Saint-Venant solutions for prismatic anisotropic beams

• Published in: International journal of solids and structures 1991, Vol.28 (7), p.917-938
• Main Authors: Kosmatka, J.B., Dong, S.B.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/0020-7683(91)90008-4

An analytical model is presented for determining the displacement and stress distributions of the Saint-Venant extension, bending, torsion and flexure problems for a homogeneous prismatic beam of arbitrary section and rectilinear anisotropy. The determination of the complete displacement field requires solving a coupled two-dimensional boundary value problem for the local in-plane deformations and warping out of the section plane. The principle of minimum potential energy is applied to a discretized representation of the cross-section (Ritz method) to calculate solutions to this problem. The behavior of an anisolropic beam is studied in detail using the resulting displacement and stress solutions, where definitions are presented for the shear center, center of twist, torsion constant and a new geometric parameter: the line of extension bending centers. Two sets of numerical results are presented to illustrate how section geometry, beam length and material properties affect the behavior of a homogeneous anisotropic cantilever beam.