NDLI: On the elastostatic significance of four boundary integrals involving biharmonic functions

Content Provider	Springer Nature Link
Author	Christiansen, S.
Copyright Year	1998
Abstract	For a biharmonic functionU, depending upon two space variables, it is known that four curve integrals, which involveU and some derivatives ofU evaluated at a closed boundary, must be equal to zero. WhenU plays the role of an Airy stress function, we investigate the elastostatic significance of the four integrals and we find that it is related to the displacements of the elastic material: Single valued displacements are obtained provided that three of the integrals are zero. (The fourth integral does not provide further information.) It is already known from the classical literature that two of the integrals are related to single valued displacements, but the elastostatical significance of the third integral seems to be a new result. The method of investigation is unconventional: For “all possible” biharmonic functions, in polar coordinates, we determine stresses, strains, displacements etc. together with the values of the four integrals. The computer algebra system Maple V has been an invaluable tool. By suitable comparisons among the various results obtained we are led to the conclusions about the elastostatic significance of the integrals.
Starting Page	37
Ending Page	43
Page Count	7
File Format	PDF
ISSN	00015970
Journal	Acta Mechanica
Volume Number	126
Issue Number	1-4
e-ISSN	16196937
Language	English
Publisher	Springer-Verlag
Publisher Date	1998-01-01
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Numerical and Computational Methods in Engineering Continuum Mechanics and Mechanics of Materials Structural Mechanics Vibration, Dynamical Systems, Control Engineering Fluid Dynamics Engineering Thermodynamics, Transport Phenomena
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering Computational Mechanics

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