Comparative static analysis of functionally graded porous curved beams: Deterministic versus stochastic approaches

Abstract

This study presents a comprehensive exploration of the comparative static analysis of functionally graded porous curved beams, examining deterministic versus stochastic approaches. The material randomness is incorporated using a stochastic finite element model. The formulation employed in this study utilizes three-noded elements and combines a higher-order shear deformation theory (HSDT) with the probabilistic first-order perturbation technique. The investigation focuses on an FGM curved beams incorporating various porosity models, including even, uneven, and sinusoidal distributions. The FGM porous curved beam is subjected to a uniform distributed load, and the study aims to determine the stochastic bending responses under these conditions. Additionally, various parameters influencing bending response, such as boundary conditions, geometric configurations, volume fraction indices, and porosity distributions, are examined. The uncertain bending responses are assessed in terms of material stochasticity using a stochastic finite element model, with validation through Monte Carlo simulation. Subsequent research endeavors within this field may investigate the impact of random fluctuations on both geometry and boundary conditions.