Product cost is one of the prominent factors that manufacturers strive to reduce through evaluating number of design alternatives. It is for this reason why simulation tools are being extensively exploited, so that conventional design can be altered to an extent where products can be developed competitively in terms of price and quality.

As such, topology optimization is being increasingly applied through finite element analysis by most of the manufacturers today, helping them in developing lighter and stronger products. While the major cost function in any product is its mass due to the amount of material invested, topology optimization as a part of product design optimization for manufacturers helps them in achieving better design alternatives, requiring less material that reduces weight and allows manufacturers a room to price the product more competitively.

However, topology optimization when not applied correctly can lead to a drastic failure of the design and can hamper the brand value of the organization. It is therefore a tool that requires a broad understanding of the constraints and load cases that would affect the product design and development. Failing to consider even a single constraint can cause the design to fail and mess up all the cost optimization goals, which were actually set to meet market requirements.

**Factors to Consider While Performing Topology Optimization**

To perform topology optimization, it is important to figure out design variables and constraints for the product under consideration. Also, the cost function is required to be defined to optimize the structure and figure out how good the design is.

Cost function could be reducing the mass, improving stiffness or maximizing stress resistance. However, reducing the cost function requires also the identification of design variables from where the reduction can be achieved. It could be possible to achieve optimized structure design by reducing its thickness, length or other design variable. These variables however are defined considering the constraints that put a limit on the extent to which the variable can be optimized. An example could be maximum stress and strain limits a structure or material can withstand.

Failing to realize any variable or constraint can lead to an under designed product that would fail prematurely. It is the reason why majority of the designers prefer not to use topology optimization. However, when done properly, it could reduce the cost to a significant level.

**Executing Topology Optimization**

Topology optimization through finite element solvers is usually performed using gradient based algorithms that calculate the local minimum (a value beyond which the design will be invalid) at each element.

**To perform the simulation run, following process is usually followed:**

- Select the most sensible cost function such as Mass of the structure, which is most usually the choice in optimization.
- Figure out the variables that software is allowed to change and maximum limit of the change.
- Find out all the possible ways for the structure to fail, i.e. ways through which the requirement of the design is not met.
- Create different load cases for failure modes (e.g. static load, buckling load, etc.)
- Define the constraints for each load case to specify when the structure will not be considered as valid. (e.g. high stresses or low factor of safety)
- Define the maximum number of allowable cycles and maximum change allowed per cycle.

The optimization solver can then be initiated to solve the equations through finite element approach and results can be visualized. The basic topology results however are not clear as it erodes the material envelope to find the stiffest shape for all the load cases. Thus, the structure design can be improved using the eroded shape as a guide to develop a smooth geometry.

The finalized design should again be simulated and change in the variables should be compared to the previous shape. If the result is unacceptable, the load cases are required to be redefined and the procedure has to be repeated until the variable values are within the permissible range.

The topology optimization approach can be utilized to build highly economical products without much effort. Lighter and stronger products mean lower development costs for manufacturers and better acceptance rate from the consumer. Reducing weight is one of the most useful parameter in vehicle development as it directly helps in bringing down emission levels, while maintaining the strength of the body.

Applications of topology optimization are many, it is however important to know the sensitivity of the approach that requires considering all the design variables and constraints to avoid catastrophic failure.

**About the Author:**

Gaurang Trivedi is engineering consultant at TrueCADD. He has applied his engineering expertise across several highly complex and big scale projects, consequently managing to flawlessly deliver as per the client requirements.

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