Nonlinear finite element analysis of functionally graded structures by enhanced assumed strain shell elements

In this work, large elastic deformation of structures made of functionally graded materials (FGMs) is investigated. Due to highly nonlinear nature of the problem, a total Lagrangian finite element formulation for a seven-parameter shell model is developed. The model accounts explicitly for thickness change, as well as normal stress and strain components through the thickness of the structure. The Green–Saint Venant strain tensor in conjunction with the Kirchhoff–Saint Venant constitutive equation is used to capture the geometric nonlinearity. To circumvent locking phenomenon at large distortions, an enhanced assumed strain formulation is adopted. Five different examples have been analyzed and the effect of enhanced strains and that of FGM exponent is investigated.