An isogeometric continuum shell element for modeling the nonlinear response of functionally graded material structures

A geometrically nonlinear continuum shell element using a NURBS-based isogeometric analysis (IGA) approach is presented for the analysis of functionally graded material (FGM) structures. IGA offers a computationally efficient and geometrically exact representation of the original shell geometry and its underlying basis functions provide high-order continuity for the solution variables. The use of high-order smooth basis functions also alleviates shear and membrane locking phenomena that commonly occurred in shell structures. In addition, the developed continuum shell element features a precise description of the thickness-varying material properties in FGM in the sense that a set of desired high-order B-spline basis functions with sufficient number of quadrature points are employed for accurate through-thickness numerical integration. A simple power-law distribution function of the FGM is adopted in the current study. The performance of the proposed IGA solid shell element is demonstrated via a variety of nonlinear shell benchmark problems. The effect of the FGM power-law exponent on the geometrically nonlinear response of the shell structures is investigated as well.