A Tube Dynamics Perspective Governing Stability Transitions: An Example Based on Snap-through Buckling

The multistable elastic behavior of a shallow dome with a cosine-curved profile is investigated in this work. The dome exhibits snap-through instability and could be used as a building block for energy dissipation mechanism in structures subjected to cyclic loading and high deformation demands. Numerical and experimental studies were carried on the geometric and material properties of the cosine-curved domes (CCD) under concentrated load at the apex. Finite element analyses (FEA), validated by experimental tests on 3D printed specimens, were conducted to study the controlling geometric and material properties of the CCD. Three types of response were recognized and discussed based on the force- and strain energy-displacement curves. Limitations on the geometric parameters that govern the recoverability of the original shape and the stability state upon load removal are also identified. In addition, empirical relations to estimate the limit-point load and displacement, and to characterize the snap-through response were developed. Good agreement was observed using the determined limits on the geometric parameters and the developed relations with the results from FEA and experimental tests.

Response characterization of multistable shallow domes with cosine-curved profile

The paper presents the response of two geodesic domes under seismic excitations. The structures subjected to seismic analysis were created by two different methods of subdividing spherical triangles (the original octahedron face), as proposed by Fulinski. These structures are characterised by the similar number of elements. The structures are made of steel, which is a material that undoubtedly gives lightness to structures and allows large spans. Designing steel domes is currently a challenge for constructors, as well as architects, who take into account their aesthetic considerations. The analysis was carried out using the finite element method of the numerical program. The two designed domes were analysed using four different seismic excitations. The analysis shows what influence particular earthquakes have on the geodesic dome structures by two different methods. The study analysed the maximum displacements, axial forces, velocities, and accelerations of the designed domes. In addition, the Time History method was used for the analysis, which enabled the analysis of the structure in the time domain. The study will be helpful in designing new structures in seismic areas and in assessing the strength of various geodesic dome structures under seismic excitation.

Numerical Analysis of Steel Geodesic Dome under Seismic Excitations

Geometry of escape and transition dynamics in the presence of dissipative and gyroscopic forces in two degree of freedom systems

Tunable bistability of a clamped elastic beam

Structural behavior of shallow geodesic lattice domes

Curved structures, such as beams, arches, and panels are capable of exhibiting snap-through buckling behavior when loaded laterally, that is they can exhibit multiple stable equilibria, sometimes after any external loading is removed. This is a consequence of highly nonlinear force-deflection relations with perhaps multiple crossings of the zero-force axis for typical equilibrium paths. However, the propensity to maintain a stable snapped-through equilibrium position (in addition to the nominally unloaded equilibrium configuration) after the load is removed depends on certain geometric properties. A number of clamped arches are used to illustrate the relation between geometry (essentially the shape) and corresponding equilibrium configuration(s), and especially those conditions for which the initial equilibrium configuration is the only stable shape possible. Furthermore, related results are obtained when a change in the thermal environment may cause a system to exhibit a stable snapped-through equilibrium even when the system at ambient thermal conditions does not. Some representative examples are produced using a 3D printer for verification purposes.

On the geometric conditions for multiple stable equilibria in clamped arches

The curse of dimensionality looms over many studies in science and engineering. Low-order systems provide conceptual clarity but often fail to reveal the extent of possible complexity, whereas high...

Stability and Bifurcation in Discrete Mechanical Systems: An Experimental and Analytical Study

This paper considers the load–deflection behavior of a pyramid-like, shallow lattice structure. It consists of four beams that join at a central apex and when subject to a lateral load, it exhibits...

A Pyramidal Lattice Frame: Pathways to Inversion

Curved structures, such as beams, arches and panels are capable of exhibiting snap-through buckling behavior when loaded laterally. However, the propensity to maintain a stable snapped-through equilibrium position (in addition to the nominally unloaded equilibrium configuration) after the load is removed depends on certain geometric properties. A number of clamped arches are used to illustrate the relation between geometry (thickness, span, initial deflection) and the corresponding equilibrium configuration(s). The finite element method and an elastica analysis compare well with a number of specifically-shaped arches produced using a 3D printer.

Yue Guan

Papers

Structural behavior of shallow geodesic lattice domes

On the geometric conditions for multiple stable equilibria in clamped arches

Stability and Bifurcation in Discrete Mechanical Systems: An Experimental and Analytical Study

A Pyramidal Lattice Frame: Pathways to Inversion

Curved Structures That Can Elastically Snap-Through