Hygro-thermal vibration of bidirectional functionally graded porous curved beams on variable elastic foundation using generalized finite element method

The aim of this paper is to present the hygro-thermal vibration behavior of bidirectional functionally graded porous (BDFGP) curved beams resting on two-layer elastic foundations (EF) using the generalized finite element method (GFEM). In which, one of these two layers is composed of Winkler springs with the variation of modulus, while the other is composed of shear springs with a fixed modulus. The enrichment is accomplished by constructing the enriched mathematical space using an enriched FE shape function. Moisture causes tensile stresses in the x-axis direction without affecting mechanical characteristics of the material, while temperature changes Young's modulus of elasticity and thermal expansion coefficients. The free vibration equation for the curved beam is developed that relied on the k-order shear deformation beam theory and Hamilton's principle. The correctness of the proposed model is evaluated by comparing obtained numerical results of the present work to the findings of credible publications in the literature. By considering the free vibration responses of the curved beam, the effects of parameters such as the grading power indexes, the porosity coefficient, the temperature and moisture change, the opening angle of the curved beam, stiffness of the EF, boundary conditions, and the thickness-to-length ratio are investigated.