Geometrically nonlinear behavior of lattice domes coupled with local Eulerian instability

Abstract

Structural analysis is an intricate subject when nonlinearities occur. They make the structural behavior complex and may have important consequences in the design choice as well. Especially for lattice domes, as snap-through phenomena and local Eulerian instabilities generally affect the structural response, linear analysis is not enough. In this paper, a semi-analytical formulation is used in order to study the geometrically nonlinear behavior of lattice domes subject to vertical loads. The formulation is derived from the equilibrium equations written in the deformed configuration, considering large displacements and taking also into account local buckling conditions. The resulted system of equations, being strongly nonlinear, has been solved by means of a numerical procedure, based on a mixed load-displacement control scheme, leading to the evaluation of the complete equilibrium path. The influence of geometrical parameters on the critical load multiplier and shape of the load-displacement curve is also discussed. In particular, a complex equilibrium path for a sixteen-member five-node lattice structure is analyzed, which is characterized by several branches which can generate ‘snapping’ conditions.

Keywords

• geometrically nonlinear analysis
• mechanical instability
• snap-through
• critical load multiplier
• local buckling
• equilibrium path