Lateral-Torsional Buckling Analysis of Axially Functionally Graded Porous Arches via the Differential Quadrature Method

An analytical study is conducted in this paper to investigate the lateral-torsional buckling (LTB) behavior of axially functionally graded porous (AFGP) circular arches under a uniformly distributed radial load. Due to the axially varying material properties, Castiglianos second theorem, the trapezoidal rule, and the Newton-Raphson method are utilized to obtain numerical pre-buckling internal forces. The governing equations for the LTB state of the AFGP arch are derived from the total energy equation using the Euler-Lagrange equations, and the LTB load is determined using the differential quadrature method (DQM). The present numerical results are validated through a comparison with finite element results. To assess the effects of the porosity coefficient and three different axial porosity distribution patterns (AO, AU, and AX), a parametric study is carried out. Results show that the porosity pattern significantly influences pre-buckling internal forces and LTB load. The AO pattern generates the highest internal forces, while AX produces the lowest. The impact on the LTB load depends on lateral boundary conditions: AO is optimal for pin-ended arches, while AX is best for fixed arches. Moreover, increasing the porosity coefficient decreases the buckling load, with the rate of decline varying by distribution pattern and lateral boundary conditions. These findings are crucial for the optimal design of AFGP arches, enabling the selection of suitable porosity distributions to tailor structural performance.