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Topology optimization is a mathematical technique that can be used to optimize the material distribution within a design space to achieve specific performance criteria. In Abaqus analysis, topology optimization can be used to create lightweight, high-performance structures.

First, what does topology mean?

The study of geometrical properties that are unaffected by the continuous change of shape or size of our required part or material; for example, when our part is twisted or bends the geometrical properties of that does not change. This is the meaning of the word topology.

What is topology optimization?

Topology optimization means removing portions of the desired model or, better to say, after removal, there are some voids or empty spaces in the desired model; however, this removal is to achieve specific goals.

To give you an idea, consider a fat guy who wants to do bodybuilding for two purposes: lose weight or reduce body fat and Gain muscle to get stronger. So he/she is kind of optimized. This can be a simple example of topology optimization.

The original design area serves as the foundation for topology optimization and includes the initial design as well as any mandated conditions (such as loads and boundary conditions). In order to satisfy the optimization constraints, such as the lowest volume or maximum displacement of a region, the optimization process modifies the density and stiffness of the elements in the initial design to determine a new material distribution. Additionally, you can include a variety of manufacturing constraints to guarantee that the suggested design can be produced using common production techniques like casting and stamping. Additionally, you can impose member size, symmetry, and coupling requirements, as well as freeze a few sections.

There are two algorithms available in topology optimization: the general algorithm, which is flexible and can be used for most problems, and the condition-based algorithm, which is more efficient but has limited capabilities. The default algorithm used in the Optimization module is the general algorithm; however, users can select which algorithm to use when creating an optimization task. Each algorithm uses a distinct method for determining the optimal solution. The general topology optimization technique involves an algorithm that modifies the density and stiffness of the design variables while attempting to meet the objective function and constraints. On the other hand, the condition-based topology optimization approach utilizes a more efficient algorithm that utilizes the input data of strain energy and node stresses, and does not require the computation of the local stiffness of the design variables.

In the general algorithm, intermediate elements are produced in the final design with relative density ranging between zero and one. However, in the condition-based optimization algorithm, the final design elements are either void, with their relative density extremely close to zero, or solid, with their relative density being equal to one.

The general optimization algorithm does not have a predetermined number of design cycles and typically runs between 30 and 45 cycles. However, the condition-based optimization algorithm is more efficient and searches for a solution until it reaches the maximum number of optimization design cycles, which is 15 by default.

The general algorithm is compatible with linear and nonlinear static responses, as well as linear eigenfrequency finite element analyses. Both algorithms support geometrical nonlinearities and contact, and many nonlinear materials are supported.

For static topology optimization in Abaqus, prescribed displacements are permitted. However, for modal analysis, prescribed displacements are not allowed. Additionally, it is possible to apply topology optimization to a composite material structure, but the individual laminates of the composite material cannot be altered using topology optimization. This means that you cannot modify the orientation of the fibers.

The general topology optimization algorithm allows for one objective function and multiple constraints, with all constraints being inequality constraints. Various design responses can be used to define the objective and constraints, such as strain energy, displacements and rotations, reaction and internal forces, eigenfrequencies, and material volume and weight. In contrast, the condition-based topology optimization algorithm is more efficient but less flexible. It only supports strain energy, which measures stiffness, as the objective function and material volume as an equality constraint.

To gain more knowledge about optimization, especially topology optimization, you can refer to the link below:

Optimization in ABAQUS

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