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In this article, nonlinear analysis of pin-ended isotropic homogeneous deep arches under rapid heating is considered. Arch is subjected to thermal shock on one surface while the other surface is kept at the reference temperature. One-dimensional heat conduction equation across the thickness of the arch was solved analytically to obtain the temperature profile. The thermally induced bending moments and compressive thermal forces are evaluated from the temperature profile and inserted into the equations of motion of the arch. The equations of motion of the arch are obtained under the assumptions of uncoupled thermoelasticity laws, kinematic assumptions of a deep arch with considerations of geometrical nonlinearity and linear stress–strain–temperature law. By using the conventional multiterm polynomial Ritz method, the governing nonlinear equations of motion are discreted. The resulting nonlinear equations are solved viaNewmark time marching scheme and Newton–Raphson linearization technique. Numerical results are presented to investigate the effects of different parameters. It is shown that thermally induced vibrations indeed exist especially for thin and shallow arches. As the arch becomes thicker or deeper, the thermally induced vibrations fade up and for sufficiently thick arches, quasi-static and dynamic responses of the arch become identical.

Nonlinear analysis of pin-ended deep arches under instantaneous heating