Accurate numerical solutions for the static analysis of functionally graded porous deep curved beams under various boundary conditions

This article presents a numerical solution for the static analysis of functionally graded porous deep curved beams with various boundary conditions. The main objective is to develop an accurate reference model for structures with high curvature and arbitrary support conditions, where simplified theories—such as higher-order shear deformation models—exhibit limited accuracy. The strong form of the governing equations is derived from two-dimensional elasticity theory for curved beams and solved using the Differential Quadrature Method, which ensures interlaminar continuity of displacements and stresses as well as boundary condition equations. Numerical validation is performed by comparison against results reported in the literature and those obtained using commercial finite element software. A parametric study is performed to investigate the influence of geometric curvature, material gradation, and porosity on the structural response. The results demonstrate the model’s capability to yield accurate solutions applicable to the design of curved structural components made of functionally graded materials.