An equilibrium‐based formulation with nonlinear configuration dependent interpolation for geometrically exact 3D beams

Abstract

This article describes a novel equilibrium-based geometrically exact beam finite element formulation. First, the spatial position and rotation fields are interpolated by nonlinear configuration-dependent functions that enforce constant strains along the element axis, completely eliminating locking phenomena. Then, the resulting kinematic fields are used to interpolate the spatial sections force and moment fields in order to fulfill equilibrium exactly in the deformed configuration. The internal variables are explicitly solved at the element level and closed-form expressions for the internal force vector and tangent stiffness matrix are obtained, allowing for explicit computation, without numerical integration. The objectivity and absence of locking are verified and some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed. The proposed formulation is successfully tested in several numerical application examples.

Utilizing Tait-Bryan Angles for Large Displacement Corotational Finite Element Static Analysis of Spatial Beams

“…Enhancing geometrically nonlinear finite element formulations for spatial beam elements has recently become a crucial objective (Santana et al, 2022;Vo and Nanakorn, 2020;Magisano et al, 2020). It makes sense that many innovative applications (Leng et al, 2022;Trapper, 2022;Liu, 2014;Xiaohang et al, 2022;Liu and Bai, 2022) that have large displacements require accurate modelling.…”

“…These formulations are the total Lagrangian, the updated Lagrangian, and the corotational formulations. The total Lagrangian formulation (Santana et al, 2022;Vo and Nanakorn, 2020;Mars et al, 2017;Crivelli, 1991;Simo and Vu-Quoc, 1986;Remseth, 1979) is the oldest formulation and is frequently used in commercial finite element softwares. This formulation uses the fixed global frame to define the terms of the system equation.…”

Corotational Finite Element Dynamic Analysis of Space Frames with Geometrically Nonlinear Behavior Based on Tait–Bryan Angles

“…With regard to geometrically nonlinear analysis, the Lagrangian formulations are commonly used in the form of total Lagrangian, updated Lagrangian, and corotational formulations. In total Lagrangian formulations [14][15][16][17], the system equation terms are defned in terms of the fxed global frame that does not change through the analysis. Tis generates relatively large strains, displacements, and rotations that need special procedures to handle.…”