Non-linear in-plane buckling of shallow concrete arches subjected to combined mechanical and thermal loading

In this paper, non-linear elastic pre-buckling and in-plane buckling analysis for a circular shallow concrete arch subjected to a uniformly distributed load and time-varying uniform temperature field is performed. Transient thermal strain and basic creep strain are considered, the latter modelled using a fractional derivative creep law, to investigate the coupling effects of time, temperature and geometric non-linearity on mechanical behaviour and stability boundaries. The first correspondence principle is invoked allowing the problem to be treated elastically and statically, with the non-linear equilibrium equations derived using the principle of virtual work. Numerical solutions to the variable order fractional derivatives are obtained through a finite-difference based discretisation scheme. Results show that the coupling effect between transient thermal strain and geometric non-linearity is significant as it influences pre-buckling behaviour and reduces buckling strength. Basic creep strain is less influential, causing a slight enhancement of the effects of transient thermal strain.