Numerical pathologies in snap-through simulations

Abstract

Aircraft structures operating in severe environments may experience snap-through, causing the curvature on part or all of the structure to invert inducing fatigue damage. This paper examines the performance of beam and continuum nonlinear finite element formulations in conjunction with several popular implicit time stepping algorithms to assess the accuracy and stability of numerical simulations of snap-through events. Limitations for the structural elements are identified and we provide examples of interaction between spatial and temporal discretizations that affect the robustness of the overall scheme and impose strict limits on the size of the time step. These limitations need to be addressed in future works in order to develop accurate, robust and efficient simulation methods for response prediction of structures encountering extreme environments.

A robust composite time integration scheme for snap-through problems

“…6 shows the solutions of Beams 1 and 2 obtained with ∆t = 10 −3 s and ∆t = 2 × 10 −4 s, respectively. These time steps are chosen such that the true solution is obtained [19,17,18]. The figure shows that the systems oscillate about their snapped configuration starting immediately after the snap-through event; the amplitude of the oscillations decreases over the time interval where the load continues to ramp up, but then remains constant when the external load is constant.…”

“…The beam elements utilized are beam elements without shear deformation with large displacement and small rotation (2 nd order theory) with cubic interpolation [43]. A study on the performance of other elements (2D beam element with shear deformation, 3D linear displacement formulation, B-bar, and enhanced formulations, and 3D quadratic element) is presented in [19,17].…”

“…In the context of fatigue life, being able to determine whether the system will continually snap between remote configurations or oscillate locally about a snapped configuration is important and constitutes the motivation for this work. However, the transient simulation of such highly nonlinear phenomena involving large deformations is very challenging, in many cases leading to inaccurate predictions [19,17,18]. With the goal of predicting postsnapped behavior, the focus is on developing a robust time integration scheme with reliable numerical dissipation for spurious high order modes to resolve numerical issues encountered in the simulation of structures undergoing snap-through.…”

A lower bound on snap-through instability of curved beams under thermomechanical loads

“…Beam and shell models, usually the most computationally efficient choice for finite element modeling of thin structural members, always involve some simplifications of the underlying threedimensional kinematics that can lead to artificial stiffness under particular load states (locking). These kinematic assumptions that are built into the formulation of structural elements can lead to inaccurate solutions [20]. In this work we avoid such issues as well as the locking sometimes present when linear elements are used by choosing to work with three-dimensional (solid) quadratic elements only.…”

Equilibria and stability boundaries of shallow arches under static loading in a thermal environment

“…This is the approach that is also taken in this paper. A different approach is usually based on non-linear finite element modelling [3,4,5]. A disadvantage of this procedure is that it requires the magnitude of independent parameters defined in the problem to be constant along the analysis.…”