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Research Papers

Additional Separated-Variable Solutions of the Biharmonic Equation in Polar Coordinates

[+] Author and Article Information
I. H. Stampouloglou

School of Applied Mathematical and Physical Sciences, Department of Mechanics–Laboratory of Testing and Materials, National Technical University of Athens, Zographou Campus, Theocaris Building, GR-157 73 Athens, Greece

E. E. Theotokoglou

School of Applied Mathematical and Physical Sciences, Department of Mechanics–Laboratory of Testing and Materials, National Technical University of Athens, Zographou Campus, Theocaris Building, GR-157 73 Athens, Greecestathis@central.ntua.gr

J. Appl. Mech 77(2), 021003 (Dec 09, 2009) (8 pages) doi:10.1115/1.3197157 History: Received December 31, 2008; Revised July 08, 2009; Published December 09, 2009; Online December 09, 2009

From the biharmonic equation of the plane problem in the polar coordinate system and taking into account the variable-separable form of the partial solutions, a homogeneous ordinary differential equation (ODE) of the fourth order is deduced. Our study is based on the investigation of the behavior of the coefficients of the above fourth order ODE, which are functions of the radial coordinate r. According to the proposed investigation additional terms, φ¯m(r,θ)(1mn) other than the usually tabulated in the Michell solution (1899, “On the Direct Determination of Stress in an Elastic Solid, With Application to the Theory of Plates,” Proc. Lond. Math. Soc., 31, pp. 100–124) are found. Finally the stress and the displacement fields due to each one additional term of φ¯m(r,θ) are determined.

Copyright © 2010 by American Society of Mechanical Engineers
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