In-plane nonlinear buckling of circular arches including shear deformations

摘要

A numerical strategy is presented to trace the pre-buckling as well as the post-buckling nonlinear equilibrium paths for elastic circular arches in which the effects of shear deformations and the geometric nonlinearity due to large deformations are taken into account. Timoshenko beam hypothesis is adopted for incorporating shear. The constitutive relations including shear effects for stress and finite strain are based on a hyperelastic constitutive model. The finite strain equilibrium equations are developed for the circular arches. Based on the derived transformed equilibrium equations and the boundary conditions, the nonlinear buckling behaviour of circular arches is investigated using the trapezoid method with Richardson extrapolation enhancement. The results are validated using available experimental results in the literature, the finite element package ANSYS and other solutions in the literature. Parametric studies are performed on examples to identify the factors that influence the nonlinear buckling of circular arches. The shear deformation effects on the nonlinear buckling behaviour and the buckling mode are investigated for circular arches under many different loading conditions and various boundary conditions.