Analytic solutions for nonlinear differential equations describing the elastica of straight bars: Theory

DOI10.1016/0016-0032(88)90037-3zbMath0655.73028OpenAlexW1999094309MaRDI QIDQ1109608

Pericles S. Theocaris, Dimitrios E. Panayotounakos

Publication date: 1988

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0016-0032(88)90037-3

zbMATH Keywords

bendingelliptic functionscompressionfunctional transformationsuniformly distributed forcesclosed form analytic solutionclosed form integration of exact differential equationend couples

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Bifurcation and buckling (74G60) Elliptic functions and integrals (33E05)

Related Items (4)

Postbuckling of elastic beam subjected to a concentrated moment within the span length of beam ⋮ Exact solutions of nonlinear equation of rod deflections involving the Lauricella hypergeometric functions ⋮ Stability of inflectional elasticae centered at vertices or inflection points ⋮ Elliptic integral solutions of spatial elastica of a thin straight rod bent under concentrated terminal forces

Cites Work

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• Exact solution for an approximate differential equation of a straight bar under conditions of a nonlinear equilibrium
• Nonlinear and buckling analysis of continuous bars lying on rigid supports

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