Use of symmetry groups for generation of complex space grids and group-theoretic vibration analysis of triple-layer grids

被引：10
作者：
Zingoni A. [1 ]
机构：
[1] Department of Civil Engineering, University of Cape Town, Rondebosch 7701, Cape Town
来源：
Engineering Structures | 2021年 / 223卷
关键词：
Group theory; Space grids; Symmetric grids; Symmetry; Triple-layer grids; Vibration analysis;
D O I：
10.1016/j.engstruct.2020.111177
中图分类号：
学科分类号：
摘要：
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 D2h and D4h 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. © 2020 Elsevier Ltd
引用
收藏
相关论文
共 58 条
[1]  
Markowski Z.S., Analysis, design, and construction of double layer grids, (1981)
[2]  
Parke G.A.R., Howard C.M., Space structures 4: Proceedings of the fourth international conference on space structures, (1993)
[3]  
Krisch U., Optimal topologies of truss structures, Comput Methods Appl Mech Eng, 72, pp. 15-28, (1989)
[4]  
Hajela P., Lee E., Genetic algorithms in truss topological optimization, Int J Solids Struct, 32, pp. 3341-3357, (1995)
[5]  
Salajegheh E., Mashayekhi M., Khatibinia M., Kaykha M., Optimum shape design of space structures by genetic algorithm, Int J Space Struct, 24, pp. 45-58, (2009)
[6]  
Mashayekhi M., Salajegheh E., Dehghani M., Topology optimization of double and triple layer grid structures using a modified gravitational harmony search algorithm with efficient member grouping strategy, Comput Struct, 172, pp. 40-58, (2016)
[7]  
Deb K., Gulati S., Design of truss-structures for minimum weight using genetic algorithms, Finite Element Analy Des, 37, pp. 447-465, (2001)
[8]  
Adriaenssens S., Block P., Veenendaal D., Williams C., Shell structures for architecture: form finding and optimisation, (2014)
[9]  
Wang Q.S., Ye J., Wu H., Gao B.Q., Shepherd P., A triangular grid generation and optimization framework for the design of free-form gridshells, Comput Aided Des, 113, pp. 96-113, (2019)
[10]  
Kaveh A., Optimal structural analysis, (1997)
123456