Node shift method for stiffness-based optimization of single-layer reticulated shells

Abstract

This paper presents a node shift method to find the optimal distribution of nodes in single-layer reticulated shells. The optimization process searches for the minimum strain energy configuration and this leads to reduced sensitivity in initial imperfections. Strain energy sensitivity numbers are derived for free shift and restricted shift where nodes can move freely in the 3D space or have to move within a predefined surface respectively. Numerical examples demonstrate the efficiency of the proposed approach. It was found that optimized structures achieve higher ultimate load and are less sensitive to imperfections than the initial structure. The configuration of the final structure is closely related to factors like the initial structural configuration, spatial conditions, etc. Based on different initial conditions, architects can be provided with diverse reasonable structures. Furthermore, by amending the defined shapes and nodal distributions, it is possible to improve the mechanical behavior of the structures.

The Influence of the Load Term of the Strain Energy Sensitivity in the Shell Shape Optimization

“…The shape optimization of structures, especially the free-form surface structure, has gained significant attention in the last few decades, because shape optimization is an effective tool to generate a free-form shell structure, and the architecture form and structure form of the free-form surface structure are very close and architecturally pristine [2][3][4][5][6][7]. Many shape optimization methods have been developed by researchers, such as the sensitivity method [7][8][9][10][11][12][13], firefly algorithm [4], genetic algorithm [14], and so on. The objective functions are usually one or several among the structural behaviors, such as the compliance [11][12][13], the buckling load [15,16], the plastic collapse load [17], the Eigen frequency, or the dynamic response [18,19], etc.…”

“…Many shape optimization methods have been developed by researchers, such as the sensitivity method [7][8][9][10][11][12][13], firefly algorithm [4], genetic algorithm [14], and so on. The objective functions are usually one or several among the structural behaviors, such as the compliance [11][12][13], the buckling load [15,16], the plastic collapse load [17], the Eigen frequency, or the dynamic response [18,19], etc.…”

“…Such methods based on strain energy sensitivity [7][8][9][10][11][12][13] assume that the load does not change with the design variables when deducing the sensitivity information of the structure. In the traditional optimization method, the structural weight is only considered as the external load, and its influence on strain energy sensitivity is not considered.…”

Grid patterns optimization for single-layer latticed domes

“…However, these types of design variables may reduce the variations of the optimized grid patterns, making it difficult to discover more mechanically sophisticated grid patterns and understand their mechanical properties quantitatively. On the other hand, Cui et al (2014) proposed a node shift method to minimize the strain energy for single-layer latticed domes. The nodes could be shifted freely on a surface defined by a mathematical formula during the optimization, yielding a variety of optimized grid patterns.…”

Analysis of Stiffening Methods and Effects on Irregular Single-layer Lattice Shell Structures

“…With more intense designing market competition and diversification of personal aesthetics, regular curved shells, such as hemispherical, cylindrical, conical, elliptical, hyperbolic, and parabolic shells, can no longer meet the demands of architects and owners. As a result, the irregular lattice shell [6], or free-curved lattice shell, has emerged. Figure 1 shows some examples of irregular lattice shells.…”