An energy‐conserving planar finite beam element for dynamics of flexible mechanisms

Abstract

Using examples of flexible mechanisms, demonstrates that while the Newmark method is unstable for nonlinear dynamics, time step refinement could in some cases lead to even earlier onset of instability in the form of a blown‐up response. As a remedy, develops a plane finite beam element based on the Simo‐Vu Quoc formulation for dynamics and integrates it with an energy‐conserving midpoint time‐stepping rule for solving problems in nonlinear dynamics. Shows that this combination produces a consistently stable and accurate dynamic analysis method even for large time steps.