Multiobjective Topology Optimization of Spatial-Structure Joints

Nanhai Zhu,Jinlei Liu

doi:10.1155/2021/5530644

Abstract

To realize the static and dynamic multiobjective topology optimization of joints in spatial structures, structural topology optimization is carried out to maximize the stiffness under static multiload conditions and maximize the first third-order dynamic natural frequencies. According to the single-objective optimization results, the objective function of the multiobjective topology optimization of joints is established by using the compromise programming method, and the weight coefficient of each static load condition is determined by using the analytic hierarchy process. Subsequently, under the constraint of the volume fraction, the multiobjective topology optimization of joints is realized by minimizing the multiobjective function. Finally, the optimized structure is smoothed to obtain a smoother joint, and its mechanical properties are compared with those of the hollow ball joint. The results indicate that the multiobjective topology optimization that considers the static stiffness and dynamic frequency can effectively improve the mechanical properties of the structure. Through the research on multiobjective topology optimization, a new type of spatial joint with reasonable stress, a novel form, and aesthetic shape can be obtained, which mitigates the shortcomings of single-objective topology optimization. In comparison to hollow spherical joints with the same weight, topology-optimized joints have a superior ability to resist deformation and improve low-order frequency, which verifies the feasibility of applying multiobjective topology optimization to the lightweight design of joints.

Highlights

Joints are the key components that interconnect structural elements, such as large-span spatial trusses, grids, and reticulated shells [1,2,3,4,5]. e amount of steel used in joints that are connected to form a structural system often comprises 15% to 45% of the total structural steel consumption [6].erefore, topology optimization is an effective way to reduce the weight of the structure and improve its mechanical properties
To mitigate the aforementioned limitations, this paper proposes a multiobjective topology optimization method for spatial-structure joints based on the compromise programming method and combines the analytic hierarchy process (AHP) to determine the weights of the three load conditions axial load, shear load, and bending moment load
Under other load conditions and the combined load condition, the optimized joint exhibits a larger reduction in stress and displacement, and the mechanical performance is significantly better than that of the hollow spherical joint. is is because the weight of the bending moment condition only accounts for 8.1% in the multiobjective topology optimization. e optimized design can improve the mechanical properties of the structure under the axial and shear conditions, which is in line with the multiobjective optimization design, whose principle is to allocate materials reasonably according to different weights of the load conditions

Summary

Introduction

Joints are the key components that interconnect structural elements, such as large-span spatial trusses, grids, and reticulated shells [1,2,3,4,5]. e amount of steel used in joints that are connected to form a structural system often comprises 15% to 45% of the total structural steel consumption [6]. Chen et al.[10] studied the topology optimization of joints under single- and multiple-load conditions and obtained models for the spatial-structure joints in additive manufacturing by averaging different load conditions. To mitigate the aforementioned limitations, this paper proposes a multiobjective topology optimization method for spatial-structure joints based on the compromise programming method and combines the analytic hierarchy process (AHP) to determine the weights of the three load conditions axial load, shear load, and bending moment load. The topology optimization of the spatial grid structure joint is carried out to maximize structural stiffness and low-order frequencies, and the initial optimization result is smoothed to obtain a new joint type that meets multiple goals and simultaneously has reasonable stress transmission

Variable Density Method

Multiobjective Topology Optimization

Topology Optimization of Spherical Spatial Grid Structure Joints

Analysis of the Results

Findings

Conclusion