Asymptotic theory and analysis for displacements and stress distribution in nonlinear elastic straight slender rods. (English) Zbl 0653.73010

From the authors’ abstract: “An asymptotic expansion method is applied to nonlinear three-dimensional elastic straight slender rods. Nonlinear ordinary differential equations for approximate displacements and explicit formulas for approximate stress distributions are obtained. Mathematical properties of these models are studied.”
This is a comprehensive paper written in clear and rigorous style. Examples include: rod clamped at both extremities; rod clamped in mean at both extremities; and rod clamped at one extremity (end). The current theory is discussed in light of strength of materials, showing that the general results are consistent with those of the simpler approach.
This paper should appeal to engineers and scientists concerned with current developments in the theory of ‘elastica’.
Reviewer: R.H.Lance


74B20 Nonlinear elasticity
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
34E05 Asymptotic expansions of solutions to ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
74G70 Stress concentrations, singularities in solid mechanics
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