Non-linear in-plane stability analysis of FG circular shallow arches under uniform radial pressure

Bateni, M.; Eslami, Mohammad H.

doi:10.1016/j.tws.2015.04.019

Cited by 48 publications

(23 citation statements)

References 21 publications

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“…Differential equations (25) to (27) are solved for nonlinear thermo-elastic analysis of shallow curved tubes with pined-pined and clamped-clamped end conditions in the next steps.…”

Section: Solutions Proceduresmentioning

confidence: 99%

“…Bateni and Eslami [24] analyzed the geometrically nonlinear behavior of functionally graded circular shallow arches under in-plane central concentrated load by an analytical approach. Also Bateni and Eslami [25] presented the geometrically nonlinear stability analysis of functionally graded circular shallow arches with various boundary supports under uniform distributed radial pressure loading. Han et al [26] proposed the closed-form solutions of nonlinear buckling analysis of shallow arches with elastic horizontal supports employing a classical shallow arches theory using analytical approach.…”

Section: Introductionmentioning

confidence: 99%

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Thermally induced large deflection analysis of shear deformable FGM shallow curved tubes using perturbation method

2018

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In the present investigation, geometrically nonlinear response of a shallow curved tube subjected to thermal loading is analyzed. The tube is made of a functionally graded material (FGM), where properties are distributed across the tube radius. Thermomechancal properties of the constituents are assumed to be temperature dependent. The simple case of uniform temperature rise loading is considered. A higher order displacement field is considered for the tube which satisfies the conditions of zero tangential tractions on the inner and outer surfaces of the tube. With the aid of von Kármán strain‐displacement relations, linear thermoelastic constitutive law, and Hamilton's principle the governing equations of the tube are obtained. These equations are reduced to new two coupled equations for the case of axially immovable tubes. These new equations are solved using the two step perturbation technique for pinned and clamped tubes. Closed form expressions are provided to estimate the deflections in the FGM temperature dependent curved tubes under uniform thermal load. The effect of boundary conditions, temperature dependency of material properties, and geometrical properties are discussed via numerical examples.

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“…Differential equations (25) to (27) are solved for nonlinear thermo-elastic analysis of shallow curved tubes with pined-pined and clamped-clamped end conditions in the next steps.…”

Section: Solutions Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermally induced large deflection analysis of shear deformable FGM shallow curved tubes using perturbation method

2018

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“…Temperature dependency of constituents was taken into account, and the arch was subjected to a uniform temperature field. In the study of Bateni and Eslami [13,14], they studied the nonlinear stability behavior of FGM circular shallow arches subjected to a central concentrated force and a uniform radial pressure, respectively. Numerical results were presented as the influences of material dispersion, geometrical characteristics, and boundary conditions on the stability behavior of the FGM circular shallow arches.…”

Section: Introductionmentioning

confidence: 99%

Geometrically Nonlinear Analysis of Functionally Graded Timoshenko Curved Beams with Variable Curvatures

Wan

Liu

2019

Advances in Materials Science and Engineering

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In this paper, geometrically nonlinear analysis of functionally graded curved beams with variable curvatures based on Timoshenko beam theory is presented. Considering the axial extension and the transversal shear deformation, geometrically nonlinear governing equations for the FGM curved beams with variable curvatures subjected to thermal and mechanical loads are formulated. Material properties of the curved beams are assumed to vary arbitrarily in the thickness direction and be independent on the temperature change. By using the numerical shooting method to solve the coupled ordinary differential equations, the nonlinear response of static thermal bending of a FGM semielliptic beams subjected to transversely nonuniform temperature rise is obtained numerically. e effects of material gradient, shear deformation, and temperature rise on the response of the curved beam are discussed in detail. Nonlinear bending of a closed FGM elliptic structure subjected to two pinching concentrated loads is also analyzed. is paper presents some equilibrium paths and configurations of the elliptic curved beam for different pinching concentrated loads.

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“…In practical engineering, a fixed arch under a linear temperature gradient field and a uniformly distributed radial load caused by fire may lose its bearing capacity due to instability which has received concerns recently. Analytical investigations on the buckling of arches subject to a uniformly distributed radial load or a radial point load are extensive [1][2][3][4][5][6][7][8][9][10][11][12][13]. Besides the external load, arches may also be under temperature field.…”

Section: Introductionmentioning

confidence: 99%

In‐Plane Instability of Fixed Arches under Linear Temperature Gradient Field and Uniformly Distributed Radial Load

Song

Liu

et al. 2019

Mathematical Problems in Engineering

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This paper focuses on an in-plane instability analysis of fixed arches under a linear temperature gradient field and a uniformly distributed radial load, which has not been reported in the literature. Combining a linear temperature gradient field and uniformly distributed radial load leads to the changes in axial expansion and curvature of arches, producing the complex in-plane nonuniform bending moment and axial force. Therefore, it is necessary to explore the in-plane thermoelastic mechanism behavior of fixed arches under a linear temperature gradient field and a uniformly distributed radial load in the in-plane instability analysis. Based on the energy method and the exact solutions of internal force before instability, the analytical solutions of the critical uniformly distributed radial load considering the linear temperature gradient field associated with in-plane thermoelastic instability of arches are derived. Comparisons show that agreements of analytical solutions against FE (finite element) results are excellent. Influences of various factors on in-plane instability are also studied. It is found that the change of the linear temperature gradient field has significant influences on the in-plane instability load. The in-plane instability load decreases as the temperature differential of the linear temperature gradient field increases.

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Non-linear in-plane stability analysis of FG circular shallow arches under uniform radial pressure

Cited by 48 publications

References 21 publications

Thermally induced large deflection analysis of shear deformable FGM shallow curved tubes using perturbation method

Thermally induced large deflection analysis of shear deformable FGM shallow curved tubes using perturbation method

Geometrically Nonlinear Analysis of Functionally Graded Timoshenko Curved Beams with Variable Curvatures

In‐Plane Instability of Fixed Arches under Linear Temperature Gradient Field and Uniformly Distributed Radial Load

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