A numerical approach for equilibrium and stability analysis of slender arches and rings under contact constraints

Silveira, Ricardo Azoubel da Mota; Nogueira, Christianne de Lyra; Gonçalves, Paulo B.

doi:10.1016/j.ijsolstr.2012.09.015

Cited by 14 publications

(4 citation statements)

References 47 publications

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“…Stability problems for circular arches and rings under uniform pressure are described in detail in [2,3]. Research in the field of stability of arches does not stop at the present time [4,5,6,7,8]. With the loss of stability of the rings and arches, either plane deformation occurs (all movements occur in the plane of the undeformed ring), or spatial (movements is perpendicular to the plane of the given ring and also torsion are present).…”

Section: Introductionmentioning

confidence: 99%

Stability of a system of circular rings reinforced with inextensible threads

Andryukova

Tarasov²

2022

J. Phys.: Conf. Ser.

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The paper deals with the problems of stability for a system of circular rings interconnected in such a way that the displacements of these rings, and the rotation angles of their sections at some points, coincide. This has been reduced to a certain variational problem with restrictions on the functions in question in the form of linear equations, and Fourier series are used to obtain a finite-dimensional approximation. The paper also presents the stability problem for a system of circular rings reinforced by inextensible threads that cannot resist compressive forces. In this case, constraints in the form of inequalities arise, and after finite-dimensional approximation the problem reduces to finding the bifurcation points for a nonlinear programming problem in the presence of inequality constraints.

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Section: Introductionmentioning

confidence: 99%

Stability of a system of circular rings reinforced with inextensible threads

Andryukova

Tarasov²

2022

J. Phys.: Conf. Ser.

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“…The stability of three-pinned arches is tackled analytically in [22] with linear and nonlinear models being compared. In [23] a novel numerical method is developed for the nonlinear stability analysis of various curved elements. The model also accounts for the foundation position and stiffness.…”

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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“…The analytical solutions are given for limit point buckling with pinned boundary conditions. Paper Silveira et al (2013) presents a new numerical strategy for the nonlinear equilibrium and stability analysis of slender curved elements under unilateral constraints. It clarifies the influence of the foundation position and its stiffness on the nonlinear behavior and stability.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear stability analysis of FGM shallow arches under an arbitrary concentrated radial force

Kiss

2019

Int J Mech Mater Des

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The nonlinear in-plane buckling behaviour of pinned-pinned shallow circular arches made of functionally graded material (FGM) is investigated using a one-dimensional Euler-Bernoulli model. The effect of the bending moment on the membrane strain is included. The material properties vary along the thickness of the arch. The external load is a radial concentrated force at an arbitrary position. The prebuckling and buckled equilibrium equations are derived using the principle of virtual work. Analytical solutions are given for both bifurcation and limit point buckling. Comprehensive studies are performed to find the effect of various parameters on the buckling load and on the behaviour. The major findings: (1) arches have multiple stable and unstable equilibria; (2) when the load is at the crown, the lowest buckling load is related to bifurcation buckling for most geometries and material compositions but when the external force is replaced, only limit point buckling is possible; (3) the position of the load has huge influence on the buckling load; (4) such arches are sensitive to small loading imperfections when loaded in the vicinity of the crown. The paper intends to improve and extend the existing knowledge about the behaviour of pinnedpinned shallow FGM arches under arbitrary concentrated radial load.

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A numerical approach for equilibrium and stability analysis of slender arches and rings under contact constraints

Cited by 14 publications

References 47 publications

Stability of a system of circular rings reinforced with inextensible threads

Stability of a system of circular rings reinforced with inextensible threads

Stability of pinned-rotationally restrained arches

Nonlinear stability analysis of FGM shallow arches under an arbitrary concentrated radial force

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