Effects of the Equivalent Geometric Nodal Imperfections on the stability of single layer grid shells

Abstract

The present paper discusses the sensitivity of the global and local stability of a hybrid single layer grid shell to a set of equivalent geometric nodal imperfections representative of the actual structural and construction imperfections. Since imperfections are hard to be measured and controlled in experimental facilities, the stability of the structure is extensively investigated in numerical experiments. The imperfections are set by means of the so-called Eigenmode Imperfection Method. The method parameter space is densely sampled, and different structural models are adopted. The results are given in terms of two bulk parameters: the well established Load Factor and the proposed Buckling Shape Length, the latter being introduced to provide a continuous measure of the degree of "globalness" of the instability. Significant and non monotonic changes in both the Load Factor and Buckling Shape Length are observed versus the growth of the imperfection amplitude. Further, a local metrics of the grid shell geometry, named nodal apex, is introduced for each structural node. Special emphasis is given to the analysis of the correlation between the apex of the initial imperfect geometry and the apex of the deformed shape at collapse. The observed high correlation suggests that the mechanical behaviour of the imperfect grid shell is significantly influenced by this local geometrical feature.

Linear buckling of quadrangular and kagome gridshells: A comparative assessment

“…A more complete study using finite element analysis to evaluate local node stiffness of patented connections has been performed by Huang et al [19]. Bruno et al assessed the influence of nodal imperfection and of Eigenmode Imperfection Method (EIM) more recently [20]. Malek et al [15] performed numerical investigations on the buckling of spherical cap domes and considered geometrical values, like grid spacing, or height over span ratio, as parameters.…”

“…However, different studies show that other imperfections shapes should be considered, as they result in a bigger reduction of the buckling capacity of gridshells. Examples of such shapes can be found in [6] with the use of dynamic eigenmodes, and a discussion on the choice of appropriate imperfections is proposed in [20]. It has to be noticed that there is no closed-form solution on the worst imperfection possible, some studies even demonstrated that higher order eigenmodes can have a more critical effect on the reduction of buckling capacity [27].…”

PSO‐Based Approach for Buckling Analysis of Shell Structures with Geometric Imperfections

“…Shell structures are widely used in large-span public construction owing to its novel shape, low dead weight, and excellent mechanical behavior. However, initial geometric imperfections, an inevitable phenomenon due to machining and construction errors, considerably influence the buckling of shell structures [1][2][3][4].…”

Influence of Random Geometrical Imperfection on the Stability of Single-Layer Reticulated Domes With Semi-Rigid Connection

“…The magnitude of maximum nodal imperfection was set to 50 mm and 100 mm. Bruno et al [21] investigated the sensitivity of the global and local stability of a hybrid single-layer grid shell to a set of equivalent geometric nodal imperfections, which represents the actual structure and construction imperfections.…”