Bending and creep buckling response of viscoelastic functionally graded beam-columns

The viscoelastic creep response of flexural beams and beam-columns made with functionally graded materials is numerically investigated. The paper highlights the challenges associated with the modeling and analysis of such structures, and presents a nonlinear theoretical model for their bending and creep buckling analysis. The model accounts for the viscoelasticity of the materials using differential-type constitutive relations that are based on the linear Boltzmann’s principle of superposition. The model is general in terms of its ability to deal with any material volume faction distribution through the depth of the beam, and with different linear viscoelastic laws, boundary conditions, and loading schemes. The governing equations are solved through time stepping numerical integration, which yields an exponential algorithm following the expansion of the relaxation function into a Dirichlet series. A numerical study that examines the capabilities of the model and quantifies the creep response of functionally graded beam-columns is presented, with special focus on the stresses and strains redistribution over time and on the creep buckling response. The results show that the creep response of such structures can be strongly nonlinear due to the variation of the viscoelastic properties through the depth, along with unique phenomena that are not observed in homogenous structures.