Geometrically nonlinear quadrature element analysis of spatial curved beams: Fid-Bau Portal

Geometrically nonlinear quadrature element analysis of spatial curved beams

Liao, Minmao / Xu, Gang / Yang, Y.B.

Highlights • A curved beam quadrature element is presented for geometrically nonlinear analysis. • The element avoids shear and membrane locking due to its high-order approximation. • The element predicts large rotations and postbuckling paths of 3D curved beams. • The element unifies the analyses for both curved and straight beams.

Abstract A novel curved beam quadrature element is presented for geometrically nonlinear analysis of spatial curved beams. Starting from the incremental virtual work equation of the curved beam, the weak form quadrature element method (QEM) is employed to derive the elastic stiffness, geometric stiffness, and induced moment matrices of the curved beam with due account taken of the large rotations in three-dimensional space. All the stiffness matrices are adopted in the incremental-iterative analysis using the generalized displacement control (GDC) method, with specific considerations for the predictor and corrector phases. By testing the constructed curved beam quadrature element with four benchmark problems, it is demonstrated that the element avoids the shear and membrane locking phenomena due to its convenient feature of high-order approximation. In addition, the element is capable of predicting large displacements and rotations, as well as postbuckling paths of spatial beams. Especially, the presented element is featured by unifying the analyses for both curved and straight beams.