Abstract
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 pre-buckling 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 pinned-pinned shallow FGM arches under arbitrary concentrated radial load.
Highlights
Curved members are frequently used in engineering structures, like in bridges or roofs, because of their favourable load carrying capabilities
Arches may be supported by pins at the ends to the ground or to adjacent members. Such members are often made of functionally graded material (FGM) with material properties continuously varying over the cross section
The analytical solutions are given for limit point buckling with pinned boundary conditions
Summary
Curved members are frequently used in engineering structures, like in bridges or roofs, because of their favourable load carrying capabilities. Comprehensive studies on the in-plane buckling of arches were published in the past (Timoshenko and Gere 1961; Szeidl 1975; Simitses 1976; Bradford et al 2002; Simitses and Hodges 2006; Bazant and Cedolin 2010) It is well-known that geometrically nonlinear model is needed when analysing the stability of shallow members because the deformations prior to buckling can be significant and the behaviour can become nonlinear. Comprehensive analytical investigations are presented for both central concentrated and constant distributed loads using the classical shallow arch theory. The authors have presented and evaluated an analytical Euler–Bernoulli model—the same as in Bradford et al (2002)—to find the nonlinear equilibria and buckling load of fixed-fixed and pinnedfixed homogeneous shallow arches under arbitrary concentrated radial load. The analytical solutions can be used as benchmark for numerical solutions
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