Response of Nonlinear Beams and Plates to Pondingby Ahmed E. Salama,
Martin L. Moody,
Serial Information: Journal of the Engineering Mechanics Division, 1969, Vol. 95, Issue 1, Pg. 195-210
Document Type: Journal Paper
The responses of beams and plates with nonlinear moment-curvature relationship and subjected to the action of ponding loads are investigated for magnification of deflections. The analysis is analogous to the problem of vibration of beams and plates with nonlinear-moment-curvature relationships, which appears to be a previously unsolved problem for the examples presented herein. A parabolic moment- curvature relationship is assumed and the governing nonlinear differential equations are derived. Approximate solutions of these equations are carried out by using a perturbation-iteration method for a set of nested simultaneous differential equations obtained by slowly changing the nonlinearity parameter. Results are presented and examples are solved.
Subject Headings: Plates | Beams | Nonlinear response | Curvature | Differential equations | Nonlinear analysis | Load factors | Displacement (mechanics) | Vibration
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