The application of fundamental solutions in static analysis of thin plates resting on the internal elastic support

• Autorzy: Pawlak Z. , Guminiak M.
• Języki publikacji: EN

Abstrakty

EN

A static analysis of Kirchhoff plates rested on the elastic internal supports has been discussed in the paper. The Finite Strip Method and Boundary Element Method have been used as an engineering tool in the analysis. Suitable fundamental solutions are applied in these method. Using BEM modified approach, there is no need to introduce the Kirchhoff forces at the plate corner and equivalent shear forces at the plate boundary. Two unknown and independent variables are considered at the boundary element node. The collocation points are located slightly outside the plate boundary, hence the quasidiagonal integrals of fundamental functions are non-singular. The constant type of boundary element has been used. According to the finite strip method a continuous structure is divided into a set of identical elements simply supported on opposite edges. The unknowns are the deflections and the transverse slope amplitudes along the nodal lines. The difference equation formulation is applied to express the equilibrium conditions of the discrete system. This reduces the number of degrees of freedom to be analyzed. The solution of one equilibrium difference equation yields the fundamental function of the considered plate strip. The fundamental solution derived in this way, can be used to solve the static problem of finite plate in analogically as in the boundary element method for continuous systems.

Słowa kluczowe

EN

finite strip method; boundary element method; Kirchhoff plates; fundamental solution

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Civil and Environmental Engineering
• Rocznik: 2008
• Tom: No. 11
• Strony: 67--96
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Pawlak Z.

autor

Guminiak M.

• Institute of Structural Engineering, Piotrowo 5, 61-238 Poznań Tel.: [phone]; fax: [phone],

Bibliografia

• 1.Brebbia, C.A., Teiles, J.C.F. and Wrobel, L.C.: Boundary Element Techniques, Theory and Applications in Engineering, Springer-Verlag, Berlin Heidelberg, New York, Tokyo, 1984.
• 2.Burczyński T.: The Boundary Element Method in Mechanics, Technical--Scientific Publishing house, Warszawa, 1995 (in Polish).
• 3.Bèzine G.: Boundary integral formulation for plate flexure with arbitrary boundary condition, Mechanics Resarch Communications, 5(4) (1978), 197-206.
• 4.Stern M.: A general boundary integral formulation for the numerical solution of plate bending problems, Int. J. Solids Structures 15 (1979), 169-782.
• 5.Vander Weeën F.: Application of the boundary integral equation method to Reissner’s plate model, Int. J. Num. Meth. Engng., 18 (1982) 1-10.
• 6.Okupniak B, Sygulski R.: Non-singular BEM analysis of Reissner plates, Proceedings of 15th International Conference on Computer Methods in Mechanics CMM-2003, 3-6 June 2003, Gliwice/Beskidy Mountains, Poland, 265-266.
• 7.Ganowicz R.: Some questions of theory Reissner and three-layers plates, Theoretical and Applied Mechanics, 1966 (in Polish).
• 8.El-Zafrany A., Debbih M. and Fadhil S.: A modified Kirchhoff theory for boundary element bending analysis of thin plates, Int. J. Solids Structures, 21 (31) (1994), 2885- 2889.
• 9.Guminiak M.: Application of the boundary element method in static analysis of thin plates (in Polish), 3nd Scientific Conference of PhD Students of Civil Engineering, Gliwice-Wisla, 21-22 November, 2002, Silesian University of Technology, Poland, 223-232.
• 10.Guminiak M.: Thin plates analysis by the boundary element method using new formulation of a boundary condition (in Polish), PhD Thesis, Poznan University of Technology, Poznan, Poland, 2004. 11.Guminiak M., Okupniak B., Sygulski R.: Analysis of plate bending by boundary element method, 2nd European Conference on Computational Mechanics ECCM-2001, June 26-29, Cracow, Poland, 1, 2001, 176-177.
• 12.Bezine G.: A boundary integral equation method for plate flexure with condition inside the domain, Int. J. Num. Meth. Engng. 15 (1981), 1647-1657.
• 13.de Paiva J. B., Venturini W. S.: Boundary element algorithm for building floor slab analysis, In International Conference of BETECH 85, Adelaide,
• Australia, Brebbia C. A., Noye B. J. (eds), Computational Mechanics Publications (1985), 201-209.
• 14.de Paiva J. B., Venturini W. S.: Analysis of building structures considering plate-beam-column interactions, In International Conference of BETECH 87, Rio de Janeiro, Brazil, Brebbia C. A., Venturini W. S. (eds), Computational Mechanics Publications (1987), 209-219.
• 15.Hartmann F., Zotemantel R.: The direct boundary element method in plate bending, Int. J. Num. Meth. Engng., 23 (1986), 2049-2069.
• 16.Abdel-Akher A., Hartley G. A.: Evaluation of boundary integrals for plate bending. Int. J. Num. Meth. Engng., 28 (1989), 75-93.
• 17.Guminiak M., Sygulski R.: The analysis of internally supported thin plates by the Boundary Element Method. Parti-Static analysis, Foundation of Civil and Environmental Engineering, 9, (2007), 17-41, Poznan University of Technology, Poznan, Poland.
• 18.Xiao J. R.: Boundary element analysis of unilateral supported Reissner plates on elastic foundations, Computational Mechanics, 27 (2001), 1-10.
• 19.Rashed Y. F.: A coupled BEM-flexibility force method for bending analysis of internally supported plates. Int. J. Num. Meth. Engng., 54 (2002), 1431--1457.
• 20.Abdel-Akher A., Hartley G. A.: Domain integration for plate bending analysis by the boundary element method, Applied Numerical Method, 5 (1989), 23-28.
• 21.Loo Y. C., Cusens A. R., The Finite Strip Method in Bridge Engineering,New York, Viewpoint Publications, 1978.
• 22.Z. Pawlak, J. Rakowski : Dynamic analysis of infinite plate strip by the finite strip method. 16th International Conference on Computer Methods in Mechanics CMM-2005, Częstochowa, Poland, 21-24 June 2005, pp. 183--184.
• 23.Rakowski J., The interpretation of the shear locking in beam elements.Comp. Structures, 37, (1990), 769-776.
• 24.Li H., Dempsey J. P.: Unbonded contact of a square plate on a elastic halfspace or a Winkler foundation, ASME, J. Appl. Mech., 55 (1988), 430-436.
• 25.Bathe K. J., Chaudary A. B.: A solution method for planar and axisymmetric contact problems, International Journal of Numerical Method in Engineering, 21 (1985), 65-88.
• 26.Bu X.M., Yan Z.D., Bending problems of rectangular thin plate with free edges laid on tensionless Winkler foundation, Appl. Math. Mech., 10(5) (1989), 435-442.