Refined Theory of Beam on Winkler Foundation
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.