A Boundary Element Algorithm for Plate Bending Problems Based on Cauchy’s Integral Formula

Reinhard E. Piltner

doi:10.1007/978-3-642-84238-2_26

A Boundary Element Algorithm for Plate Bending Problems Based on Cauchy’s Integral Formula

Reinhard E. Piltner

Mathematical Sciences

Research output: Contribution to book or proceeding › Chapter

Abstract

A representation for plate bending solutions (Kirchhoff-plate theory) in terms of two arbitrary complex valued functions is considered. The complex functions are chosen in the form of Cauchy integrals which are discretized along the boundary of the plate. Using the complex representation we a priori ensure the satisfaction of the homogeneous plate equation. An inhomogeneous (particular) solution is added. The constructed boundary functions for the deflection, the moments and the shear forces are compatible.

Original language	American English
Title of host publication	Boundary Element Methods in Engineering: Proceedings of the International Symposium on Boundary Element Methods
DOIs	https://doi.org/10.1007/978-3-642-84238-2_26
State	Published - Oct 2 1989

Disciplines

Mathematics

Keywords

Boundary Element Algorithm
Cauchy’s Integral Formula
Plate Bending Problems

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Cite this

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title = "A Boundary Element Algorithm for Plate Bending Problems Based on Cauchy{\textquoteright}s Integral Formula",

abstract = " A representation for plate bending solutions (Kirchhoff-plate theory) in terms of two arbitrary complex valued functions is considered. The complex functions are chosen in the form of Cauchy integrals which are discretized along the boundary of the plate. Using the complex representation we a priori ensure the satisfaction of the homogeneous plate equation. An inhomogeneous (particular) solution is added. The constructed boundary functions for the deflection, the moments and the shear forces are compatible.",

keywords = "Boundary Element Algorithm, Cauchy{\textquoteright}s Integral Formula, Plate Bending Problems",

author = "Piltner, \{Reinhard E.\}",

note = "A representation for plate bending solutions (Kirchhoff-plate theory) in terms of two arbitrary complex valued functions is considered. The complex functions are chosen in the form of Cauchy...",

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N2 - A representation for plate bending solutions (Kirchhoff-plate theory) in terms of two arbitrary complex valued functions is considered. The complex functions are chosen in the form of Cauchy integrals which are discretized along the boundary of the plate. Using the complex representation we a priori ensure the satisfaction of the homogeneous plate equation. An inhomogeneous (particular) solution is added. The constructed boundary functions for the deflection, the moments and the shear forces are compatible.

AB - A representation for plate bending solutions (Kirchhoff-plate theory) in terms of two arbitrary complex valued functions is considered. The complex functions are chosen in the form of Cauchy integrals which are discretized along the boundary of the plate. Using the complex representation we a priori ensure the satisfaction of the homogeneous plate equation. An inhomogeneous (particular) solution is added. The constructed boundary functions for the deflection, the moments and the shear forces are compatible.

KW - Boundary Element Algorithm

KW - Cauchy’s Integral Formula

KW - Plate Bending Problems

UR - https://doi.org/10.1007/978-3-642-84238-2_26

U2 - 10.1007/978-3-642-84238-2_26

DO - 10.1007/978-3-642-84238-2_26

M3 - Chapter

BT - Boundary Element Methods in Engineering: Proceedings of the International Symposium on Boundary Element Methods

ER -

A Boundary Element Algorithm for Plate Bending Problems Based on Cauchy’s Integral Formula

Abstract

Disciplines

Keywords

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