Dynamic snap-through of shallow arches under thermal shock

Abstract

In the present research, dynamic buckling of a shallow arch subjected to transient type of thermal loading is investigated following the Budiansky–Hutchinson criterion. Arch is subjected to thermal shock on one surface while the other surface is kept at reference temperature. Transient heat conduction equation across the arch thickness is established and solved analytically. The induced bending moment and compressive thermal force are obtained and inserted into the equations of motion of the arch. To model the arch, classical arch theory suitable for thin arches is employed. The von Kármán type of strain-displacement relation suitable for small strains and large deformations is used. The governing nonlinear equations of motion are presented as the coupled nonlinear algebraic equations. These equations are established using the conventional Ritz method, where the shape functions are constructed employing the polynomial functions. The resulting equations are solved by means of the Newmark time marching scheme and the Newton–Raphson linearization technique. By means of the Budiansky criterion, critical thermal shock parameters are distinguished. Dynamic buckling temperatures are also verified using the phase-plane presentation, also known as the Hoff–Hsu criterion. It is verified that the shallow arches may undergo dynamic snap-through type of motion under rapid surface heating when certain geometrical constrains are met.