Bone Growth Analogy for Steel Truss Structures

Introduction: Bone Growth Analogy for Steel Truss Structure Optimisation: A 2025 Perspective

Structural optimisation has become essential in modern engineering, especially for steel truss structures. Advances in computational power and algorithms have made it possible to design structures that use material efficiently and respond to changing loads.

This report explores structural optimisation, focusing on the bone growth analogy and its application to steel truss structures. The analogy draws from the way bones adapt to stress, guiding the development of new optimisation methods that mimic biological processes.

Structural Optimisation: Background and Motivation

Historical Context

Structural optimisation has evolved from a theoretical pursuit to a practical necessity. Early methods were limited by computational resources, but modern tools allow for complex analyses and efficient designs. The field now integrates advanced algorithms and draws inspiration from natural systems.

Inefficiency in Traditional Design

Traditional steel truss designs often result in underused material. For example, in a simply-supported beam, most of the material experiences less than 75% of the maximum stress. This inefficiency highlights the need for optimisation methods that fully utilise materials.

Fully Stressed Design

The fully stressed design concept aims for all structural elements to experience similar stress levels, close to the material’s maximum capacity. This approach minimises weight, cost, and environmental impact. However, real-world structures face multiple load cases, making absolute optimisation challenging. Instead, engineers seek the best compromise across all scenarios.

Classes of Optimisation

Topology, Shape, and Size Optimisation

Structural optimisation focuses on three main aspects:

• Topology: Arranging the connections and elements within a structure.
• Shape: Adjusting the geometry and layout of nodes and elements.
• Size: Modifying the cross-sectional areas or properties of members.

Each type addresses different aspects of efficiency and performance.

Truss vs Continuum Optimisation

Optimisation methods fall into two categories:

• Truss Optimisation: The designer defines all possible connections in advance. The method searches for the best arrangement within these constraints.
• Continuum Optimisation: The design space is treated as a mesh, allowing for more flexible solutions. The quality of results depends on mesh density and computational resources.

Optimisation Criteria

Defining Objectives

Optimisation usually aims to minimise weight or a related function, such as cost or embodied carbon. The criteria for evolution often relate to structural failure, using measures like stress or strain.

Stress Criteria

For ductile isotropic materials like steel, von Mises stress is the standard criterion. It combines normal and shear stresses to assess whether a material is near its elastic limit. When the von Mises stress reaches the yield strength, the material is at risk of yielding.

Existing Optimisation Methods

Evolutionary Structural Optimisation (ESO)

ESO removes under-stressed elements from a structure, allowing it to evolve towards an optimal form. The process is iterative and simple, but it can get stuck in local optima and cannot add material back once removed.

Additive Evolutionary Structural Optimisation (AESO)

AESO starts with a minimal structure and adds material where needed. This method can create efficient outer shapes but may leave under-stressed regions that cannot be removed.

Bi-Directional Evolutionary Structural Optimisation (BESO)

BESO combines ESO and AESO, allowing both the addition and removal of material. This flexibility helps avoid some limitations of the parent methods, but BESO still focuses mainly on topology and shape, not size.

Ant Colony Optimisation (ACO)

ACO mimics the behaviour of ants searching for food. Paths represent design solutions, and pheromone trails guide the search towards optimal configurations. This method is effective for exploring large design spaces and finding global optima.

Particle Swarm Optimisation (PSO)

PSO is inspired by the social behaviour of flocks and swarms. Particles represent possible solutions and move through the design space, sharing information to improve their positions. PSO is reliable for topology optimisation and adapts well to complex problems.

Big Bang-Big Crunch Optimisation (BB-BC)

BB-BC generates random solutions (Big Bang) and then contracts them towards a centre of mass (Big Crunch). The process repeats, refining the search for optimal solutions. The method is effective in fine-tuning but may struggle with initial exploration.

Hybrid Big Bang-Big Crunch Optimisation (HBB-BC)

HBB-BC combines BB-BC with PSO elements to improve initial exploration and convergence. This hybrid approach enhances the ability to find global optima but increases algorithmic complexity.

Recent Developments in Optimisation

Simultaneous Topology, Shape, and Size (TSS) Optimisation

Recent research focuses on integrating topology, shape, and size optimisation for truss structures. Allowing zero values for cross-sectional areas enables elements to be removed, blending topology and size optimisation. Integrated PSO methods have shown competitive results for complex problems.

