Application of the boundary-domain element method to the pre/post-buckling problem of von Kármán plates

Tanaka, Masataka; Matsumoto, Toshiro; Zheng, Zhudong

doi:10.1016/s0955-7997(98)00102-7

Cited by 9 publications

(12 citation statements)

References 9 publications

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“…In [Ruta et al 2006] some simple examples of flexural-torsional buckling and postbuckling phenomena have been investigated, showing the coincidence of the results with those in the literature, for instance in [Timoshenko and Gere 1961;Grimaldi and Pignataro 1979]. Further applications of the refined model are found in [Ruta et al 2008] where, for a simply supported compressed beam, the effect of warping constraints at the beam ends has been examined and the relevant critical loads have been presented.…”

Section: Introduction: a Direct One-dimensional Model For Thin-walledmentioning

confidence: 67%

“…Let the x 3 -axis of the chosen cartesian system coincide with the symmetry axis of the cross-section. The geometric and inertial quantities have been derived by means of standard calculations and well-known tables, such as those in [Timoshenko and Gere 1961]. Let the material of the beam be elastic and isotropic and characterized by E = 206 GPa, G = 79 GPa.…”

Section: Buckling Of a Compressed Beam With A Warping Stiffenermentioning

confidence: 99%

“…Two benchmark cases have been considered, characterized by two different cross sections exhibiting two and one axes of symmetry, respectively: a wide flange HEA240 and a channel (U-shape) with outer dimensions 100 mm (web) and 60 mm (flanges) and a uniform thickness of 3 mm. By assuming the local coordinate systems as in Figure 9, the geometric and inertial quantities of the cross-section are obtained by standard calculations and well-known tables [Timoshenko and Gere 1961;Pignataro et al 1991]:…”

Section: Bifurcations In a Two-bar Framementioning

confidence: 99%

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2009

JOMMS

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See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $600 a year (print and electronic); $460 a year (electronic only). Subscriptions, requests for back issues, and changes of address should be sent toThis paper investigates the singular integral equation method for examining the stress intensity factor and the T-stress in the asymptotic solution of a kinked crack with an infinitesimal kink length. A numerical technique for the branch crack problem is introduced, which depends upon distribution of dislocation along the crack face. The technique reduces the branch crack problem to the solution of a singular integral equation. The kinked cracked problem can be considered as a particular case of the branch crack, and this problem can be solved by using the suggested technique. It is found from the computed results that the available asymptotic solution can give qualitatively correct results for stress intensity factors and the T-stress. In addition, the available asymptotic solution can only give sufficiently accurate results in a narrow range of the length of the kinked portion and the inclined kink angle.Numerical procedures are developed for the homogenization and evaluation of the stress field in a composite as a consequence of the presence of embedded SMA (shape-memory alloy) wires. In particular, the elastic field developed at the end of the SMA wire self-strain process is studied, knowledge of which is necessary to evaluate the feasibility of such a hybrid composite.First, the numerical procedures are applied to the study of both a representative volume element (RVE) included in a theoretically infinite periodic medium and a RVE located near the medium free boundary, in order to evaluate the tangential stress field generated at the end of the fiber; then they are applied to the study of a plate able to bend after the effect of self-strain of the SMA wire.Observations are reported about the obtained results and about the similarities and the differences between the two problems.The Lyapunov exponent and moment Lyapunov exponent of two degree-of-freedom linear systems subjected to white noise parametric excitation are investigated. Through a perturbation method we obtain the explicit asymptotic expressions for these exponents in the presence of low intensity noise. The Lyapunov exponent and moment Lyapunov exponents are important characteristics for determining the almostsure and moment stability of a stochastic dynamical system. As an example, we study the almost-sure and moment stability of the flexural-torsion stability of a thin elastic beam subjected to a stochastically fluctuating follower force. The validity of the approximate results for moment Lyapunov exponents is checked by a numerical Monte Carlo simulation for these stochastic systems.A method was devised to evaluate the adhesion between a film and a substrate. A front-end coated bullet is accelerated by a gas gun and hits the substrate of the specimen under test. The impact generates a compressive stre...

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Section: Introduction: a Direct One-dimensional Model For Thin-walledmentioning

confidence: 67%

Section: Buckling Of a Compressed Beam With A Warping Stiffenermentioning

confidence: 99%

Section: Bifurcations In a Two-bar Framementioning

confidence: 99%

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2009

JOMMS

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“…Early works on geometrically nonlinear shear deformable plates by boundary element method include [Lei et al 1990;He and Qin 1993], while Marczak and de Barcellos [1998] reported on a nonlinear stability analysis in shear deformable plates by the BEM. Other works contributing to BEM analysis of nonlinear buckling of thin plates have been made [Kamiya et al 1984;Qin and Huang 1990;Tanaka et al 1999].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear buckling formulations and imperfection models for shear deformable plates by the boundary element method

Purbolaksono

Aliabadi

2010

JOMMS

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This paper presents a nonlinear buckling analysis of shear deformable plates. Two models of imperfections are introduced: small uniform transverse loads and distributed transverse loads, according to the number of half-waves indicated by the eigenvectors from linear elastic buckling analysis. A simple numerical algorithm is presented to analyze the problems. Numerical examples with different geometries, loading and boundary conditions are presented to demonstrate the accuracy of the formulation.

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“…Owing to their high computational accuracy/efficiency and much reduced effort in meshing, these methods are advantageous compared to the domain-based finite element (FE) method. However, for von Karman's plates undergoing finite deformation, such an IE formation would in addition involve a term of domain integral (Ye and Liu 1985;Qin and Huang 1990;Tanaka et al 1999). The resulting numerical method is thus of a boundary-domain element (BDE) type, involving discretization over the subdomain of finite deformation as well as along the boundaries.…”

Section: Introductionmentioning

confidence: 99%

A novel boundary-domain element method of initial stress, finite deformation and discrete cracks in multilayered anisotropic elastic solids

2006

Int J Fract

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We introduce a novel boundary-domain element method of initial stress, finite deformation (due to large rotation) and discrete cracks in multilayered anisotropic elastic solids. Because the special Green's function that satisfies the interfacial continuity and surface boundary conditions is employed, the numerical discretization is reduced to be along one side of the cracks and over the subdomains of finite deformation. Two examples are presented. First, the process of interfacial delamination is simulated around a growing through-thickness crack in a pre-stretched film bonded to a flexible substrate. It is shown that the progression of delamination damage is stable but the initiation of delamination crack can be a snap-back instability. This simultaneous damage and fracture process is approached by the cohesive zone model. Second, the postbuckling of a circular delaminated and pre-compressed film is simulated on a flexible substrate. It is shown that the compliance of substrate can play a significant role on the critical behavior of buckling. If the substrate is more compliant or stiffer than the film, the instability initiates as a subcritical hard or a supercritical soft bifurcation. The critical magnitude of pre-strain for the initiation of buckling increases with substrate stiffness.Also, the transition of buckling from the first to the second mode is captured in the simulation.

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Application of the boundary-domain element method to the pre/post-buckling problem of von Kármán plates

Cited by 9 publications

References 9 publications

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Nonlinear buckling formulations and imperfection models for shear deformable plates by the boundary element method

A novel boundary-domain element method of initial stress, finite deformation and discrete cracks in multilayered anisotropic elastic solids

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