Topography Optimization

[Henrietta Naughton]

Topologyoptimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions and constraints with the goal of maximizing the performance of the system. Topology optimization is different from shape optimization and sizing optimization in the sense that the design can attain any shape within the design space, instead of dealing with predefined configurations.

The conventional topology optimization formulation uses a finite element method (FEM) to evaluate the design performance. The design is optimized using either gradient-based mathematical programming techniques such as the optimality criteria algorithm and the method of moving asymptotes or non gradient-based algorithms such as genetic algorithms.

Topology optimization has a wide range of applications in aerospace, mechanical, bio-chemical and civil engineering. Currently, engineers mostly use topology optimization at the concept level of a design process. Due to the free forms that naturally occur, the result is often difficult to manufacture. For that reason the result emerging from topology optimization is often fine-tuned for manufacturability. Adding constraints to the formulation in order to increase the manufacturability is an active field of research. In some cases results from topology optimization can be directly manufactured using additive manufacturing; topology optimization is thus a key part of design for additive manufacturing.

Evaluating u ( ρ ) \displaystyle \mathbf u(\rho ) often includes solving a differential equation. This is most commonly done using the finite element method since these equations do not have a known analytical solution.

Solving topology optimization problems in a discrete sense is done by discretizing the design domain into finite elements. The material densities inside these elements are then treated as the problem variables. In this case material density of one indicates the presence of material, while zero indicates an absence of material. Owing to the attainable topological complexity of the design being dependent on the number of elements, a large number is preferred. Large numbers of finite elements increases the attainable topological complexity, but come at a cost. Firstly, solving the FEM system becomes more expensive. Secondly, algorithms that can handle a large number (several thousands of elements is not uncommon) of discrete variables with multiple constraints are unavailable. Moreover, they are impractically sensitive to parameter variations.[1] In literature problems with up to 30000 variables have been reported.[2]

There are several commercial topology optimization software on the market. Most of them use topology optimization as a hint how the optimal design should look like, and manual geometry re-construction is required. There are a few solutions which produce optimal designs ready for Additive Manufacturing.

A stiff structure is one that has the least possible displacement when given certain set of boundary conditions. A global measure of the displacements is the strain energy (also called compliance) of the structure under the prescribed boundary conditions. The lower the strain energy the higher the stiffness of the structure. So, the objective function of the problem is to minimize the strain energy.

On a broad level, one can visualize that the more the material, the less the deflection as there will be more material to resist the loads. So, the optimization requires an opposing constraint, the volume constraint. This is in reality a cost factor, as we would not want to spend a lot of money on the material. To obtain the total material utilized, an integration of the selection field over the volume can be done.

Some techniques such as filtering based on image processing[9] are currently being used to alleviate some of these issues. Although it seemed like this was purely a heuristic approach for a long time, theoretical connections to nonlocal elasticity have been made to support the physical sense of these methods.[10]

Fluid-structure-interaction is a strongly coupled phenomenon and concerns the interaction between a stationary or moving fluid and an elastic structure. Many engineering applications and natural phenomena are subject to fluid-structure-interaction and to take such effects into consideration is therefore critical in the design of many engineering applications. Topology optimisation for fluid structure interaction problems has been studied in e.g. references[11][12][13] and.[14] Design solutions solved for different Reynolds numbers are shown below. The design solutions depend on the fluid flow with indicate that the coupling between the fluid and the structure is resolved in the design problems.

Thermoelectricity is a multi-physic problem which concerns the interaction and coupling between electric and thermal energy in semi conducting materials. Thermoelectric energy conversion can be described by two separately identified effects: The Seebeck effect and the Peltier effect. The Seebeck effect concerns the conversion of thermal energy into electric energy and the Peltier effect concerns the conversion of electric energy into thermal energy.[15] By spatially distributing two thermoelectric materials in a two dimensional design space with a topology optimisation methodology,[16] it is possible to exceed performance of the constitutive thermoelectric materials for thermoelectric coolers and thermoelectric generators.[17]

The current proliferation of 3D printer technology has allowed designers and engineers to use topology optimization techniques when designing new products. Topology optimization combined with 3D printing can result in less weight, improved structural performance and shortened design-to-manufacturing cycle. As the designs, while efficient, might not be realisable with more traditional manufacturing techniques.[citation needed]

Internal contact can be included in topology optimization by applying the third medium contact method.[18][19][20] The third medium contact (TMC) method is an implicit contact formulation that is continuous and differentiable. This makes TMC suitable for use with gradient-based approaches to topology optimization.

Topology optimization is a technology for developing optimized structures considering design parameters like expected loads, available design space, materials, and cost. Embedded early in the design process, it enables the creation of designs with minimal mass and maximal stiffness.

Altair OptiStruct is the original topology optimization structural design tool. While some are still discovering how this technology can help designers and engineers rapidly develop innovative, lightweight, and structurally efficient designs, for over two decades OptiStruct has driven the design of products you see and use every day.

An ability to design automotive systems with optimum parameters has become very crucial in the competitive industry. Today, there are many shape optimization algorithms to choose, depending on the nature of the design parameters. Compared with the topology optimization, a topography optimization can be a good alternative. Because of the less number of design variables required for the same optimization model, the topography optimization process is generally faster. In this study, an assembly consisting of several identical sheet metal components is employed for demonstrating the effectiveness of topography optimization, in which various beads are to be derived with appropriate heights and widths, where needed, at the discretion of the algorithm to attempt to render the design variables within the constraints. The identical pieces are arranged around an axis of revolution such that the geometric shape is cyclic symmetric at a constant angular spacing. Despite the geometric symmetry, however, the entire 360-degree assembly has to be modeled in the finite element analysis, to account for the overall lateral stiffness. Thus, during the course of optimization, it is necessary to impose a constraint known as pattern repetition for the evolved shapes of the design such that each component has the identical features for the purpose of simplicity and cost-effectiveness in manufacturing. The responses from the finite element solution in the form of lateral and rotational stiffness as well as maximum stresses are used as the design constraints and objective function. It turns out that the topography algorithm used in this study seems smart enough to figure out a set of design variables to meet some seemingly contradictory constraints.

Where does good design meet function? As computer-aided design (CAD) continues to evolve and advanced manufacturing techniques like 3D printing become more widespread, making it possible to create complex parts easier than ever before, designers and engineers can leverage topology optimization software to push boundaries and find new ways to maximize design efficiency.

Topology optimization (TO) is a shape optimization method that uses algorithmic models to optimize material layout within a user-defined space for a given set of loads, conditions, and constraints. TO maximizes the performance and efficiency of the design by removing redundant material from areas that do not need to carry significant loads to reduce weight or solve design challenges like reducing resonance or thermal stress.

Designs produced with topology optimization often include free forms and intricate shapes that are complex or impossible to manufacture with traditional production methods. However, TO designs are a perfect match for additive manufacturing processes that have more forgiving design rules and can easily reproduce complex shapes without additional costs.

In a way, topology optimization serves as the foundation for generative design. Generative design takes the process a step further and eliminates the need for the initial human-designed model, taking on the role of the designer based on the predefined set of constraints.

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