Thinking of using ABAQUS to optimize the structure of your product? The software can help you find the optimum design through a process called Structural Optimization. When you use ABAQUS for optimization, you need to know how to set up the program and which settings to use for best results. If you’re new to structural optimization in ABAQUS, this article will get you up to speed and help you get started as quickly as possible. It explains how the module works, what inputs it requires, and what outputs it produces. You’ll also learn about different cost functions, constraint types, and other concepts essential for effective optimization.

1- What is structural optimization?

Structural optimization is a process where you design a product to be as light as possible while meeting certain design requirements. The process usually involves applying mathematical algorithms to find the optimum design. You can use structural optimization to solve a wide range of problems, from designing the optimum size of a building support to determining the ideal design for an airplane wing. When using ABAQUS for structural optimization, you specify the inputs and desired outputs. For instance, you can use the program to find the optimum design that maximizes the strength of a structure while minimizing its weight. Structural optimization involves a number of concepts and techniques, such as finding the optimum weight of a structure, minimizing weight, maximizing strength, minimizing bending moments, and so on.  To better understand this issue, just take a look at the figure below. This mechanical part is optimized based on its performance and available loads in the final weight. This figure shows the progressive removal and grouping of elements from the topology optimization analysis. At the volume constraint of 95%, the top surface and the two opposing arm locations of the bell crank demonstrated a potential for element removal. Once the volume constraint was reduced to 90%, a significant material reduction was observed on the left arm region. From the 85% to 80% volume constraint results, significant reductions of material on both arm regions, as well as on the edges at the top of the bell crank, were achieved. The 75% volume constraint in the topology optimization featured the highest amount of material removal.

2- Why use ABAQUS for structural optimization?

The ABAQUS optimization module is the perfect tool for structural optimization. It has all the features required for this task and is easy to use. The module is part of the ABAQUS standard solver, which is used in thousands of industries worldwide. So, if you want an efficient, easy-to-use software for structural optimization, ABAQUS is the way to go. Equally important, ABAQUS comes with an optimization module that can help you find the optimum design. You can use it in various industries, such as aerospace, automotive, marine, and others. The program is highly versatile and can be used for a wide range of applications.

3- Setting up the ABAQUS optimization module

Before you launch the optimization module, make sure you select the correct loading type. In most cases, you’ll want to select Plane Strain. At this point, you can choose to apply load as either static or dynamic. For most design optimization, you’ll want to apply static load. You can now proceed to set up the optimization module. You can follow the example shown below. The example works for a 2D frame analysis. If you’re using a 3D model, you’ll need to follow the same steps, but in 3D. Most importantly, when setting up the module, make sure you set the type of optimization you want to conduct. For structural optimization, you’ll want to set up a global or local optimization, or a hybrid of both. Global optimization saves the best design, while local optimization lets you save multiple designs.

4- Specialized vocabulary of structural optimization in Abaqus

Structural optimization needs to know its specialized vocabulary. The following terms are frequently used in Abaqus software documentation. Hence, the accurate knowledge and understanding of these words is of special importance.

Design Area: An area of ​​the model on which the optimization process takes place. This area can include the whole model or a selected sub-region of the whole model. The topological optimization process removes or adds material from the design area, and the shape optimization process optimizes the surfaces related to the design area by moving the surface nodes.

Design Variables: In an optimization process, design variables represent parameters that must be changed during optimization. In topology optimization, the density of elements is considered as design variable. The Abaqus optimization module changes the density of the elements in each iteration of the optimization and relates the hardness of elements to the corresponding density. The optimization mechanism in this method is such that the elements whose hardness value is low enough and practically do not affect the overall response of the structure are removed. Next, the geometric model with the new material is analyzed by Abaqus.

In the shape optimization, surface nodes corresponding to the design area are considered as a part of the design variable. During the optimization process, the Abaqus optimization module moves the surface nodes outwards or inwards or leaves its position unchanged. The constraints applied to the problem affect the amount that the surface nodes can move and determine the direction in which these nodes can move. Optimization process directly modifies only the position of the corner nodes in the elements; The Abaqus optimization module interpolates the position of the middle nodes from the displacement value of the corner nodes.

Design cycle: Optimization is an iterative process in which design variables are updated, the modified model is analyzed by Abaqus, and the results are reviewed to ensure that a step towards optimization has been taken. Each iteration in the optimization process is called a design cycle.

Optimization task: An optimization task generally includes the definition of the optimization process in the problem, such as design response, optimization objectives, constraints and geometric constraints. To run an optimization process, we need to create an optimization task.

Design responses: The inputs of the optimization process are known as design responses. These design responses can be read directly from the Abaqus output file (.odb) such as stiffness, tension, natural frequency and displacement. Also, the Abaqus optimization module can read relevant data from an output database file and calculate design response from your model, such as calculating weight, center of mass or relative displacement.

A design response is linked to an area of ​​the model; However, this design response can include a scalar value (such as the maximum stress in a region or the total volume of a model). In addition, a design response can only be linked to a specific step or load case.

Objective functions: Objective functions generally determine the goal of the optimization process. An objective function is a scalar variable extracted from the design response of your problem, such as maximum displacement or maximum stress. An objective function can be formulated from the combination of several design responses. If you determine that the objective function minimizes or maximizes the corresponding design response, ATOM or the Abaqus optimization module calculates the value of the objective function by adding the value of each of the design responses. In addition, if you have several objective functions in your problem, you can determine the contribution of each function in the optimization process by applying the weighting factor.

Constraints: Constraints are also a scalar value that is extracted from design responses; However, one adverb cannot be obtained from the combination of several design responses. Constraints limit the amount of design responses. For example, you can specify that the volume of the part must be reduced by 45% or that the absolute displacement in an area must not exceed 1 mm. You can also apply construction and geometry constraints to the problem that are independent of optimization; For example, a structure must be able to be produced by casting or forging, or the diameter of a bearing surface must not change.

Stop conditions: A global stop condition determines the maximum possible number of iterations in an optimization process. In contrast, a local stopping condition specifies that an optimization process should stop when a local optimum (minimum or maximum) has occurred.

5- Which settings to use during structural optimization?

When you’re conducting structural optimization with ABAQUS, the number of iterations (or the number of times the software will run) will have a major impact on the outcome. The more iterations, the shorter the time it will take to find the optimum design. However, it will also use more computer time. So, if you need the software to finish quickly, 10 iterations will do the trick. On the other hand, if you need to find the very optimum design, you’ll need to conduct 100 iterations. At the end of each iteration, the program will show you the current minimum weight. You can then decide if it’s close enough to the optimum design or not. Apart from the number of iterations, you’ll also want to keep in mind the following settings when conducting structural optimization with ABAQUS: – Structural loading – The loads applied to the structure. – Cost Function – The type of cost function you want to apply during the optimization. – Constraints – The types of constraints you want to apply during the optimization.

The optimization process is actually an iterative process where the structure of the model created by you is improved by searching for an optimal solution based on a set of objectives and constraints. The optimization module included in Abaqus allows you to easily prepare two major categories of problems in this domain: topology optimization (topographical science of object placement) and geometry (or shape) optimization. In the first case, by having a raw material distribution (left figure), topology optimization using relative density factorization in the design range will lead to improvements in the problem (right figure).

The second mode refers to instructions that lead to the prediction of a boundary (or geometry) in a design with the aim of optimizing the shape of the part. To perform an optimization process according to the above chart, you must first specify its type (topology optimization/geometry optimization). Each of the next steps in the process is introduced below.

Design Responses: Provides the variables required for the optimization solver. Strain energy and displacement are examples in this field.

Objective Functions: This option determines how the variables of the previous step should be used in the optimization process, that is, which of the variables should be minimized and which should be maximized, or if a special relationship between the variables should be defined. For example, your goal may be to minimize the strain energy (maximize the stiffness) in a problem.

Constraints: In this section, you must determine the desired boundaries for the optimization solver. For example, you can specify that the volume is less than 35% of the original volume.

Geometric Restrictions: Provides design restrictions and limitations.

Stop Condition: The maximum number of repetitions of the optimization process is determined in this section.

After going through the above steps, it is time to define the optimization process and implement it in order to reach the optimal solution, and in a repetition loop that is displayed in the flowchart, the repetition process continues until reaching the optimal solution.

6- Finding the optimum design using ABAQUS

When the optimization module has completed the iterations, the program will show you the current minimum weight. This is the optimum design. – If the current minimum weight is close enough to the desired design (which you specified while setting up the optimization module), then you don’t need to do anything. The program has found the optimum design. – If, however, the current minimum weight is far away from the desired design, then you need to do one of two things: – You can increase the number of iterations by selecting more iterations in the settings. This will use more computer time, but will help the module find the optimum design faster. – You can change the settings of the optimization module. For example, you can change the cost function, or add more constraints.

7- Concluding Words

The ABAQUS optimization module is an excellent tool for structural optimization. It allows you to find the optimum design for a wide range of structures. Equally important, the module is easy to use and requires very little programming experience. When conducting structural optimization with ABAQUS, make sure you set up the optimization module correctly. You can then use the settings to change the type of cost function and constraints to find the optimum design faster.

The Structural Numerical Research Center of has presented various problem for you regarding the Structural optimization. You can get some of these products by referring to link 1 and link 2. Keep in mind that to increase your modeling knowledge in Abaqus software, the best reference is the software help, along with the tutorials on our website.