Incremental Approach to the Finite Deflection Problem of Thin Elastic Plates Via Boundary-Domain-Element Method

Tanaka, Michihiko; Matsumoto, Toshiro; Zheng, Zhudong

doi:10.1007/978-94-011-5706-3_32

Cited by 3 publications

(2 citation statements)

References 7 publications

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“…Such a response can either be generated as a bifurcation from the fundamental equilibrium path at the critical load [9,10] or initiated by imperfections [11]. There has not been any known attempt at analysing the post-buckling behaviour of anisotropic laminated plates using a BEM-based technique.…”

Section: Introductionmentioning

confidence: 99%

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Boundary element modelling of non-linear buckling for symmetrically laminated plates

Syngellakis¹,

Cherukunnath²

2009

Mesh Reduction Methods

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The non-linear buckling of composite laminates, triggered by geometric imperfections, is here analysed adopting a boundary element methodology. The non-linear theory for thin anisotropic plates couples in-plane forces causing buckling with the consequent bending deformation. The adopted formulation for in-plane forces in terms of the stress function is mathematically identical to that for the bending problem, thus boundary integral equations and fundamental solutions of the same form are used. Differential equations governing increments of the stress function and the deflection are obtained; the resulting integral equations include irreducible domain integrals depending on powers or products of the second derivatives of the stress function and the deflection. The latter are calculated through complementary integral equations obtained from the original ones by differentiating the field variables in the domain. The solution process accounts for the domain integrals through an iterative scheme; thus there is no need for modelling any field variables in the plate domain although domain meshing is necessary for performing numerical integrations. The boundary is meshed into quadratic discontinuous elements while the domain is divided into triangular cells with linear discontinuous variation of the relevant field variables for integration purposes. The analysis is implemented through a suit of C codes and applied to a rectangular symmetrically laminated plate. Its predictions are compared with published results obtained by other methods. The accuracy and limitations of the formulation are discussed and alternative approaches for expanding its scope pointed out.

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Section: Introductionmentioning

confidence: 99%

“…The compatibility condition is obtained by eliminating the in-plane displacements from eqn (10). This is accomplished by defining the operator and applying it to both sides of eqn (10) leading to:…”

Section: Introductionmentioning

confidence: 99%

Boundary element modelling of non-linear buckling for symmetrically laminated plates

Syngellakis¹,

Cherukunnath²

2009

Mesh Reduction Methods

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Analysis of plates stiffened by parallel beams

Sapountzakis

Mokos

2006

Numerical Meth Engineering

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SUMMARYIn this paper a general solution for the analysis of plates stiffened by parallel beams subjected to an arbitrary loading is presented. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, taking into account the arising tractions in all directions at the fictitious interfaces. The aforementioned integrated tractions result in the loading of the beams as well as the additional loading of the plate. Their distribution is established by applying continuity conditions in all directions at the interfaces. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account second-order effects. Six boundary value problems with respect to the plate transverse deflection, to the plate inplane displacement components, to the beam transverse deflections, to the beam axial deformation and to the beam non-uniform angle of twist are formulated and solved using the analog equation method (AEM), a boundary element method (BEM)-based method employing a boundary integral equation approach. The solution of the aforementioned plate and beam problems, which are non-linearly coupled, is achieved using iterative numerical methods. The adopted model describes better the actual response of the plate beams system and permits the evaluation of the shear forces at the interfaces in both directions, the knowledge of which is very important in the design of prefabricated ribbed plates. The evaluated lateral deflections of the plate-beams system are found to exhibit considerable discrepancy from those of other models, which neglect inplane and axial forces and deformations.

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Shear deformation effect in the dynamic analysis of plates stiffened by parallel beams

Sapountzakis

Mokos

2008

Acta Mech

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Incremental Approach to the Finite Deflection Problem of Thin Elastic Plates Via Boundary-Domain-Element Method

Cited by 3 publications

References 7 publications

Boundary element modelling of non-linear buckling for symmetrically laminated plates

Boundary element modelling of non-linear buckling for symmetrically laminated plates

Analysis of plates stiffened by parallel beams

Shear deformation effect in the dynamic analysis of plates stiffened by parallel beams

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