Line finite element method for geometrically nonlinear analysis of functionally graded members accounting for twisting effects

Functionally graded materials with spatially varying properties have gained widespread use in various engineering disciplines due to their exceptional mechanical characteristics. Nevertheless, these materials can lead to non-symmetric properties of cross-sections and an offset between centroid and shear center of functionally graded (FG) members, thereby significantly affecting the mechanical behavior. This phenomenon, known as twisting effects, poses a substantial challenge for the geometrically nonlinear analysis of FG members, as existing methods rely on traditional line elements that assume the centroid and shear center of the section coincide. Thus, this paper proposes a new framework for geometrically nonlinear analysis of FG members, incorporating twisting effects through a novel Timoshenko line element. An efficient finite-element-based approach that employs the nonhomogeneous plane triangle (NPT) element for calculating the cross-sectional properties of arbitrary FG cross-sections is presented. These cross-sectional properties are then utilized within the advanced line-element formulation to perform geometrically nonlinear analysis of FG structures considering twisting effects. The accuracy of the proposed method is validated through three examples, followed by several case studies to examine the impact of twisting effects on FG members. Furthermore, the proposed cross-section analysis method is integrated into a new structural analysis software MSASect2 to facilitate its application.