Thermally induced large deflection of FGM shallow micro-arches with integrated surface piezoelectric layers based on modified couple stress theory

Based on the modified couple stress theory, nonlinear thermally induced large deflection analysis of shallow sandwich arches is studied. A functionally graded material (FGM) micro-arch with piezoelectric layers integrated into the surfaces and with immovable pinned and fixed edges is analyzed. Temperature and position dependence of the thermomechanical properties for an FGM micro-arch are taken into account. The piezo-FGM arches are subjected to different types of thermal loads such as uniform temperature, linear temperature, and heat conduction. A modified couple stress theory is combined with the uncoupled thermoelasticity assumptions to derive the governing equations of the arch by using the virtual displacement principle. The von Kármán type of geometrical nonlinearity and first-order shear deformation theory are also used to obtain the equilibrium equations. The nonlinear governing equilibrium equations of the piezo-FGM sandwich arch under different thermal loads are solved analytically. The solutions of the system of ordinary differential equations for both cases of boundary conditions are established by employing the two-step perturbation technique. Comparison is made with the existing results for the cases of FGM arch without couple stress and piezoelectric layers under uniform temperature rise, and good agreement is obtained. Also, parametric studies are proposed to show the effects of couple stress, piezoelectric layers, volume fraction index, geometrical parameters, and temperature dependence, the thermally induced deflection of the piezo-FGM sandwich arch.