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Boundary integral equations for multiply connected plates. (English) Zbl 0957.74025

Summary: An algebra of boundary operators is constructed for a multiply connected finite plate with transverse shear deformation, which is then used to solve the boundary integral equations arising from the representation of the solution in terms of modified single layer and double layer potentials.

MSC:

74K20 Plates
31A10 Integral representations, integral operators, integral equations methods in two dimensions
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References:

[1] Constanda, C., A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation. A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation, Pitman Res. Notes Math. Ser., 215 (1990), Longman: Longman Harlow · Zbl 0692.73058
[2] Lions, J.-L.; Magenes, E., Non-homogeneous Boundary Value Problems and Applications (1972), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York · Zbl 0223.35039
[3] Chudinovich, I.; Constanda, C., Weak solutions of interior boundary value problems for plates with transverse shear deformation, IMA J. Appl. Math., 59, 85-94 (1997) · Zbl 0891.73037
[4] I. Chundinovich, and, C. Constanda, Solution of bending of elastic plates by means of area potentials, Z. Angew. Math. Mech, to appear.; I. Chundinovich, and, C. Constanda, Solution of bending of elastic plates by means of area potentials, Z. Angew. Math. Mech, to appear.
[5] I. Chudinovich, and, C. Constanda, The solvability of boundary integral equations for the Dirichlet and Neumann problems in the theory of thin elastic plates, Math. Mech. Solids, to appear.; I. Chudinovich, and, C. Constanda, The solvability of boundary integral equations for the Dirichlet and Neumann problems in the theory of thin elastic plates, Math. Mech. Solids, to appear. · Zbl 1018.74023
[6] Maz’ya, V. G., Sobolev Spaces (1985), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York/Tokyo · Zbl 0727.46017
[7] I. Chudinovich, and, C. Constanda, On Two Boundary Value Problems for Plates with Combined Boundary Conditions, Strathclyde Math. Res. Report No, 38, 1997.; I. Chudinovich, and, C. Constanda, On Two Boundary Value Problems for Plates with Combined Boundary Conditions, Strathclyde Math. Res. Report No, 38, 1997. · Zbl 0891.73037
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