A thermally-coupled elastic large-deformation model of a multilayered functionally graded material curved beam

A thermally-coupled elastic large-deformation model of a multilayered functionally graded material (FGM) curved beam with an arbitrary undeformed configuration is established based on two-variable geometrical relations that consider the effect of the curvature of an arbitrary undeformed configuration of a beam, thermally coupled constitutive relations, and balanced forces. By use of a reference strain and reference undeformed and deformed curvatures at the same reference layer of a multilayered FGM curved beam, the difficulty of determining the position of the neutral axis of a beam in its classical analysis is resolved. The differential quadrature method is used to solve the strongly nonlinear coupled model proposed in this work. As applications, thermally-coupled large-deformation analyses of a multilayered straight beam and FGM and multilayered FGM curved beams under thermal-mechanical loads are studied in detail. Numerical results show that there are significant differences between the current thermally coupled analysis and conventional thermoelastic analysis with a thermally-uncoupled constitutive relation. Various snap-through phenomena occur when the FGM curved beam is under thermal-mechanical loads.