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 . According to the proposed investigation additional terms, 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 are determined.
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March 2010
Research Papers
Additional Separated-Variable Solutions of the Biharmonic Equation in Polar Coordinates
I. H. Stampouloglou,
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
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E. E. Theotokoglou
E. E. Theotokoglou
School of Applied Mathematical and Physical Sciences, Department of Mechanics–Laboratory of Testing and Materials,
e-mail: stathis@central.ntua.gr
National Technical University of Athens
, Zographou Campus, Theocaris Building, GR-157 73 Athens, Greece
Search for other works by this author on:
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, Greecee-mail: stathis@central.ntua.gr
J. Appl. Mech. Mar 2010, 77(2): 021003 (8 pages)
Published Online: December 9, 2009
Article history
Received:
December 31, 2008
Revised:
July 8, 2009
Online:
December 9, 2009
Published:
December 9, 2009
Citation
Stampouloglou, I. H., and Theotokoglou, E. E. (December 9, 2009). "Additional Separated-Variable Solutions of the Biharmonic Equation in Polar Coordinates." ASME. J. Appl. Mech. March 2010; 77(2): 021003. https://doi.org/10.1115/1.3197157
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