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In this chapter we revisit the extension of rods, torsion of circular shafts and bending of beams in Chap. 1 where one-dimensional models were used. This chapter uses the three-dimensional theory of linear elasticity. Torsion is generalized to non-circular bars by warping function and stress function. A bar with an elliptical cross section is analyzed as an example. Bending is limited to the special case of pure bending.

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Saint-Venant’s Problem

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  • 发表日期：

    2025年

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  • Jiashi Yang

摘要

In this chapter we revisit the extension of rods, torsion of circular shafts and bending of beams in Chap. 1 where one-dimensional models were used. This chapter uses the three-dimensional theory of linear elasticity. Torsion is generalized to non-circular bars by warping function and stress function. A bar with an elliptical cross section is analyzed as an example. Bending is limited to the special case of pure bending.