Mastering Structural Optimization: Topology & Shape Optimization in Abaqus

Imagine designing a bridge that is not only strong enough to handle heavy traffic but also uses 30% less material, reducing costs and environmental impact. This is the power of optimization. Whether in aerospace, automotive, or civil engineering, optimization enables engineers to achieve lightweight, cost-efficient, and high-performing structures by refining their designs with precision. But why is optimization so vital? Because in today’s competitive world, achieving the perfect balance between performance and resource efficiency isn’t just desirable—it’s essential.

Structural optimization is the process of enhancing a design to meet specific goals, such as reducing weight, minimizing stress, or maximizing stiffness, all within defined constraints. It comes in several types: topology optimization removes unnecessary material to create a lighter structure, while shape optimization fine-tunes the geometry to reduce stress concentrations. By iterating through design cycles, tools like Abaqus apply optimization algorithms that improve the structure step by step, ensuring it meets performance requirements with minimal waste. This systematic approach transforms how engineers tackle design challenges.

In this blog, we explore optimization in Abaqus, focusing on two key techniques: topology and shape optimization. You’ll learn the terminology, algorithms, and setup steps needed to use these methods effectively. We also delve into practical applications, showing how these techniques are used to optimize bridges, automotive components, and aerospace designs. Finally, we discuss common challenges, like managing computational resources, and offer strategies to overcome them. By the end, you’ll understand how mastering optimization in Abaqus can revolutionize your design approach.

Learn structural optimization in Abaqus with our comprehensive tutorials! From foundational concepts to advanced techniques, we cover everything—topology and shape optimization, detailed algorithms, and practical examples with full explanations of settings. Whether you’re starting from scratch or enhancing your skills, these guides have you covered.

1. What Is Structural Optimization and Why It Matters

Structural optimization is the process of finding the best possible design of a structure under given loading conditions, constraints, and performance objectives. It aims to improve performance while minimizing material usage, weight, and costs. In essence, it’s about making structures stronger, lighter, and more efficient. To help you understand better, see figure 1. It demonstrates how the optimization works. As shown in the figure, first we need to determine the optimization task and design area, then specify design responses such as stiffness, stress, and volume. In the end, the goal of optimization is determined and the optimized model will be achieved.

But here is the detailed version for more understanding:

• Define Optimization Task:
  • Identify the objectives of the optimization (e.g., minimize stress, maximize stiffness, reduce volume).
  • Specify constraints (e.g., material properties, load conditions, boundary conditions).
• Design Area:
  • Define the geometric domain or design space where the optimization will be applied.
  • Specify the initial design or model that will be optimized.
• Analyze Initial Model:
  • Perform a structural analysis (e.g., using finite element analysis) to evaluate the initial model’s performance.
  • Key metrics to analyze include stiffness, stress distribution, and volume.
• Set Optimization Goals for example:
  • Minimize Stress: Aim to reduce the maximum stress in the structure to improve durability.
  • Maximize Stiffness: Aim to increase the stiffness to enhance structural rigidity.
  • Minimize Volume: Aim to reduce material usage while maintaining performance.
• Run Optimization:
  • Apply optimization algorithms (e.g., topology optimization, shape optimization) to iteratively improve the design.
  • The software (e.g., Abaqus) adjusts the design within the specified constraints to meet the optimization goals.
• Evaluate Optimized Model:
  • Analyze the optimized model to ensure it meets the desired performance criteria.
  • Verify that the stress, stiffness, and volume are within acceptable limits.

Figure 1: Structural Optimization

1.1. Optimization Process

The optimization process is an iterative procedure that interprets the defined optimization task within the Optimization module of Abaqus. It seeks to identify an optimized solution by evaluating the objective functions and constraints outlined in the optimization task. Figure 2 demonstrates the iterative nature of the optimization process, which involves updating the design variables, adjusting the finite element model, and executing Abaqus analyses in pursuit of an optimized solution.

When you submit an optimization process, this is what happens in every cycle: An Abaqus analysis is performed at first. Next, the optimization module comes in and checks whether the model satisfies the objective functions and constraints; if it doesn’t, then it modifies the model. This is the end of one cycle. The modified model will be analyzed in the next cycle, and then again, the optimization checks it. If the model was not OK, then the optimization module modifies it again and will be analyzed in the next cycle. This routine goes on until the optimization process has converged to an optimal solution or the maximum number of design cycles has been reached.

Figure 2: Optimization process

When you want to create an optimization process, when you run it, you must Combine the analysis results and optimization results so you can see the results in the Visualization module of Abaqus!! What? How? Why? Excellent questions. You can find all these answers at the end of the Topology Optimization Lesson.

1.2. Types of Structural Optimization

The four categories of structural optimization are:

• Topology optimization: A topology optimization process involves the removal or addition of material from elements within the design space in pursuit of an optimal configuration that is lighter and stronger. (See figure 3)

Figure 3: Topology Optimization

• Shape optimization: Shape optimization entails the alteration of the design area’s surface by repositioning surface nodes (See figure 4). The primary aim of shape optimization is to reduce stress concentrations by utilizing the outcomes of stress analysis to alter the surface geometry of a component until the desired stress level is achieved.

Figure 4: Shape Optimization

• Sizing optimization: Sizing optimization focuses on adjusting the thickness of the design area by varying the thickness of shell elements (See figure 5). Typically, the objective of a sizing optimization is to maximize the stiffness of a component while satisfying a weight objective.

Figure 5: Sizing Optimization

• Bead optimization: Bead optimization consists of relocating nodes of shell elements within the design area along the direction of the shell normal (See figure 6). The objective of bead optimization is to maximize the stiffness of a component or to minimize the displacement of critical nodes.

Figure 6: Bead Optimization

The topology and shape optimizations are the most common optimization processes in engineering design that will be explained in the next sections.

1.3. The Role of Structural Optimization in Engineering and Industries

Structural optimization is essential in engineering design because it allows engineers to create structures that perform better, more durable, and less expensive. By optimizing structures, designers can ensure that they meet safety standards while also minimizing the resources required for construction, reducing material waste, and improving overall performance. Structural optimization has wide-reaching benefits across various industries:

• Aerospace: Minimizing weight while maintaining strength to improve fuel efficiency.
• Automotive: Enhancing safety and performance through lightweight structures.
• Civil Engineering: Designing stronger, more efficient buildings and bridges with less material.
• Energy: Reducing energy consumption in large-scale infrastructure projects.

2. Terminology in Structural Optimization in Abaqus

Structural optimization encompasses a unique set of terminology. The subsequent terms are utilized consistently within the Abaqus documentation and the Abaqus/CAE user interface:

• Design Area: The design area refers to the section of your model that is subject to modification through structural optimization.
• Design Response: The inputs to the optimization are called the design responses. In other words, you could say that the design responses are the goals of the optimization; I mean which one of the characteristics of the model you want to be changed or better to say to be optimized.
• Design Variables: In the context of an optimization problem, design variables are the parameters that will be altered during the optimization process.
• Geometric Restrictions: You can also apply geometric and manufacturing constraints that are independent of the optimization; for example, a structure must be able to be cast or stamped or the diameter of a bearing surface cannot be changed.
• Design Cycle: The optimization process is iterative, involving the updating of design variables, conducting an Abaqus analysis on the revised model, and evaluating the results to ascertain whether an optimized solution has been achieved. Each iteration of this optimization is termed a design cycle.
• Optimization Task: An optimization task encompasses the parameters of your optimization, including design responses, objectives, constraints, and geometric limitations.
• Objective Function: It is a quantity that is to be maximized or minimized. These can be single term design responses or combinations of design responses. The objective function is a tool that can maximize or minimize specified design responses.
• Constraints: quantities that will place bounds on the optimization problem (design responses). In other words, Constraints restrict the value of a design response. For example, you want to decrease the mass of the model by 25 percent and the Constraints do this job.
• Stop Conditions: A global stop condition establishes the upper limit on the number of iterations that an optimization process may execute.

3. Understanding Topology Optimization

An example to illustrate topology optimization is an overweight individual who aims to begin a workout regimen for two primary objectives: to lose weight, or in other terms, to decrease body fat, and to simultaneously build muscle to enhance physical strength, thereby achieving optimal fitness. In this section, we’ll introduce topology optimization concepts in Abaqus briefly and explain their significance in the structural optimization process.

3.1. What Is Topology Optimization in Abaqus?

Topology Optimization initiates with a preliminary design, which is regarded as the maximum physical extent of the component. It seeks to establish a new distribution of material by adjusting the density and stiffness of the elements within the initial design while adhering to the optimization constraints. Topology optimization is a mathematical approach that determines the best distribution of material within a given design space. It aims to maximize performance by removing unnecessary material while maintaining structural integrity. The result is often an unconventional, highly efficient design.

To better understand this issue, just take a look at the figure 7. This example of a nonlinear brake pedal illustrates the advancement of a topology optimization process aimed at enhancing stiffness while achieving a 50% reduction in volume.

Figure 7: A topology optimization for a brake pedal

Figure 8 depicts the configuration and subsequent processing involved in the topology optimization of a spur gear and shaft assembly utilizing the Abaqus topology optimization module.

Figure 8: The topology optimization of a spur gear and shaft assembly

3.2. Algorithms of Topology Optimization in Abaqus

Topology optimization encompasses two distinct algorithms:

• The general algorithm: which offers greater flexibility and applicability to a wide range of problems
• The condition-based algorithm: is more efficient but has certain limitations.

By default, the Optimization module employs the general algorithm; however, users have the option to select their preferred algorithm when initiating the optimization task. Each algorithm utilizes a unique methodology for arriving at the optimized solution.

The differences between the topology algorithms are presented in the following table; the table is just an overview! Want to know exactly how these algorithms operates? you can learn that in the Topology Optimization Lesson.

Figure 9: General VS Condition-Based Algorithms

3.3. Topology Optimization Setup in Abaqus

Topology optimization setup in Abaqus includes:

• Defining optimization task: The first step in setting up topology optimization in Abaqus is defining the optimization task, which outlines the overall goal of the optimization process.
• Defining design responses (inputs): Next, you need to define the design responses, which are the inputs. There are the characteristics of the model you want to be changed or better to say to be optimized. The following table shows which design responses can be used as the objective function, constraint, or both.

Did you know that the design responses can be single-term or combined together? Well you can learn all about it in our tutorial.

Figure 10: Design Responses of General Algorithm

• Creating objective functions: Afterward, you create objective functions that represent a value that should be either maximized or minimized.
• Creating constraints: Constraints are then created to impose limitations on the design, ensuring the optimized structure meets specific performance or design criteria.
• Creating geometric restrictions: Finally, geometric restrictions are applied to control the shape or size of the design domain, ensuring the solution remains feasible within practical manufacturing limits.

3.4. Applications of Topology Optimization in Engineering Design

Topology optimization in Abaqus is widely used in industries like aerospace, automotive, and civil engineering. It helps create lightweight, strong structures, such as aircraft components, car chassis, and building frameworks, all optimized for performance and material usage.

4. Achieving Precision with Shape Optimization

In this section, we will provide a brief overview of shape optimization concepts and elucidate their importance in the structural optimization process. Shape optimization falls within the domain of optimal control theory. The primary objective is to identify the shape that minimizes a specific cost functional while adhering to established constraints.

4.1. What is Abaqus Shape Optimization?

Abaqus Shape Optimization is employed after the design process, when the overall configuration of a component is established, permitting only slight modifications through the adjustment of surface nodes in designated areas. This process initiates with a finite element model that requires minor enhancements or with a model produced through topology optimization.

The primary aim of shape optimization is to reduce stress concentrations by utilizing the outcomes of stress analysis to alter the surface geometry of a component until the desired stress levels are achieved. An illustration in figure 11 depicts a section at the base of a connecting rod, where surface nodes have been adjusted through shape optimization to mitigate the impact of stress concentration.

Figure 11: Abaqus Shape Optimization

4.2. Algorithms of Shape Optimization in Abaqus

Shape optimization employs two algorithms:

• The general algorithm
• The condition-based algorithm

The most comment differences between the shape optimization algorithms are in the design responses. More design responses are available in the general than in the condition-based algorithm as shown in figure 12.

Figure 12: Design responses of shape optimization algorithms

4.3. Shape optimization Setup in Abaqus

Shape optimization setup in Abaqus includes:

• Defining optimization task: The initial step in setting up shape optimization in Abaqus involves defining the optimization task. This task establishes the primary goal of the optimization process.
• Defining design responses (inputs): The next step is to define the design responses, which represent the objectives of the optimization, indicating which specific characteristics of the model you aim to modify or enhance.
• Creating objective functions: At this stage, objective functions refer to a value that is intended to be either maximized or minimized.
• Creating constraints: Constraints are then introduced to define the permissible range of a design response.
• Creating geometric restrictions: Finally, geometric restrictions are imposed to regulate the shape or size of the design domain, ensuring that the final solution remains feasible for practical manufacturing. More you can understand of geometric restrictions in Shape Optimization Lesson of our tutorial.
• Creating stop conditions: Stop conditions are defined to determine when the optimization process should be halted, typically based on criteria such as reaching a maximum number of iterations, achieving a desired level of convergence, or meeting specific performance targets.

4.4. Advantages of Shape Optimization in Abaqus

Abaqus offers powerful shape optimization tools that allow for precise control over the design geometry. Engineers can fine-tune the shape to ensure it performs optimally under various conditions, making Abaqus an invaluable tool for enhancing structural performance. Shape optimization can be used to fine-tune a design, allowing engineers to refine their designs for maximum performance and efficiency.

5. How Topology and Shape Optimization Work Together

While both topology and shape optimization can be performed separately, they often work best when combined. Topology optimization is used to create a lightweight structure by finding the optimal material distribution, while shape optimization is used to fine-tune the outer geometry for better performance. The synergy between topology and shape optimization allows engineers to create structures that are both lightweight and strong, with optimized material distribution and geometry. This combined approach is particularly useful in industries like aerospace and automotive engineering.

5.1. Practical Examples of Combined Optimization Techniques

For example, in aerospace, a wing component may first undergo topology optimization to reduce weight and material usage. The resulting design can then be refined using shape optimization to ensure it is aerodynamically efficient, robust, and manufacturable. In Abaqus, this combination results in a design that performs at peak efficiency, with optimized material usage and an aerodynamic shape.

6. Step-by-Step Guide to Running Optimization Simulations in Abaqus

It should be noted that install TOSCA structure software before starting the optimization process in Abaqus. There are various steps to running optimization simulations in Abaqus. Figure 13 shows the user actions and Abaqus actions in the optimization process.

Figure 13: User actions and automated Abaqus actions in the optimization process

Here’s a detailed guide to running optimization simulations in Abaqus:

6.1. Preparing Your Model for Optimization

Before running an optimization simulation in Abaqus, ensure that your model is properly set up. This includes defining material properties, boundary conditions, and loading conditions. Additionally, identify the optimization objectives and constraints that will guide the design process. It is worth mentioning that you should run a complete analysis of your model and make sure that it runs to completion before you attempt to run an optimization process.

6.2. Setting Up and Defining Optimization Parameters

Once the model is ready, define the optimization parameters in Abaqus. As shown in figure 14 (from left to right, respectively), this includes selecting:

(a) Type of optimization task,

(b) Design Response,

(c) Objective functions,

(d) Constraint,

(e) Create optimization process,

(f) Submit the optimization process.

Figure 14: Defining optimization parameters in Abaqus

If you look at the figure above, you can see that there are a lot of settings for each window and each step; seems overwhelming, right? well we have explained them all in detail and how they operates in our tutorial.

6.3. Interpreting Results from Optimization Simulations

After running the optimization simulation, Abaqus provides results that show the optimized design (See figure 15). It’s essential to carefully interpret these results to assess whether the design meets all performance, safety, and material-use goals. Adjustments can be made based on these results to fine-tune the design.

Figure 15: Schematics of results from optimization simulations

7. A Practical Example: Bridge Optimization in Abaqus

In this section, a practical example will be explained to learn how to use the topology optimization module in Abaqus. Let’s consider a steel bridge structure that needs to be optimized for material efficiency and strength (Left side of figure 16). The goal is to create a lightweight, cost-effective bridge design that can handle the expected loads without compromising safety (Figures 16 and 17).

Figure 16: Problem objectives

Figure 17: Problem boundary conditions

7.1. How to Model the Bridge

Model the bridge in Abaqus by defining its geometry. Assign properties such as steel’s density (7850 kg/m³) and Young’s modulus (210 GPa). Define loading conditions as clamped supported (Figure 17). Ensure that the model represents the key aspects of the bridge’s design, such as supports, spans, and load-bearing components. Then use the appropriate mesh (Figure 18).

Figure 18: Meshing the bridge

7.2. Run without optimization

First, you should run the static problem and check the results as shown in figure 19. As you see, maximum torsion is equal to 2 Mpa in some regions. Now we want to reduce the weight of the bridge and maximize the stiffness.

Figure 19: Stress results from the static analysis

7.3. How to Run an Optimization Task in Abaqus

Set up an optimization task in Abaqus by choosing topology optimization and defining the appropriate constraints and objectives (See figure 20).

Figure 20: Choosing topology optimization task

To not have any changes in load and boundary conditions, you can select the two options shown in Figure 21. By selecting these options, you can freeze load and boundary conditions regions.

Figure 21: Freezing loading and boundary conditions

Create a constraint for the volume. Enter 0.3 for the fractional of the initial value to decrease volume to 30 percent (See figure 22). It should be noted that the geometry restrictions must be applied so that there is no problem during manufacturing. But in this example, geometry restriction is not considered.

Figure 22: Define the volume reduction percentage

Create an optimization process with a maximum cycle of 20 and save it for every cycle (See figure 23).

Figure 23: Creating optimization process and defining the maximum design cycle

Run the simulation and evaluate the results, making adjustments as needed to meet the design goals (See figures 24 and 25).

Figure 24: The optimized bridge

Figure 25: Stress contour of the optimized bridge

8. Common Challenges in Topology and Shape Optimization (And How to Overcome Them)

While optimization in Abaqus offers incredible benefits, it’s not without its challenges. Some common issues include:

• Convergence Issues and Solution Strategies

One of the challenges in optimization is ensuring that the solution converges to a feasible and optimal design. Adjusting parameters such as mesh density, solver settings, and boundary conditions can help address convergence issues.

• Handling Complex Geometries and Constraints

Complex geometries and constraints can complicate the optimization process. Simplifying the design or applying advanced meshing techniques in Abaqus can help overcome these challenges.

• Managing Computational Resources Effectively

Optimization simulations can be computationally intensive. By using high-performance computing resources and optimizing the simulation setup in Abaqus, engineers can manage computational resources effectively and reduce processing times.

By understanding these challenges and applying best practices, such as carefully selecting constraints and verifying results with physical tests, engineers can overcome these hurdles and achieve optimized designs.

9. Case Studies: Real-World Applications of Optimization in Abaqus

Optimization in Abaqus finds application in various domains, including the automotive industry, aerospace industry, and civil engineering.

• Automotive Industry: Lightweight Component Design

Abaqus is widely used in the automotive industry to design lightweight components, such as chassis and suspension parts (See figure 26). Topology optimization helps create stronger, lighter components that improve fuel efficiency and safety.

Figure 26: Automotive chassis topology optimization

• Aerospace Industry: Structural Integrity and Weight Reduction

In the aerospace industry, optimization techniques in Abaqus are used to design lightweight yet strong aircraft structures, reducing fuel consumption and improving performance (See figure 27).

Figure 27: The resulting topology, actual design, and manufactured the front part of an airplane wing

• Civil Engineering: Optimizing Building and Bridge Structures

In civil engineering, Abaqus enables the optimization of large-scale structures, such as bridges and buildings, ensuring they are both efficient and durable.

5. Conclusion

This article explored the subject of structural optimization using Abaqus, focusing on its importance, methods, and practical applications. Structural optimization, which includes techniques like topology and shape optimization, plays a critical role in designing efficient, lightweight, and cost-effective structures. It enables engineers to meet performance requirements while conserving resources and minimizing waste, making it an essential tool in industries like aerospace, automotive, and civil engineering.

The article began by defining structural optimization and its significance, explaining how it enhances performance while reducing material use. It then delved into the optimization process, describing how iterative cycles in Abaqus refine designs. Types of structural optimization, including topology optimization, which focuses on material distribution, and shape optimization, which fine-tunes geometry, were introduced alongside their respective algorithms and setups. Practical examples, such as optimizing bridges and automotive components, illustrated the application of these methods. Finally, challenges like convergence issues and computational demands were addressed, along with strategies for overcoming them.

In conclusion, this article demonstrated how mastering topology and shape optimization in Abaqus enables engineers to create optimized designs that balance performance, efficiency, and sustainability. By understanding the process, terminology, and practical applications, readers can leverage these techniques to tackle complex design challenges and achieve superior results in their projects.