Elastic/plastic buckling of thick plates

Wang, Chen; Xiang, Yang; Chakrabarty, J.

doi:10.1016/s0020-7683(01)00144-5

Cited by 69 publications

(57 citation statements)

References 21 publications

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“…Zhang and Wang [8] confirmed the reported results given by Ref. [23]. Kadkhodayan and Maarefdoust [9] studied the elastic/plastic buckling of thin To the best knowledge of the authors, there is no solution available in the open literature for plastic buckling analysis of skew plates under R-shear and S-shear loading. In the current study, the differential equations of elastic/ plastic buckling of skew plates are derived and the GDQ method is used for solving those equations.…”

Section: Introductionsupporting

confidence: 73%

“…However, their boundary conditions were limited to clamped and simply supported types. Wang et al [23,24] investigated the elastic-plastic buckling of thin and thick plates based on deformation and incremental theories by use of separation of variables solution and Ritz method. They came to the conclusion that the deformation theory predicts a lower buckling stress factor, and as the thickness increases and hardening decreases (Ramberg-Osgood constant increases), the differences between the two theories increase.…”

Section: Introductionmentioning

confidence: 99%

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Elastic/plastic buckling analysis of skew plates under in-plane shear loading with incremental and deformation theories of plasticity by GDQ method

Maarefdoust

Kadkhodayan

2014

J Braz. Soc. Mech. Sci. Eng.

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The present study is concerned with the elastic/ plastic buckling analysis of a skew plate under in-plane shear loading. The governing equations for moderately thick skew plates are analytically derived based on firstorder shear deformation theory, whereas the incremental and deformation theories of plasticity are employed. Two types of shear loads, i.e. rectangular shear (R-shear) and skew shear (S-shear) have been investigated. The buckling coefficient values are significantly affected by the direction of stresses. Since the problem is geometrically and physically nonlinear, the generalized differential quadrature method as an accurate, simple and computationally efficient numerical tool is adopted to discretize the governing equations and the related boundary conditions. Then, a direct iterative method is employed to obtain the buckling coefficients of skew plates. To demonstrate the accuracy of the present analytical solution, a comparison is made with the published experimental and numerical results in literature. The influences of the aspect and thickness ratios, skew angle, incremental and deformation theories and various boundary conditions are examined for R-shear and S-shear buckling coefficients. Finally, some mode shapes of the skew thick plates are illustrated. The present results may serve as benchmark solutions for such plates.

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Section: Introductionsupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Elastic/plastic buckling analysis of skew plates under in-plane shear loading with incremental and deformation theories of plasticity by GDQ method

Maarefdoust

Kadkhodayan

2014

J Braz. Soc. Mech. Sci. Eng.

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“…From the table we can see that the differences between the present solutions and solutions of Ref. [17] are small. This indicates the validity of the present method.…”

Section: Elasto-plastic Buckling Analysis Of Orthotropic Platesmentioning

confidence: 49%

“…[17]. Table 1 shows the comparison of the elasto-plastic buckling load of isotropic plate under different geometric parameters.…”

Section: Elasto-plastic Buckling Analysis Of Orthotropic Platesmentioning

confidence: 99%

Elasto-plastic postbuckling of damaged orthotropic plates

Tian

2008

Appl. Math. Mech.-Engl. Ed.

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Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.

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“…Then another test example is calculated for elasto-plastic buckling problems of isotropic single-layer plates when the interfacial damage is not taken into consideration, and the material parameters are taken as [19]: E = 77.783 GPa, ν = 0.32, 11 = 423.338 MPa. Table 1 shows the elastic critical buckling load of laminated plates including interfacial damage under the acting of uniaxial compress, and Fig.…”

Section: Numerical Examples and Discussionmentioning

confidence: 99%

Elasto-plastic buckling analysis of laminated plates including interfacial damage

Tian

2009

Arch Appl Mech

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Elasto-plastic buckling of orthotropic laminated plates, which include interfacial damage, is analyzed in detail. Firstly, a novel mixed hardening yield criterion, as an improvement of Hill's counterpart, is proposed for the orthotropic materials on the basis of the plastic theory. And differing from Hill's theory, the present yield criterion is related to the spherical tensor of stress. Then, the incremental elasto-plastic constitutive relations of the mixed hardening orthotropic materials are presented. Secondly, the incremental static equilibrium equations for laminated plates including interfacial damage are established based on Von-Karman type theory and the principle of minimum potential energy. Finally, the elasto-plastic buckling of laminated plates are solved by adopting the Galerkin method and iteration scheme. The numerical results show that buckling of the plate occurs easier due to the existence of interfacial damage, and the critical load trends to constant when the interfacial damage approaches a certain degree. Also, the effect of anisotropy on buckling is obvious and the analysis of elasto-plastic buckling is necessary.Laminated structures are extensively used in automotive and aerospace applications, and the stability problem of which is an important subject in the solid mechanics at all times. As these structures can still bear loads when exceeding the material yield limit, the traditional elastic design scheme generally used in engineering is conservative in safety consideration. So it is uneconomical and the more reasonable elasto-plastic analysis is necessary. On the other hand, due to the technology problems in the machine-shaping and some external factors, the layers are difficult to be bonded perfectly. The interfacial damage, which has evident influence on the mechanical property of structures, will always develop in the operating circumstance.Determination of elasto-plastic constitutive relation is one of the essential issues in the analysis of mechanical property for laminated structures, and researches have achieved great progress on this aspect [1][2][3][4]. Most of these models, however, are based on the Hill's yield criterion, which suppose that material yield is independent of the spherical tensor of stress. Actually, the structures will be distorted due to the different elastic constants in every principal direction under the acting of the spherical tensor of stress. According to the Mises distortion energy yield criterion, the materials will get into plastic stage if the distortion energy approaches a certain value. Moreover, the materials have apparent Bauchinger effect under the acting of the complex stresses. Hence, Hill's hypothesis is inconsistent with the practical situation.

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Elastic/plastic buckling of thick plates

Cited by 69 publications

References 21 publications

Elastic/plastic buckling analysis of skew plates under in-plane shear loading with incremental and deformation theories of plasticity by GDQ method

Elastic/plastic buckling analysis of skew plates under in-plane shear loading with incremental and deformation theories of plasticity by GDQ method

Elasto-plastic postbuckling of damaged orthotropic plates

Elasto-plastic buckling analysis of laminated plates including interfacial damage

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