Material distribution optimization of functionally graded arch subjected to external pressure under temperature rise field

This paper investigates the material spatial redistribution optimization of the conventional functionally graded material (CFGM) arch. An inverted functionally graded material (IFGM) arch is developed to promote the critical buckling pressure of the heated arch without variation of the volume portion of the material constituents of the CFGM arch. Based on the classical thin-walled arch theories and admissible displacement functions, the total potential energy function of the IFGM arch is obtained. By variation of this energy function, the non-linear bifurcation equilibrium equations are established, and the analytical prediction of the critical buckling pressure is obtained for the IFGM arch. Subsequently, a two-dimensional (2D) finite element model (FEM) is established to trace the pressure-displacement equilibrium paths to obtain the maximum pressure (critical buckling pressure). The numerical results show very close agreement with the present analytical solutions. Furthermore, the IFGM arch shows a substantial increase of the critical buckling pressure compared with the CFGM arch. In addition, the critical buckling pressure of the heated homogeneous arch is compared with the available other closed-form expressions. Finally, to further understand the stability of the pressurized IFGM arch under temperature rise field, parametric studies are performed to examine the effects of the various involved parameters, such as the volume fraction exponent and temperature rise on the bending moment, the hoop force, the hoop strain and stress, the radial and hoop displacement through the arch span.