Working Model 2d Student Edition 16

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Although your model may not always be an exact miniature of a full-scale building, the materials you select to represent it are important. Firstly, you want your model to narrate something about your project; having carefully chosen materials, as opposed to a model entirely made of card, will help to immerse others in that narrative far more effectively. Secondly, you want to make sure that the materials you use are easy enough for you to work with; a model should supplement your project, not hijack all of your time.

Ensuring that your working environment is properly lit is essential in preventing your eyes from straining themselves, as well as enabling you to see the details in your model and avoid mistakes. Models can also result in beautiful photographs, but only if you have proper lighting set up.

One of the ways you can simplify and reduce the size of a finite element model is by using any symmetries present in your model. Whether you are building the geometry natively in COMSOL Multiphysics or importing a design from an external file, there are modeling strategies as well as features in the software that you can use to take advantage of such symmetries. In this article, we will explain how you can take advantage of symmetry in your simulation to reduce its size and discuss the functionality in the software that enables you to easily do so.

Reducing the size of your model is advantageous because of the amount of computational time and memory that can be saved when solving the equations for your model. These savings can be significant when working with large models and multiphysics models. It is also beneficial regardless of the phase of model development that you are currently working in. If you are starting a model from scratch, by using a reduced, simplified version of your design, you can take less time to set up and build your model and reach results. From there, you can continue to expand the scope of your simulation and increase complexity.

If you are working with a geometry that has already been fully built, reducing its size can help you reach solutions for the model equations more quickly. You can then perform postprocessing in order to visualize the solution for the entire model geometry. Additionally, reducing your model size enables you to catch and resolve any errors in your model setup more quickly.

By using the symmetries in a model, you can reduce its size by half or more, making this an efficient method for solving large models. This applies to cases where both the geometry and modeling assumptions include symmetries. It can also be the case that neglecting, or omitting, some geometric or other modeling features will allow for additional symmetry to be used. Some common types of symmetries are axial symmetry as well as symmetric and antisymmetric planes and lines. Modeling in axial symmetry in particular is very efficient, but often involves assuming that some modeling features can be neglected.

The geometry for a flange. In lieu of modeling the entire flange, the axisymmetric nature of the design can be used to reduce its model size by half, a quarter, an eighth, and down to a cross section. Reducing to axial symmetry is valid if it can be assumed that the bolt holes do not significantly affect the solution.

Axial symmetry is common for cylindrical and similar 3D geometries. If the geometry is axisymmetric, there are variations in the radial (r) and vertical (z) direction only, i.e., not in the angular () direction. You can then solve a 2D problem in the rz-plane instead of the full 3D model, which can save significant computational memory and time. Most physics interfaces in COMSOL Multiphysics are available in axisymmetric versions and take the axial symmetry into account. In addition, several interfaces allow for an assumed form of azimuthal variation, including:

The Free Convection in a Light Bulb tutorial model. An axisymmetric cross section (right) of the 3D light bulb (left) is used to build the model, after which the results are postprocessed to visualize the heat transfer throughout the entire bulb.

Symmetry planes and lines are common in both 2D and 3D models. Symmetry means that a model is identical on either side of a dividing line or plane. For a scalar field, the normal flux is zero across the symmetry line. In structural mechanics, the symmetry conditions are different. Many physics interfaces have symmetry conditions directly available as features.

The Shell-and-Tube Heat Exchanger tutorial model geometry (left). The design and physics are symmetric along the XZ-plane, enabling us to simplify the geometry by removing half (right).To take advantage of symmetry planes and symmetry lines, all of the geometry, material properties, and boundary conditions must be symmetric, and any loads or sources must be symmetric or antisymmetric. You can then build a model of the symmetric portion, which can be half, a quarter, or an eighth of the full geometry, and apply the appropriate symmetry or antisymmetry boundary conditions.

Antisymmetry planes and lines means that the loading of a model is oppositely balanced on either side of a dividing line or plane. For a scalar field, the dependent variable is 0 along the antisymmetry plane or line. Structural mechanics applications have other antisymmetry conditions. Many physics interfaces have symmetry conditions directly available as features.

