Nonlinear in-plane buckling of fixed shallow arches with an orthotropic thin-walled section under uniform radial and thermal loading

This paper presents a comprehensive investigation of nonlinear in-plane buckling of fixed shallow arches with an orthotropic thin-walled section under uniform radial and thermal loading. For convenience of analysis, the stretching-bending coupling within section internal forces is decoupled by utilizing a neutral plane concept. The principle of minimum total potential energy in conjunction with the first-order shear deformation theory is used to derive the differential equation of equilibrium and the buckling equation and a modified slenderness ratio is proposed to govern the buckling behaviors of laminated arches. The closed-form solutions for the limit point buckling and bifurcation buckling are obtained. Effects of environment temperature increases and the stacking sequences on the buckling load are discussed in detail. Comparisons with finite elements results show that the presented analytical solution can precisely predict the nonlinear behaviors of thin-walled laminated arches. This paper presents a comprehensive investigation of nonlinear in-plane buckling of fixed shallow arches with an orthotropic thin-walled section under uniform radial and thermal loading. For convenience of analysis, the stretching-bending coupling within section internal forces is decoupled by utilizing a neutral plane concept. The principle of minimum total potential energy in conjunction with the first-order shear deformation theory is used to derive the differential equation of equilibrium and the buckling equation and a modified slenderness ratio is proposed to govern the buckling behaviors of laminated arches. The closed-form solutions for the limit point buckling and bifurcation buckling are obtained. Effects of environment temperature increases and the stacking sequences on the buckling load are discussed in detail. Comparisons with finite elements results show that the presented analytical solution can precisely predict the nonlinear behaviors of thin-walled laminated arches.