On the St. Venant problems for inhomogeneous circular bars

F. Rooney, M. Ferrari

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

The classical St. Venant problems, i.e., simple tension, pure bending, and flexure by a transverse force, are considered for circular bars with elastic moduli that vary as a function of the radial coordinate. The problems are reduced to second-order ordinary differential equations, which are solved for a particular choice of elastic moduli. The special case of a bar with a constant shear modulus and the Poisson's ratio varying is also considered and for this situation the problems are solved completely. The solutions are then used to obtain homogeneous effective moduli for inhomogeneous cylinders. Material inhomogeneities associated with spatially variable distributions of the reinforcing phase in a composite are considered. It is demonstrated that uniform distribution of the reinforcement leads to a minimum of the Young's modulus in the class of spatial variations in the concentration considered.

Original languageEnglish (US)
Pages (from-to)32-40
Number of pages9
JournalJournal of Applied Mechanics, Transactions ASME
Volume66
Issue number1
DOIs
StatePublished - Jan 1 1999

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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