Buckling instability and dynamic response of a planar gridshell under thermal load

Abstract

We introduce a discrete model to predict the buckling instability and the vibration performance of an elastic gridshell which experiences a thermal load. With both thermal stress and temperature-dependent material property considered, a discrete framework for the simulation of hollow grid is developed based on a well-established Discrete Elastic Rods (DER) method and a specific mapping technique. It is found that the critical temperatures which induce a structural instability are identical for single rod system and multiple rods network, regardless of rod density. Meanwhile, its natural frequency linearly enhances with the growth of rod number. Moreover, the increase of environmental temperature will result in that the resonant peak of displacement response moves toward a lower frequency. Interestingly, we found that the natural frequency of gridshell is closer to the beam model, while its displacement response distribution shows similarity to plate theory. The free vibration frequencies of one-dimensional (1D) beam and two-dimensional (2D) plate with a simply-supported boundary condition under thermal effects are also derived analytically for cross-validation. We hope our findings could provide a fundamental insight in structural dynamics and further facilitate the designs in mechanical and aerospace engineering, e.g., deployable structures and smart metamaterials.