Monasa, Frank; Lewis, Gilbert Large deflections of point loaded cantilevers with nonlinear behaviour. (English) Zbl 0503.73026 Z. Angew. Math. Phys. 34, 124-130 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 Documents 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 Keywords:thin beams; flexible; curve with large deflections; sufficiently large transverse loads; nonlinear theory of bending; transverse concentrated loads; exact expression of curvature of deflected shape; Bernoulli-Euler relationship; second order nonlinear differential equation; fourth-order Runge-Kutta method; arc length; Simpson’s rule PDFBibTeX XMLCite \textit{F. Monasa} and \textit{G. Lewis}, Z. Angew. Math. Phys. 34, 124--130 (1983; Zbl 0503.73026) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.