Use of symmetry groups for generation of complex space grids and group-theoretic vibration analysis of triple-layer grids. (15th November 2020)

• Record Type: Journal Article
• Authors: Zingoni, Alphose
• Is Part Of: Engineering structures. Volume 223(2020)
• Publication Date: 2020-11-15
• Subjects: Symmetry -- Group theory -- Symmetric grids -- Space grids -- Triple-layer grids -- Vibration analysis; Structural engineering -- Periodicals; Structural analysis (Engineering) -- Periodicals; Construction, Technique de la -- Périodiques; Génie parasismique -- Périodiques; Pression du vent -- Périodiques; Earthquake engineering; Structural engineering; Wind-pressure; Periodicals; 624.105
• DOI: 10.1016/j.engstruct.2020.111177
• Languages: English
• ISSNs: 0141-0296

Abstract

Highlights: The innovative use of symmetry groups to create new types of space grids is shown. Complex space grids with pre-determined symmetry properties are generated. The group-theoretic method for the vibration analysis of space grids is explained. Predictions are made and new insights gained on vibration behaviour of space grids. A new finding on the subspace with the lowest and the highest frequency is made. Abstract: Space grids often exhibit a highly regular structure which is formed by repeated structural units. In the past, various algorithms have been developed to generate more complex structural assemblies using simple commands. In this paper, we explore the innovative use of symmetry groups to create various configurations of space grids, ranging from rectangular grids and their variants, to triangular and hexagonal grids, as well as grid forms of more complex shape. The advantage of this approach is that the generated space grid has pre-determined symmetry properties; this represents a shift in current design philosophy. A second objective is to show how group theory may be used to simplify the vibration analysis of layered space grids. The procedure is applied to the transverse vibrations of triple-layer space grids of D 2 h and D 4 h symmetries, modelled as discrete-parameter systems. A study of the symmetry of subspace basis vectors allows some important predictions to be made on the pattern of the motions and the location of stationary nodes. It is found that the lowest and highest frequencies of space grids of this type occur in the first subspace of the system, a finding that has significant computational importance.