Linear and geometrically nonlinear analysis of non-uniform shallow arches under a central concentrated force

Tsiatas, George; Babouskos, Nick G.

doi:10.1016/j.ijnonlinmec.2017.03.019

Cited by 44 publications

(16 citation statements)

References 36 publications

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“…Both simulations and experiments are described and compared. An integral equation procedure is described and solved with the analog equation method in [28] for arches with a geometrically nonuniform cross-section. The stability of three-pinned arches is tackled analytically in [22] with linear and nonlinear models being compared.…”

Section: Introductionmentioning

confidence: 99%

Stability of pinned-rotationally restrained arches

Kiss

2021

Theor appl mech (Belgr)

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The article aims to find the buckling loads for pinned-rotationally restrained shallow circular arches in terms of the rotational end stiffness, geometry and material distribution. The loading is a concentrated vertical force placed at the crown. A geometrically nonlinear model is presented which relates not only the axial force but also the bending moment to the membrane strain. The nonlinear load-strain relationship is established between the strain and load parameters. This equation is then solved and evaluated analytically. It turns out that the stiffness of the end-restraint has, in general, a significant effect on the lowest buckling load. At the same time, some geometries are not affected by this. As the stiffness becomes zero, the arch is pinned-pinned and as the stiffness tends to infinity, the arch behaves as if it were pinned-fixed and has the best load-bearing abilities.

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Section: Introductionmentioning

confidence: 99%

Stability of pinned-rotationally restrained arches

Kiss

2021

Theor appl mech (Belgr)

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“…They showed the deformation process of toggles at various stages during the snapthrough process. Tsiatas and Babouskos [14] studied the linear and geometrically nonlinear problem of non-uniform shallow arches under a central concentrated force. They determined the value of the buckling load for the given parameters and presented the normal displacement, the axial force, the shear force and the bending moment diagrams corresponding to the loads which were equal, smaller and larger than the buckling load.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Behavior of Beams Having Initially Small Imperfection Subjected to Sinusoidal Load

Atacan

Yükseler

2020

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi

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In the present study, the buckling and postbuckling behaviors of beams having initially small sinusoidal imperfection with pinned ends subjected to sinusoidal loading are examined by using Euler-Bernoulli beam theory. The governing differential equations of the geometrically nonlinear problem consisting of the equilibrium equations, kinematical equations and the constitutive equations are converted into algebraic equations via the finite differences and solved numerically by using the Newton-Raphson method. The values of buckling loads and buckling deflections are determined by drawing load-deflection curves. The effect of the initial imperfection on the buckling values is investigated. It is seen that as the value of the small initial imperfection is increased, the buckling force is increased and buckling deflection is decreased. Unlike previous studies on the subject, the diagrams of the deformed shapes of the beam having initially small imperfection as well as the diagrams of the internal forces at various stages of the deformation including the prebuckling, buckling and postbuckling states are presented for various values of the initial imperfection.

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“…Pydah and Sabale [27] investigated the static analysis of curved beams made of bi-directional functionally graded materials based on the classical Euler-Bernoulli arches theory subjected to various tip loads. Other investigations about nonlinear analysis of curved structures can be followed in the works of Bouras and Vrcelj [28] , Tsiatas and Babouskos [29] , She et al [30] , among others. Bouras and Vrcelj [28] studied the non-linear in-plane stability analysis of shallow concrete arches under combined mechanical and thermal loads by employing an analytical method.…”

Section: Introductionmentioning

confidence: 99%

“…Bouras and Vrcelj [28] studied the non-linear in-plane stability analysis of shallow concrete arches under combined mechanical and thermal loads by employing an analytical method. Tsiatas and Babouskos [29] researched the geometrically linear and nonlinear behavior of non-uniform shallow arches subjected to a central concentrated load by using an analytical approach. Finally, She et al [30] presented a study on the nonlinear bending analysis of FGM long cylindrical shallow shells resting on two-parameter elastic foundation under uniform transverse load by employing a two-step perturbation technique.…”

Section: Introductionmentioning

confidence: 99%

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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Linear and geometrically nonlinear analysis of non-uniform shallow arches under a central concentrated force

Cited by 44 publications

References 36 publications

Stability of pinned-rotationally restrained arches

Stability of pinned-rotationally restrained arches

Nonlinear Behavior of Beams Having Initially Small Imperfection Subjected to Sinusoidal Load

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

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