Browse > Article
http://dx.doi.org/10.12989/sem.2007.26.1.043

Bilinear plate bending element for thin and moderately thick plates using Integrated Force Method  

Dhananjaya, H.R. (Dept. of Civil Engineering, Manipal Institute of Technology)
Nagabhushanam, J. (Dept. of Aerospace Engineering, Indian Institute of Science)
Pandey, P.C. (Dept. of Civil Engineering, Indian Institute of Science)
Publication Information
Structural Engineering and Mechanics / v.26, no.1, 2007 , pp. 43-68 More about this Journal
Abstract
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.
Keywords
stress-resultant fields; flexibility matrix; equilibrium matrix; displacement fields; Mindlin-Reissner theory; Integrated Force Method;
Citations & Related Records

Times Cited By Web Of Science : 3  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
연도 인용수 순위
1 Krishnam Raju, N.R.B. and Nagabhushanam, J. (2000), 'Non-linear structural analysis using integrated force method', Sadhana, 25(4), 353-365   DOI
2 Stricklin, J.A., Haislor, W., Tisdale, P. and Ganderson, R. (1969), 'A rapidly converging triangular plate element', AIAA J., 7, 180-181   DOI
3 Kaneko, L., Lawo, H. and Thierauf, G. (1983), 'On computational procedures for the force method', Int. J. Numer. Meth. Eng., 18, 1469-1495   DOI
4 Bathe, K.J. and Dvorkin, E.H. (1985), 'A four node plate bending element based on Mindlin/Reissner plate theory and mixed interpolation', Int. J. Numer. Meth. Eng., 21, 367-383   DOI   ScienceOn
5 Jane Liu, Riggs, H.R. and Alexander Tessler (2000), 'A four node shear-deformable shell element developed via explicit Kirchhoff constraints', Int. J. Numer. Meth. Eng., 49, 1065-1086   DOI
6 Kikuchi, F. and Ando, Y. (1972), 'Some finite element solutions for plate bending problems by simplified hybrid displacement method', Nucl. Eng. Des., 23, 155-178   DOI   ScienceOn
7 Love, A.E.H. (1944), A Treatise on the Mathematical Theory of Elasticity, Dover, New York
8 Malkus, D.S. and Hughes, T.J.R. (1978), 'Mixed finite element methods-reduced and selective integration Techniques: A unification concept', Comput. Method Appl. Mech. Eng., 15, 63-81   DOI   ScienceOn
9 'ANSYS' Software and Manual (Version 5.6)
10 Batoz, J.L. and Tahar, M.B. (1982), 'Evaluation of a new quadrilateral thin plate bending element', Int. J. Numer. Meth. Eng., 18, 1655-1677   DOI
11 Dhananjaya, H.R. (2004), 'A family of plate bending finite elements using Integrated Force Method' - Ph.D thesis, Department of Civil Engineering, Indian Institute of Science, Bangalore-12, India
12 Dhatt, G. (1969), 'Numerical analysis of thin shells by curved triangular elements based on discrete Kirchhoff Hypothesis', Symposium, Nashville, ASCE, November, 255-278
13 'NISA' Software and Manual (Version 9.3)
14 Patnaik, S.N. (1973), 'An integrated force method for discrete analysis', Int. J. Numer. Meth. Eng., 41, 237-251
15 Patnaik, S.N. (1986), 'The variational energy formulation for the Integrated Force Method', AIAA J., 24, 129-137   DOI   ScienceOn
16 Nagabhushanam, J. and Srinivas, J. (1991), 'Automatic generation of sparse and banded compatibility matrix for the Integrated Force Method', Computer Mechanics '91, Int. Conf. on Comput. Eng. Sci., Patras, Greece, 20-25
17 Nagabhushanam, J. and Patnaik, S.N. (1990), 'General purpose program to generate compatibility matrix for the Integrated Force Method', AIAA J., 28, 1838-1842   DOI
18 Mallikarjuna Rao, K. and Srinivasa, U. (2001), 'A set of pathological tests to validate new finite elements', Sadhana, 26(6), 549-590   DOI
19 Timoshenko, S.P. and Krieger, S.W. (1959), Theory of Plates and Shells, Second Edition, McGraw Hill, New York
20 Wanji Chen and Cheung Y.K. (2000), 'Refined quadrilateral element based on Mindlin/Reissner plate theory', Int. J. Numer. Meth. Eng., 47, 605-627   DOI
21 Patnaik, S.N., Igor, K., Hopkins, D.A. and Sunil Saigal. (1996), 'Completed Beltrami-Michell Formulation for analyzing mixed boundary value problems in elasticity', AIAA J., 34(1), 143-148   DOI
22 Zienkiewicz, O.C., Taylor, R.L. and Too, J.M. (1971), 'Reduced integration technique in general analysis of plates and shells', Int. J. Numer. Meth. Eng., 3, 275-290   DOI
23 Reissner, E. (1945), 'The effect of transverse shear deformation on bending of plates', J. Appl. Mech., 12, A69-A77
24 Robinson, J. and Haggenmacher, G.W. (1971), 'Some new developments in matrix force Analysis', Proc. of Recent Advances in Matrix Methods of Structural Analysis and Design, University Alabama, 183-228
25 Patnaik, S.N. and Yadagiri, S. (1976), 'Frequency analysis of structures by Integrated Force Method', Comput. Method. Appl. Mech. Eng., 9, 245-265   DOI   ScienceOn