Solution of an Orthotropic Beam Problem by Fourier Series<sup>1</sup>


  • R. C. Tang
  • B. A. Jayne


An exact solution of the characteristic fourth-order partial differential equation for plane orthotropic elasticity is obtained by using the Fourier method. Particular emphasis is given to the orthotropic beam subjected to a concentrated load. Stress distributions calculated from the resulting series are compared with those given by elementary bending theory.


Goodier, J. N. 1932. Compression of rectangular blocks, and the bending of beams by nonlinear distributions of bending forces. J. Appl. Mech., Trans. ASME, 54: 173-183.nJayne, B. A., and M. O. Hunt. 1969. Plane stress and plane strain in orthotropic and anisotropic media. Wood and Fiber, 1(3): 236-247.nJayne, B. A., and R. C. Tang. 1970. Power series stress function for anisotropic and orthotropic beams. Wood and Fiber, 2(2): 96-104.nLekhnitskii, S. G. 1947. Anisotropic plates. O.G.I.Z. Gostekhizdat M-L.nPickett, G. 1944. Application of the Fourier method to the solution of certain boundary problems in the theory of elasticity. J. Appl. Mech., Trans. ASME, 66: 176-182.nRibiere, M. C. 1889. Sur divers cas de la flexion des prismes rectangles. Compt. Rend., 126: 402-404, 1190-1192.nTimoshenko, S., and J. N. Goodier. 1951. Theory of elasticity. 2nd ed. McGraw-Hill, New York.n






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