Summary
Through generalizing the method developed by the refined theory of straight beams, a refined theory of rectangular curved beams is derived by using Papkovich-Neuber (shortened form P-N) solution in polar coordinate system and Lur'e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by four displacement functions. For the beam under surface loads, the approximate governing differential equations are derived directly from the refined beam theory and are almost the same as those of other well-known theoretical models. To illustrate the application of the beam theory developed, a pure bending curved beam is examined, which indicates that the stress expressions derived are an exact solution and are consistent with the results gained by exact beam theory of elasticity.
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Gao, Y., Wang, M.Z. & Zhao, B.S. The refined theory of rectangular curved beams. Acta Mechanica 189, 141–150 (2007). https://doi.org/10.1007/s00707-006-0413-9
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DOI: https://doi.org/10.1007/s00707-006-0413-9