Topology Optimization of Square Concrete-Filled Steel Tube Truss Structures Using Quasi-Full Internal Force Genetic Algorithm

Literature Overview

The paper by Xie Jun, Guo Fei, Zhu Shouqin, Liang Jinxiao, Yan Jie, and Dong Jie, published in Journal of Jinan University (2023, Vol. 37, No. 2, pp. 247-252), presents an advanced topology optimization method for square concrete-filled steel tube (CFST) truss structures. The research was supported by the National Natural Science Foundation of China (Grant No. 5187083428), the Hebei Provincial Higher Education Science and Technology Research Project (No. ZD2021041), and the Zhangjiakou Municipal Science and Technology Development Program (No. 1911030A).

Core Technical Methodology

Optimization Framework

The study addresses the discrete variable topology optimization problem for CFST truss structures, which is fundamentally different from continuous variable optimization because:

• Section sizes are discrete (standard steel tube sizes)
• Concrete strength grades are discrete (C30, C40, C50, etc.)
• Member presence/absence is binary
• The search space is combinatorial and non-convex

Quasi-Full Internal Force Genetic Algorithm

The proposed optimization method combines three algorithmic components:

1. Genetic algorithm (GA): Randomly generates initial topology configurations and performs evolutionary search through selection, crossover, and mutation operations.
2. Quasi-full internal force algorithm: Provides a heuristic starting point by identifying members that carry significant internal forces, generating high-quality initial population members.
3. Heuristic correction: Checks and corrects generated topology configurations for structural feasibility (stability, connectivity, minimum span requirements).

Optimization Variables and Objective

Algorithm Enhancement

The study introduces two key improvements to the traditional genetic algorithm:

1. Initial population enhancement: Part of the initial population is generated from the quasi-full internal force algorithm solution, providing a high-quality starting point that accelerates convergence.
2. Penalty function improvement: The traditional penalty function approach is modified to improve GA efficiency by more effectively handling constraint violations during the evolutionary process.

Engineering Practice Integration

CFST Truss Structural Applications

Square CFST truss structures find extensive application in:

• Long-span roof structures (airports, stadiums, exhibition halls)
• Industrial buildings with large clear spans
• Bridge structures (cable-stayed, arch bridges)
• Tower structures (communication, observation)
• Space frames for complex architectural geometries

Steel Tube Selection for Truss Members

The optimization process considers standard square steel tube sizes, which must be available in the market and conform to manufacturing standards:

Welding and Connection Requirements

CFST truss structures require careful attention to connection details:

• Gusset plate connections: Most common for truss joints, requiring full-penetration welds between tube ends and gusset plates.
• Direct connections: Tube-to-tube connections with internal or external reinforcement plates.
• Bolted connections: Using end-plate or flange connections for field assembly.
• Semi-rigid connections: Accounting for partial moment transfer in analysis.

Fabrication Quality Control

The topology optimization results must be translated into manufacturable designs, requiring:

• Verification of weld accessibility for all connections
• Confirmation that optimized section sizes are available in standard lengths
• Assessment of fabrication complexity and cost implications
• Development of welding procedure specifications (WPS) for all joint types
• Non-destructive testing (NDT) planning for critical welds

Case Study Results

The 12-bar truss optimization example demonstrated significant improvements:

The optimized topology showed that:

1. The number of structural members was reduced while maintaining or improving structural performance.
2. Each remaining member was sized to fully utilize its load-carrying capacity.
3. The overall structural cost was lower than both the pure quasi-full internal force algorithm and the pure genetic algorithm solutions.
4. The convergence rate was improved compared to traditional GA approaches.

Study Insights and Engineering Recommendations

This research represents a significant advancement in the structural optimization of CFST truss systems, with several important implications for engineering practice:

1. Cost optimization: The proposed method achieves lower total structural costs by simultaneously optimizing topology, section sizes, and material grades, rather than optimizing these parameters sequentially.
2. Material efficiency: The optimization ensures that each member is properly sized for its specific load function, eliminating over-design and under-design.
3. Practical applicability: By using discrete variables corresponding to standard product sizes, the optimization results are directly implementable without requiring custom manufacturing.

For steel pipe manufacturers, this research highlights the importance of:

• Maintaining a comprehensive range of standard square tube sizes and wall thicknesses to accommodate optimized designs
• Ensuring consistent quality across all product sizes to support reliable structural performance
• Developing technical support capabilities to assist engineers with CFST truss design and optimization
• Providing accurate mechanical property data for each product batch to enable precise structural analysis

The integration of advanced optimization algorithms with practical CFST structural design represents the future direction of structural engineering, enabling more efficient, economical, and sustainable infrastructure development.

Concluding Summary

These five research papers collectively represent a comprehensive technical landscape spanning CFST structural engineering, from materials science (concrete mix design) through structural mechanics (post-buckling behavior, axial compression) to seismic design methodology and advanced structural optimization. The common thread connecting all studies is the composite action between steel tubes and concrete fill, which creates structural systems with superior performance characteristics compared to either material used independently.

For steel pipe manufacturers and fabricators, the key takeaway is that CFST applications demand higher quality standards in steel tube production, including tighter dimensional tolerances, certified mechanical properties, controlled residual stress levels, and comprehensive quality documentation. The structural performance of CFST systems is directly dependent on the quality of the steel tube component, making the manufacturing process a critical link in the structural performance chain.

The evolution from basic mix proportion research through post-buckling analysis, seismic design methodology, and advanced topology optimization reflects the maturation of CFST technology from experimental research to sophisticated engineering practice. This progression demands that steel pipe manufacturers continuously improve their production capabilities, quality systems, and technical support services to meet the increasingly demanding requirements of CFST structural applications. The integration of computational optimization with practical manufacturing constraints represents the frontier of CFST structural engineering, and manufacturers who invest in understanding and supporting these advanced design methodologies will be best positioned to serve the growing CFST market.