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Refined Theory of Beam on
Zhao Baosheng(1),Wang Minzhong(2),Yu Xin(1)
(1 School of Mechanical Engineering and Automation, Anshan University of Sc ience and Technology, Anshan, 114044)
(2 State Key Laboratory foe Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing, 100871)
Abstract: Cheng's refined theory is extended to
investigate the beam on the elastic foundation, and an exact analysis for the beam on the
elastic foundation is carried out. The expressions of the displacements and stress
components are obtained in term of the midsurface displacement and the derivatives. With
Lur'e method, the refined theory of the beam on the elastic foundation is aquired from the
Winkler Foundation boundary conditions. If the higher-order terms are omitted, the
deflection equation of the refined theory is degenerated into the classic governing
equation of beam on the elastic foundation.
Keywords: refined theory, the elastic foundation, beam, Papkovich-Neuber general solution.