A Finite Element for Spatial Static Analyses of Curved Thin-Walled Rectangular Beams Considering Eight Cross-Sectional Deformation Modes

摘要

A new two-node finite element is proposed for the spatial static analyses of thin-walled curved beams with rectangular box sections considering eight cross-sectional deformationmodes. Thesemodes are determined with crosssectional deformation shape functions and are used to construct the mid-plane contour displacement field and the threedimensional displacement field. The coupling between the eight deformations and the curvature effect is carefully treated in the deduction of the beam potential energy. Then, the governing equations of the thin-walled curved beam are formulated involved with the principle ofminimum potential energy. For the finite element implementation, the governing equations are approximated with C~0 continuous interpolation function. The validity of this study is verified through numerical examples.