Vector formulae for non-homogeneous prismatic bars

Ecsedi, István and Dluhi, Kornél (2014) Vector formulae for non-homogeneous prismatic bars. JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS, 9 (2). pp. 149-169. ISSN 1586-2070

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Abstract

By using the Timoshenko type beam theory a simple solution is obtained for the bending–tension–shearing problem of non-homogeneous prismatic bars. Within this framework the elastic moduli can vary arbitrarily over the bar's cross section. Vector formulas for normal stress, shear flow and strain variables such as longitudinal strain and curvature for arbitrary cross section are derived. A vector–tensor formulation of the first-order shear deformation theory for thin-walled beams is presented. Applications of formulas obtained are illustrated in the case of thin-walled open and closed cross section deriving the formulas of shear centre and shear rigidity tensor.

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