Buckling of plates with variable thickness—an analog equation solution

Nerantzaki, M. S.; Katsikadelis, John T.

doi:10.1016/s0955-7997(96)00045-8

Cited by 40 publications

(14 citation statements)

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“…This method had been demonstrated in solving boundary value problems for many research areas, i.e. thermal conductivity in non-homogenous or nonlinear bodies [125], nonlinear flexural vibrations of plates [135], integration of nonlinear equations of motion [121], linear and nonlinear plate bending problems [132,160], plane elastostatic problems [128,129], finite deformation analysis of elastic cables [123,127], plate buckling problems [161], inverse problems [162], soap bubble problem [131], nonlinear analysis of shells [273], finite equationless problems in nonlinear bodies using only boundary data [133], large deflection analysis of beams [137], nonlinear static and dynamic analysis of membranes [122,130,136,138,139], ponding problem on membranes [134,163] and meshless approach on 2D elastostatic problem [124]. Since it is considered as boundary-only method, this method only deals with discretization and integration on the boundary only.…”

Section: Analog Equation Methodsmentioning

confidence: 99%

Development and implementation of some BEM variants—A critical review

Kadarman

Djojodihardjo

2010

Engineering Analysis with Boundary Elements

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a b s t r a c tDue to rapid development of boundary element method (BEM), this article explores the evolution of BEM over the past half century. We here summarize the overall development and implementation of several well-known BEM variants that includes collocation BEM, galerkin BEM, dual reciprocity BEM, complex variable BEM and analog equation method. Their theoretical and mathematical backgrounds are carefully described and a generalized Laplace's equation (and Poisson's equation) is utilized in demonstrating the different approaches involved. An up-to-date review on characteristics and implementation for each of the five variants is presented and also highlighted their significant contributions in boundary element research. In addition, this article tries to cover whole aspect of interests including efficiency, applicability and accuracy in order to give better understanding of BEM evolution. Comparisons and techniques of improvement for these variants are also discussed.

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Section: Analog Equation Methodsmentioning

confidence: 99%

Development and implementation of some BEM variants—A critical review

Kadarman

Djojodihardjo

2010

Engineering Analysis with Boundary Elements

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“…Shi [1] applied the BEM formulation for vibration and the initial stability problem of orthotropic thin plates and used the Bèzine technique [2] to establish the vector of plate curvatures inside a plate domain. Nerantzaki and Katsikadelis [3] solved the buckling problem of a plate with variable thickness. The authors applied the Analog Equation Method (AEM) connected to pure BEM [4].…”

Section: Introductionmentioning

confidence: 99%

An initial stability of plates in various conservative load conditions by the boundary element method

Guminiak¹

2015

J. Appl. Math. Comput. Mech.

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Abstract. An initial stability of Kirchhoff plates by the Boundary Element Method (BEM) is presented in the paper. A plate is subjected by external in-plane normal and tangential conservative loadings acting in two perpendicular directions. The Betti's theorem is used to derive the boundary-domain integral equations. The direct version of the Boundary Element Method is presented with combination to simplified boundary conditions. The singular and non-singular approach of the boundary integrals derivation is used.

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“…Manolis et al [5] developed a direct boundary element formulation for linear stability analysis. Syngellakis and Elzein [6] presented an extended boundary element formulation to incorporate different combination of loading and support conditions, while Nerantzaki and Katsikadelis [7] presented a boundary element formulation for buckling of plates with variable thickness. A more general boundary element formulation for linear buckling with different boundary conditions and arbitrary planar shapes was presented by Lin et al [8].…”

Section: Introductionmentioning

confidence: 99%