# zbMATH — the first resource for mathematics

Buckling analysis of shear deformable shallow shells by the boundary element method. (English) Zbl 1195.74216
Summary: In this work a boundary element (BE) formulation for buckling problem of shear deformable shallow shells is presented. A set of five boundary integral equations are obtained by coupling two-dimensional plane stress elasticity with shear deformable plate bending (Reissner). The domain integrals appearing in the formulation (due to the curvature and due to the domain load) are transferred into equivalent boundary integrals. The BE formulation is presented as an eigenvalue problem, to provide direct evaluation of critical load factors and buckling modes. Several examples are presented. The BE results for a cylindrical shallow shell with different curvatures are compared with other numerical solutions and good agreements are obtained.

##### MSC:
 74S15 Boundary element methods applied to problems in solid mechanics 74G60 Bifurcation and buckling 74K25 Shells
LAPACK
Full Text:
##### References:
 [1] Timoshenko, S.; Gere, J.M., Theory of elastic stability, (1961), McGraw-Hill New York [2] Brush, D.O.; Almroth, B.O., Buckling of bars, plates and shells, (1975), McGraw-Hill New York · Zbl 0352.73040 [3] Gerard G, Becker H. Handbook of structural stability part III—buckling of curved plates and shells. NACA TN 3783, Washington, 1957. [4] Bushnell, D., Computerized buckling analysis of shells, (1985), Martinus Nijhoff Publishers Dordrecht [5] Manolis, G.D.; Beskos, D.E.; Pineros, M.F., Beam and plate stability by boundary elements, Comput struct, 22, 917-923, (1986) · Zbl 0578.73070 [6] Syngellakis, S.; Elzein, A., Plate buckling loads by the boundary element method, Int J numer method eng, 37, 1763-1778, (1994) · Zbl 0804.73073 [7] Nerantzaki, M.S.; Katsikadelis, J.T., Buckling of plates with variable thickness—an analog equation solution, Eng anal boundary elem, 18, 149-154, (1996) [8] Lin, J.; Duffield, R.C.; Shih, H.R., Buckling analysis of elastic plates by boundary element method, Eng anal boundary elem, 23, 131-137, (1999) · Zbl 0953.74072 [9] Reissner, E., On bending of elastic plates, Q appl math, 5, 55-68, (1947) · Zbl 0030.04302 [10] Purbolaksono, J.; Aliabadi, M.H., Buckling analysis of shear deformable plates by the boundary element method, Int J numer methods eng, 62, 537-563, (2005) · Zbl 1077.74055 [11] Baiz, P.M.; Aliabadi, M.H., Linear buckling analysis of shallow shells by the boundary domain element method, Comput modelling eng sci, 13, 19-34, (2006) · Zbl 1357.74034 [12] Aliabadi, M.H., The boundary element method, vol II: applications to solid and structures, (2002), Wiley Chichester [13] Reissner, E., On a variational theorem in elasticity, J math phys, 29, 90-95, (1950) · Zbl 0039.40502 [14] Dirgantara, T.; Aliabadi, M.H., A new boundary element formulation for shear deformable shells analysis, Int J numer methods eng, 45, 1257-1275, (1999) · Zbl 0930.74072 [15] Dirgantara, T.; Aliabadi, M.H., Dual boundary element formulation for fracture mechanic analysis of shear deformable shells, Int J solids and struct, 28, 7769-7800, (2001) · Zbl 1024.74046 [16] Wen, P.H.; Aliabadi, M.H.; Young, A., Application of dual reciprocity method to plates and shells, Eng anal boundary elem, 24, 583-590, (2000) · Zbl 1010.74077 [17] Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J, et al. LAPACK users’ guide, 3rd ed. Society for Industrial and Applied Mathematics, 1999. · Zbl 0934.65030 [18] Donnell LH. Stability of thin walled tubes under torsion. NACA Report 479, 1933. [19] ANSYS, Inc. Version 9.0, 1994.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.