Incremental analysis of finite deflection of elastic plates via boundary-domain-element method

Tanaka, Michihiko; Matsumoto, Toshiro; Zheng, Zhudong

doi:10.1016/0955-7997(96)00008-2

Cited by 13 publications

(17 citation statements)

References 7 publications

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“…A non-linear system of equations for large deflection analysis of shear deformable plates similar to Equations (28) and (29), except of course for the presence of the curvature terms, was first proposed by Purbolaksono and Aliabadi [15].…”

Section: Boundary Non-linear Term In the Out-of-plane Integral Equationmentioning

confidence: 99%

Post buckling analysis of shear deformable shallow shells by the boundary element method

Baiz

Aliabadi

2010

Numerical Meth Engineering

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SUMMARYThis paper presents four boundary element formulations for post buckling analysis of shear deformable shallow shells. The main differences between the formulations rely on the way non-linear terms are treated and on the number of degrees of freedom in the domain. Boundary integral equations are obtained by coupling boundary element formulation of shear deformable plate and two-dimensional plane stress elasticity. Four different sets of non-linear integral equations are presented. Some domain integrals are treated directly with domain discretization whereas others are dealt indirectly with the dual reciprocity method. Each set of non-linear boundary integral equations are solved using an incremental approach, where loads and prescribed boundary conditions are applied in small but finite increments. The resulting systems of equations are solved using a purely incremental technique and the Newton-Raphson technique with the Arc length method. Finally, the effect of imperfections (obtained from a linear buckling analysis) on the post-buckling behaviour of axially compressed shallow shells is investigated. Results of several benchmark examples are compared with the published work and good agreement is obtained.

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Section: Boundary Non-linear Term In the Out-of-plane Integral Equationmentioning

confidence: 99%

Post buckling analysis of shear deformable shallow shells by the boundary element method

Baiz

Aliabadi

2010

Numerical Meth Engineering

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“…The numerical procedure to solve the system of equations has been chosen considering the results obtained in [6], [9] and [17]; the system of non-linear equations generated is solved using an incremental load approach. Following [17] the load is divided into several quasi-linear steps, in which the new integrals containing the large de ‡ection terms are considered as an additional load to be computed from the previous step.…”

Section: Iterative Proceduresmentioning

confidence: 99%

“…The Dual Reciprocity Method (DRM) is implemented to transfer to the boundary the domain integrals of the large de ‡ection contribution, as shown in [17]. Boundary element application to large de ‡ection theory for plates can be found in [7], [9] and [6].…”

Section: Introductionmentioning

confidence: 99%

Dual boundary method for assembled plate structures undergoing large deflection

Pisa

Aliabadi

Young

2011

Numerical Meth Engineering

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In this paper, the Dual Boundary Element Method is combined with a multi-region formulation to simulate plate assembly undergoing large de ‡ection. The incremental load approach is used to treat the geometrical non-linearity and Radial Basis Functions are used to approximate the derivatives of the large de ‡ection terms. The Dual Reciprocity Method is used to transfer to the boundary all the domain integrals. Once the solution at the boundary is obtained for the assembly, a J-integral for large de ‡ection is implemented to extract the fracture parameters.

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“…The first BEM formulation to analyze plate-bending problems within the context of von Kármán hypothesis is due to Ye and Liu [3], who have used a fictitious loading distributed over the domain to model the non-linear effects. Von Kármán hypothesis was also adopted by Tanaka et al [4] to develop a more elaborated BEM incremental formulation to deal with finite deflections of thin elastic plates. Wang et al [5] have also worked on von Kármán plates introducing the dual reciprocity approach based on global radial functions to approximate the correcting integral term.…”

Section: Introductionmentioning

confidence: 99%

Analysis of von Kármán plates using a BEM formulation

Waidemam¹,

Venturini²

2007

WIT Transactions on Modelling and Simulation, Vol 44

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This work deals with non-linear geometrical plates in the context of von Kármán theory. The formulation is written in a way to require only boundary in-plane displacement and deflection integral equation for boundary collocations. At internal points only out of plane rotation, curvature and in-plane internal force representations are used. The non-linear system of algebraic equations to be solved is reduced to internal point collocation relations. The solution is solved by using a Newton scheme for which a consistent tangent operator was derived.

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Incremental analysis of finite deflection of elastic plates via boundary-domain-element method

Cited by 13 publications

References 7 publications

Post buckling analysis of shear deformable shallow shells by the boundary element method

Post buckling analysis of shear deformable shallow shells by the boundary element method

Dual boundary method for assembled plate structures undergoing large deflection

Analysis of von Kármán plates using a BEM formulation

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