Abstract
Plates with rectangular openings develop stress concentrations under bending. While these stresses can be determined using finite elements, in many problems this would be difficult because a high density mesh would be needed in the neighborhood of every opening corner. In this paper, it is shown how a complex-variable conformal mapping approach can be numerically coupled with the finite element method to analyze these corner stresses. This approach can be used even with relatively coarse meshes where the finite element results, by themselves, do not resolve the stress concentrations. In essence, the method relies on finite element analysis to obtain information on the stress field in a region surrounding the plate opening; this information is subsequently used to set up the parameters of the conformal mapping approach to obtain the near field stresses at the opening corners.
Original language | English (US) |
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Pages (from-to) | 1991-2004 |
Number of pages | 14 |
Journal | International Journal of Solids and Structures |
Volume | 48 |
Issue number | 13 |
DOIs | |
State | Published - Jun 15 2011 |
Externally published | Yes |
Keywords
- Complex variable
- Conformal mapping
- Plate bending
- Rectangular hole
- Regression
- Stress concentration
ASJC Scopus subject areas
- Modeling and Simulation
- General Materials Science
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics