Analysis of stiffened plates composed by different materials by the boundary element method

Title & Authors
Analysis of stiffened plates composed by different materials by the boundary element method
Fernandes, Gabriela R.; Neto, Joao R.;
Abstract
A formulation of the boundary element method (BEM) based on Kirchhoff`s hypothesis to analyse stiffened plates composed by beams and slabs with different materials is proposed. The stiffened plate is modelled by a zoned plate, where different values of thickness, Poisson ration and Young`s modulus can be defined for each sub-region. The proposed integral representations can be used to analyze the coupled stretching-bending problem, where the membrane effects are taken into account, or to analyze the bending and stretching problems separately. To solve the domain integrals of the integral representation of in-plane displacements, the beams and slabs domains are discretized into cells where the displacements have to be approximated. As the beams cells nodes are adopted coincident to the elements nodes, new independent values arise only in the slabs domain. Some numerical examples are presented and compared to a wellknown finite element code to show the accuracy of the proposed model.
Keywords
plate bending;boundary elements;stiffened plates;membrane effects;stretching problem;
Language
English
Cited by
1.
A boundary element formulation to perform elastic analysis of heterogeneous microstructures, Engineering Analysis with Boundary Elements, 2018, 87, 47
References
1.
Aliabadi, M.H. (1998), Plate Bending Analysis with Boundary Elements, Advanced boundary elements series, Computational Mechanics Publications, Southampton.

2.
Beskos D.E. (1991), Boundary Element Analysis of Plates and Shells, Springer Verlag, Berlin.

3.
Bezine, G.P. (1981), "A boundary integral equation method for plate flexure with conditions inside the domain", Int. J. Numer. Meth. Eng., 17, 1647-1657.

4.
Bezine, G.P. (1978), "Boundary integral formulation for plate flexure with arbitrary boundary conditions", Mech. Res. Comm., 5(4), 197-206.

5.
Fernandes, G.R. and Venturini, W.S. (2007), "Non-linear boundary element analysis of floor slabs reinforced with rectangular beams", Eng. Anal. Bound. Elem., 31, 721-737.

6.
Fernandes, G.R. and Venturini, W.S. (2002), "Stiffened plate bending analysis by the boundary element method", Comput. Mech., 28, 275-281.

7.
Fernandes, G.R. (2009), "A BEM formulation for linear bending analysis of plates reinforced by beams considering different materials", Eng. Anal. Bound. Elem., 33, 1132 - 1140.

8.
Fernandes, G.R. and Venturini, W.S. (2005), "Building floor analysis by the Boundary element method", Comput. Mech., 35, 277-291.

9.
Fernandes, G.R., Denipotti, G.J. and Konda, D.H. (2010), "A BEM formulation for analysing the coupled stretching-bending problem of plates reinforced by rectangular beams with columns defined in the domain", Comput. Mech., 45, 523 - 539.

10.
Hartley, G.A. (1996), "Development of plate bending elements for frame analysis", Eng. Anal. Bound. Elem., 17, 93-104.

11.
Hu, C. and Hartley, G.A. (1994), "Elastic analysis of thin plates with beam supports", Eng. Anal. Bound. Elem., 13, 229-238.

12.
Paiva, J.B. and Aliabadi, M.H. (2004), "Bending moments at interfaces of thin zoned plates with discrete thickness by the boundary element method", Eng. Anal. Bound. Elem., 28, 747-751.

13.
Paiva, J.B. and Aliabadi, M.H. (2000), "Boundary element analysis of zoned plates in bending", Comput. Mech., 25, 560-566.

14.
Paiva, J.B. and Venturini, W.S. (1992), "Alternative technique for the solution of plate bending problems using the boundary element method", Adv. Eng. Softw., 14, 265-271.

15.
Sapountzakis, E.J. and Katsikadelis, J.T. (2000a), "Analysis of plates reinforced with beams", Comput. Mech., 26, 66-74.

16.
Sapountzakis, E.J. and Katsikadelis, J.T. (2000b), "Elastic deformation of ribbed plates under static, transverse and inplane loading", Comput. Struct., 74, 571-581.

17.
Sapountzakis, E.J. and Mokos V. G. (2007), "Analysis of plates stiffened by parallel beams", Int. J. Numer. Meth. Eng., 70, 1209-1240.

18.
Stern, M.A. (1979), "A general boundary integral formulation for the numerical solution of plate bending problems", Int. J. Solid. Struct., 15, 769-782.

19.
Tanaka, M. and Bercin, A.N. (1997), "A boundary element method applied to the elastic bending problems of stiffened plates", Bound. Elem. Meth. XIX, Eds. C.A. Brebbia et al., CMP, Southampton.

20.
Tanaka, M., Matsumoto, T. and Oida, S. (2000), "A boundary element method applied to the elastostatic bending problem of beam-stiffened plate", Eng. Anal. Bound. Elem., 24,751-758.

21.
Tottenhan, H. (1979), "The boundary element method for plates and shells", Developments in boundary element methods, Eds. Banerjee, P.K. and Butterfield, R., 173-205.

22.
Venturini, W.S. and Paiva, J.B. (1993), "Boundary elements for plate bending analysis", Eng. Anal. Bound. Elem., 11, 1-8.

23.
Venturini, W.S. and Waidemam, L. (2009a), "An extended BEM formulation for plates reinforced by rectangular beams", Eng. Anal. Bound. Elem., 33, 983-992.

24.
Venturini, W.S. and Waidemam, L. (2009b), "BEM formulation for reinforced plates", Eng. Anal. Bound. Elem., 33, 830-836.

25.
Waidemam, L. and Venturini, W.S. (2010), "A boundary element formulation for analysis of elastoplastic plates with geometrical nonlinearity", Comput. Mech., 45, 335-347.

26.
Wutzow, W.W., Venturini, W.S. and Benallal, A. (2006), "BEM poroplastic analysis applied to reinforced solids", Advances in Boundary Element Techniques, Paris.