The Permanent Magnet tutorial model geometry with material color and texture displayed (left). The model geometry exhibits mirror symmetry along the XZ-plane as well as the XY-plane, while the magnetic fields of the model are antisymmetric, enabling us to remove all but one-fourth of the geometry (right).

The Cross Section operation enables you to go from modeling a solid to a plane. A work plane is used in combination with this operation to extract a cross section from a 3D geometry, which can be used within a 2D or 2D axisymmetric model component.

The Projection operation enables you to project 3D objects in order to create 2D curves. The geometry can be projected onto a work plane in a 3D model component or in a 2D model component. This is useful for complex geometries, as you can specify what 3D entities (objects, domains, boundaries, edges, points) you want to project into 2D. This is an alternative to having a work plane cut through the geometry and the entire geometric object, such as what is done for the Cross Section operation.

As noted earlier, there are a plethora of physics interfaces that are available in 2D and 2D axisymmetric versions. Additionally, there are many physics interfaces that have different types of symmetry conditions available as physics feature nodes. These include Symmetry, Symmetry Plane, and Antisymmetry boundary conditions, among other types of symmetry boundary conditions (e.g., Sector Symmetry), which enable you to specify the symmetry planes or lines of symmetry in your model.

The Symmetry Plane boundary condition that is used in the Permanent Magnet tutorial model, where we specify the antisymmetry of the magnetic field. There are also several other ways you can use symmetry to simplify magnetic field modeling.

There are some cases where the results of structural mechanics models are not purely symmetric, even though the problem may appear so at first. You should note such cases, which include the following:

There are several blog posts that discuss taking advantage of the symmetries in a model for different application areas. There are also several tutorial models available in the Application Libraries that show different implementations of taking advantage of the symmetries in a geometry. From these you can explore, learn from, and understand the logic that was used for reducing the computational domain as a result of any symmetries. A small sample of the available examples are listed below.

The development of computational methods to predict three-dimensional (3D) protein structures from the protein sequence has proceeded along two complementary paths that focus on either the physical interactions or the evolutionary history. The physical interaction programme heavily integrates our understanding of molecular driving forces into either thermodynamic or kinetic simulation of protein physics16 or statistical approximations thereof17. Although theoretically very appealing, this approach has proved highly challenging for even moderate-sized proteins due to the computational intractability of molecular simulation, the context dependence of protein stability and the difficulty of producing sufficiently accurate models of protein physics. The evolutionary programme has provided an alternative in recent years, in which the constraints on protein structure are derived from bioinformatics analysis of the evolutionary history of proteins, homology to solved structures18,19 and pairwise evolutionary correlations20,21,22,23,24. This bioinformatics approach has benefited greatly from the steady growth of experimental protein structures deposited in the Protein Data Bank (PDB)5, the explosion of genomic sequencing and the rapid development of deep learning techniques to interpret these correlations. Despite these advances, contemporary physical and evolutionary-history-based approaches produce predictions that are far short of experimental accuracy in the majority of cases in which a close homologue has not been solved experimentally and this has limited their utility for many biological applications.

We demonstrate in Fig. 2a that the high accuracy that AlphaFold demonstrated in CASP14 extends to a large sample of recently released PDB structures; in this dataset, all structures were deposited in the PDB after our training data cut-off and are analysed as full chains (see Methods, Supplementary Fig. 15 and Supplementary Table 6 for more details). Furthermore, we observe high side-chain accuracy when the backbone prediction is accurate (Fig. 2b) and we show that our confidence measure, the predicted local-distance difference test (pLDDT), reliably predicts the Cα local-distance difference test (lDDT-Cα) accuracy of the corresponding prediction (Fig. 2c). We also find that the global superposition metric template modelling score (TM-score)27 can be accurately estimated (Fig. 2d). Overall, these analyses validate that the high accuracy and reliability of AlphaFold on CASP14 proteins also transfers to an uncurated collection of recent PDB submissions, as would be expected (see Supplementary Methods 1.15 and Supplementary Fig. 11 for confirmation that this high accuracy extends to new folds). 153554b96e

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