NDLI: A variational method for the solution of biharmonic problems for a rectangular domain

Content Provider	Springer Nature Link
Author	Chekurin, V. F. Postolaki, L. I.
Copyright Year	2009
Abstract	We develop a variational method for the solution of biharmonic problems for a rectangular domain where, at one pair of its opposite sides, the unknown function and its normal derivative take zero values, and, at the other pair, certain inhomogeneous conditions are valid. The cases of semiinfinite and finite domain are considered. The method is based on the minimization of a quadratic functional determining the deviation of the solution from the given inhomogeneous conditions in the norm of L $_{2}$. To solve this variational problem, we apply the expansion of the solution in the systems of complex biharmonic functions (the so-called Papkovich homogeneous solutions), which satisfy identically the given homogeneous conditions at the pair of opposite sides of the rectangle. This representation of the solution is somewhat different from that proposed earlier [V. F. Chekurin, “A variational method for the solution of direct and inverse problems of the theory of elasticity for a semiinfinite strip,” Izv. Ross. Akad. Nauk, Mekh. Tverdogo Tela, No. 2, 58–70 (1999)]. We consider several variants of inhomogeneous boundary conditions arising in the problems of the two-dimensional theory of elasticity. Finally, we give an example of applying the proposed method for the determination of stress distributions in a rectangular area one of whose sides is rigidly fastened and the opposite one is subjected to the action of normal forces.
Starting Page	386
Ending Page	399
Page Count	14
File Format	PDF
ISSN	10723374
Journal	Journal of Mathematical Sciences
Volume Number	160
Issue Number	3
e-ISSN	15738795
Language	English
Publisher	Springer US
Publisher Date	2009-06-23
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistics and Probability

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