×

zbMATH — the first resource for mathematics

Stability analysis of the thin plates with arbitrary shapes subjected to non-uniform stress fields using boundary element and radial integration methods. (English) Zbl 1403.74201
Summary: In this paper, a boundary element method is applied to buckling analysis of thin plates with arbitrary shapes under various load types. The governing differential equation is converted into equivalent integral equation using the static fundamental solutions of the biharmonic equation. The arising domain integrals due to in-plane stresses are evaluated applying the radial integration method. The in-plane stresses are implemented through Gaussian integration points along radial direction in the convex domains. For the concave domains, an idea has been introduced to compute radial integration along new direction from an auxiliary point to the field point. This method can be easily applied to buckling analysis of thin plates with arbitrarily distributed and concentrated edge loading. Six sample problems are presented to illustrate the effectiveness and accuracy of the proposed method.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
74H55 Stability of dynamical problems in solid mechanics
74K20 Plates
74G60 Bifurcation and buckling
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Wang, X.; Wang, Y.; Ge, L., Accurate buckling analysis of thin rectangular plates under locally distributed compressive edge stresses, Thin-Walled Struct, 100, 81-92, (2016)
[2] Mijušković, O., Analytical model for buckling analysis of the plates under patch and concentrated loads, Thin-Walled Struct, 101, 26-42, (2016)
[3] Mijušković, O.; Ćorić, B.; Šćepanović, B., Exact stress functions implementation in stability analysis of plates with different boundary conditions under uniaxial and biaxial compression, Thin-Walled Struct, 80, 192-206, (2014)
[4] Liu, Y., Elastic stability analysis of thin plate by the boundary element method—a new formulation, Eng Anal, 4, 3, 160-164, (1987)
[5] Tsiatas, G. C.; Yiotis, A. J., A BEM-based meshless solution to buckling and vibration problems of orthotropicplates, Eng Anal Boundary Elem, 37, 3, 579-584, (2013) · Zbl 1297.74159
[6] Syngellakis, S.; Elzein, A., Plate buckling loads by the boundary element method, Int J Numer Methods Eng, 37, 10, 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, 2, 149-154, (1996)
[8] Gao, X.-W., The radial integration method for evaluation of domain integrals with boundary-only discretization, Eng Anal Boundary Elem, 26, 10, 905-916, (2002) · Zbl 1130.74461
[9] Albuquerque, E.; Sollero, P.; Portilho de Paiva, W., The radial integration method applied to dynamic problems of anisotropic plates, Commun Numer Methods Eng, 23, 9, 805-818, (2007) · Zbl 1130.74050
[10] Aliabadi, M.; Baiz, P.; Albuquerque, E., Stability analysis of plates, Recent advances in boundary element methods, 1-14, (2009), Springer · Zbl 1161.74499
[11] Paiva, W. P.; Sollero, P.; Albuquerque, E. L., Modal analysis of anisotropic plates using the boundary element method, Eng Anal Boundary Elem, 35, 12, 1248-1255, (2011) · Zbl 1259.74062
[12] Aliabadi, M. H.; Baiz, P. M.; Albuquerque, E. L., Stability analysis of plates, (Manolis, G. D.; Polyzos, D., Recent advances in boundary element methods: a volume to honor professor Dimitri Beskos, (2009), Springer Netherlands Dordrecht), 1-14 · Zbl 1161.74499
[13] Doval, P. C.M.; Albuquerque, É. L.; Sollero, P., Stability analysis of elastic plates under non-uniform stress fields by the boundary element method, de Mecánica computacional, (2010), Argentina
[14] Katsikadelis, J. T., The boundary element method for plate analysis, Vol. 1, (2014), Elsevier Inc. UK · Zbl 1325.74002
[15] Movahedian, B.; Boroomand, B., Inverse identification of time-harmonic loads acting on thin plates using approximated Green’s functions, Inverse Prob Sci Eng, 24, 8, 1475-1493, (2016) · Zbl 1348.65176
[16] Johnston, P. R.; Elliott, D., A sinh transformation for evaluating nearly singular boundary element integrals, Int J Numer Methods Eng, 62, 4, 564-578, (2005) · Zbl 1119.65318
[17] Gu, Y.; Chen, W.; Zhang, C., The sinh transformation for evaluating nearly singular boundary element integrals over high-order geometry elements, Eng Anal Boundary Elem, 37, 2, 301-308, (2013) · Zbl 1352.65586
[18] Liu, Y., Elastic stability analysis of thin plate by the boundary element method—a new formulation, Eng Anal Boundary Elem, 4, 3, 160-164, (1987)
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.