Continuum Optimisation and Practical Challenges

Continuum methods remain challenging due to computational demands. The results are often difficult to translate directly into buildable designs. However, advances in 3D printing may soon allow structures to match continuum-optimised forms.

Bone Growth Analogy in Structural Optimisation

Biological Inspiration

The human skeletal system adapts to external forces through atrophy (shrinking) and hypertrophy (growth). Bones strengthen or weaken in response to stress, maintaining efficiency and reducing injury risk. This process is continuous and dynamic, ensuring the body remains fit for its environment.

Applying the Analogy to Steel Truss Structures

The bone growth analogy inspires new optimisation algorithms for steel truss structures. Atrophy and hypertrophy correspond to removing and adding material, similar to BESO methods. Changes in cross-sectional area at the cellular level suggest a path towards full TSS optimisation.

Proposed Bone Growth Analogy Optimisation (BGA)

BGA combines evolutionary optimisation with biological principles. The algorithm removes under-stressed elements (atrophy) and adds material where stress exceeds thresholds (hypertrophy). The process continues until the structure reaches equilibrium, like bones adapting to their environment.

Key Features of BGA

• Dynamic Evolution: The structure evolves in response to changing loads and conditions.
• Material Efficiency: Only necessary material remains, reducing weight and cost.
• Visualisation: Designers can observe the structure’s evolution at each stage.

• Adaptability: The method can handle multiple load cases and changing support conditions.

Implementing BGA in Steel Truss Design

Algorithm Overview

1. Initialisation: Define the design space, loads, and supports.
2. Meshing: Discretise the space into elements and nodes.
3. Analysis: Calculate stresses in each element using FEA.
4. Atrophy: Remove elements with stress below a set threshold.
5. Hypertrophy: Add or enlarge elements where stress exceeds a higher threshold.
6. Iteration: Repeat analysis and adjustments until equilibrium is reached.

Control Parameters

The algorithm uses control parameters to set stress thresholds for atrophy and hypertrophy. These parameters can be tuned based on the desired balance between safety and efficiency.

Handling Multiple Load Cases

BGA can accommodate multiple load cases by considering the most critical stress in each element across all scenarios. The structure evolves to withstand all required loads without excess material.

Integration with Modern Tools

Modern FEA software and optimisation platforms can implement BGA. Automation allows rapid iteration and real-time visualisation of the evolving structure.

Case Study: Steel Truss Bridge

Problem Definition

A steel truss bridge must span a set distance and support variable loads. The goal is to minimise weight while ensuring safety and durability.

Applying BGA

1. Initial Design: Start with a dense mesh covering the design space.
2. Load Application: Apply all relevant load cases, including dead and live loads.
3. FEA Analysis: Calculate stresses in each element.
4. Atrophy Step: Remove elements below the atrophy threshold.
5. Hypertrophy Step: Add or enlarge elements above the hypertrophy threshold.
6. Iteration: Repeat until the structure stabilises.

Results

The final structure uses material efficiently, with all elements stressed close to their optimal capacity. The bridge meets safety requirements and minimises cost and environmental impact.

Advantages of the Bone Growth Analogy

Efficiency

BGA ensures that only necessary material remains in the structure, reducing waste and cost.

Adaptability

The method adapts to changing loads and conditions, making it suitable for a wide range of applications.

Visualisation and Control

Designers can observe the structure’s evolution and intervene at any stage, allowing for greater control and understanding.

Biological Relevance

BGA mirrors natural processes, providing a robust and intuitive framework for optimisation.

Computational Demands

BGA requires significant computational resources, especially for large or complex structures.

Parameter Sensitivity

The choice of stress thresholds affects the outcome, and improper tuning can lead to suboptimal designs.

Practical Implementation

Translating optimised forms into buildable designs remains a challenge, especially for continuum-inspired solutions.

Future Directions

Integration with Advanced Manufacturing

3D printing and advanced fabrication methods may soon allow the construction of structures that closely match BGA-optimised forms.

Real-Time Adaptation

Future algorithms could enable structures to adapt in real time, responding to changing loads and environments.

Multi-Objective Optimisation

BGA can be extended to consider multiple objectives, such as cost, carbon footprint, and durability, alongside weight.

Conclusion

The bone growth analogy offers a powerful framework for optimising steel truss structures. By mimicking biological processes, engineers can design structures that use material efficiently, adapt to changing conditions, and meet modern performance standards. BGA represents a significant step forward in structural optimisation, blending evolutionary algorithms with insights from nature to create the next generation of efficient, adaptable, and sustainable steel truss structures.

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