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Structural Engineering and Mechanics Volume 26, Number 1, May10 2007 , pages 43-68 DOI: https://doi.org/10.12989/sem.2007.26.1.043 |
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Bilinear plate bending element for thin and moderately thick plates using Integrated Force Method |
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H. R. Dhananjaya, J. Nagabhushanam and P. C. Pandey
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| Abstract | ||
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Using the Mindlin-Reissner plate theory, many quadrilateral plate bending elements have been developed so far to analyze thin and moderately thick plate problems via displacement based finite element method. Here new formulation has been made to analyze thin and moderately thick plate problems using force based finite element method called Integrated Force Method (IFM). The IFM is a novel matrix formulation developed in recent years for analyzing civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper the force based new bilinear quadrilateral plate bending element (MQP4) is proposed to analyze the thin and moderately thick plate bending problems using Integrated Force Method. The Mindlin-Reissner plate theory has been used in the formulation of this element which accounts the effect of shear deformation. Standard plate bending benchmark problems are analyzed using the proposed element MQP4 via Integrated Force Method to study its performance with respect to accuracy and convergence, and results are compared with those of displacement based 4-node quadrilateral plate bending finite elements available in the literature. The results are also compared with the exact solutions. The proposed element MQP4 is free from shear locking and works satisfactorily in both thin and moderately thick plate bending situations. | ||
| Key Words | ||
| stress-resultant fields; flexibility matrix; equilibrium matrix; displacement fields; Mindlin-Reissner theory; Integrated Force Method. | ||
| Address | ||
| H. R. Dhananjaya: Dept. of Civil Engineering, Manipal Institute of Technology, Manipal - 576 104, India J. Nagabhushanam: Dept. of Aerospace Engineering, Indian Institute of Science, Bangalore - 560 012, India P. C. Pandey: Dept. of Civil Engineering, Indian Institute of Science, Bangalore - 560 012, India | ||