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The objective function itself is formulated such that the absolute magnitude is on the order of unity.

We can begin by defining the variation of the thickness of the dielectric layers using the Deformed Geometry interface. The Deformed Geometry interface is necessary because we want to compute the analytic sensitivities without having to remesh the geometry as we change the dimensions. Since we will be changing the sizes of the two dielectrics, we want to define these deformations as completely as possible. We will do this with a Prescribed Deformation domain feature, as shown in the screenshot below.

The capacitor itself is originally sketched such that it is centered at the origin so the original, undeformed part has a coordinate system: Xg,Yg,Zg. For this simple Cartesian geometry, we can use this coordinate system to directly define the deformation as the thicknesses of the dielectric layers are changed.

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The change in the thicknesses of the dielectric layers is controlled with a Prescribed Deformation feature. For this simple problem, we can just add an Optimization feature to our study sequence, as shown in the screenshot below. This minimization problem statement and scaling can be implemented entirely within the Optimization study node, as shown in the screenshot below.

The upper and lower limits are specified to prevent zero, or negative, thicknesses. Lastly, we apply a scaling to dT , the design parameter, based upon the original thickness, D , such that the optimized value will have an order of magnitude near unity. The optimization solver settings.

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The voltage field in the original model and the optimized structure are shown below, along with the finite element mesh. Observe that the finite element mesh is stretched and compressed, but that no remeshing has occurred. The original and final structure.

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The voltage field and mesh are shown. The geometric deformation demonstrated here is also quite simple. As you consider more complex geometries and more complex geometric changes, you will not always be able to directly use the undeformed spatial coordinates to define the deformation.

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In such cases, you will need to add equations to the model to help define the deformation. Of course, you may also want to consider more complex deformations, not just simple dimensional changes. We will cover this topic in an upcoming blog post on optimization. In the meantime, if you have any questions about this technique and would like to use the Optimization Module for your design needs, please contact us.

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Changing the Dimensions of a Model Using Shape Optimization

PDF instructions are not included with every blog post. If you are having trouble following the instructions presented here, I would encourage you to reach out to the COMSOL support team for assistance. Very informative. Thanks for sharing.

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Can we define a deformation simply as dT such that dT varies fro 0 to say some value 0. We want to completely define the deformation, if possible, when using Deformed Geometry. Of course, of you want, you can also try out your approach and observe the differences. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' or the latest version listed if standards is not an option.

The utilization of 6D-BIM technology can result in more complete and accurate energy estimates earlier in the design process. It also allows for measurement and verification during building occupation, and improved processes for gathering lessons learned in high performance facilities.


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The utilization of 7D-BIM technology can result in easier and quicker parts replacements, optimized compliance and a streamlined asset life cycle management over time. Improved visualization of the project, communication of design intent 2. Improved multidisciplinary collaboration 3. IM 3D, 4D, 5D. All rights reserved. View on Mobile.