and systems
74B20 Nonlinear elasticity
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References:

[1] R. Frisch-Fay,Flexible bars. Butterworths, London 1962.
[2] H. J. Barten,On the deflection of a cantilever beam. Q. Appl. Math.2, 168-171 (1944) and ibid.3, 275-276 (1945). (Note: The second article corrects a mistake in the first one.) · Zbl 0063.00222
[3] K. E. Bisshopp, and D. C. Drucker,Large deflections of cantilever beams. Q. Appl. Math.3, 272-275 (1945). · Zbl 0063.00418
[4] G. Lewis and F. Monasa,Large deflections of cantilever beams of nonlinear materials. J. Computers and Structures14 (N 5-6), 357-360 (1981). · doi:10.1016/0045-7949(81)90054-7
[5] G. Prathap and T. K. Varadan,The inelastic large deformation of beams. J. Appl. Mech. ASME43, 689-690 (1976). · doi:10.1115/1.3423957
[6] C. C. Lo and S. D. Gupta,Bending of a non-linear rectangular beam in large deflection. J. Appl. Mech. ASME45, 213-215 (1978). · doi:10.1115/1.3424238
[7] R. Frisch-Fay,Large deflections of a cantilever under two concentrated loads. J. Appl. Mech. ASME29 (N 1), 200-201 (1962). · Zbl 0125.14102
[8] Alfred M. Freudenthal,The Inelastic behavior of engineering materials and structures, p. 203, John Wiley & Sons, New York 1950.
[9] A. Nadai,The theory of flow and fracture of solids. Vol. 2, 136-146, McGraw-Hill, New York 1963.
[10] A. A. Denton,Plane strain bending with work hardening. J. Strain Anal.1 (N 5), 196-203 (1966). · doi:10.1243/03093247V013196
[11] M. B. Bassett and W. Johnson,The bending of plate using a three-roll pyramid type plate bending machine. J. Strain Anal.1 (N 5), 398-414 (1966). · doi:10.1243/03093247V015398
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