The Statistics button in the Mesh ribbon tab (top, right) is used to quickly evaluate the number of mesh elements, among other mesh statistics, in the model. It is also available through the Mesh ribbon tab, in the Evaluate ribbon group, through the Statistics button. The number of mesh elements in your model is presented in the Log window each time you create a new mesh or modify an existing one by clicking the Build All button. The total number of degrees of freedom is given by: (# degrees of freedom) = (# nodes) * (# dependent variables). Upon calculating the total number of nodes, you can then calculate the total number of degrees of freedom. Quadrilateral (quad) meshes have roughly twice as many nodes as triangular meshes, and hexahedral (brick) meshes have about six times as many nodes as tetrahedral meshes. The following are approximate relations between the number of nodes and the number of elements in 2D and 3D for Lagrange elements of different order. Additional background information on the degrees of freedom in a model can be found in the blog post that discusses how much memory is needed to solve large models, under the section of text explaining what degrees of freedom are.
![calculate degree of freedom mechanics calculate degree of freedom mechanics](https://static.docsity.com/documents_first_pages/2019/11/05/1b9a8cb3b131f9c270aac75bc915a0b2.png)
![calculate degree of freedom mechanics calculate degree of freedom mechanics](https://d2vlcm61l7u1fs.cloudfront.net/media/a7e/a7e44bfa-2875-461a-8023-a6721884a8ec/phpT9IU73.png)
For thin geometries, where a large proportion of the elements lie on the boundary, the number of nodes per element is a bit higher. The relation is only approximate, since it depends on the ratio of the elements that lie on the boundary of the geometry. The relation between the number of nodes and the number of elements depends on the order of the elements and differs between 2D and 3D. This means that the number of degrees of freedom is given by the number of nodes multiplied by the number of dependent variables. It is often desirable to be able to estimate the number of degrees of freedom based on the number of elements in the model.įor most physics interfaces, each dependent variable is present in all nodes in the mesh. The solution time and memory requirements to compute a model are strongly related to the number of degrees of freedom in the model. What Does Degrees of Freedom Mean in COMSOL Multiphysics ®? In this article, we explain the importance of the degrees of freedom for a model and how to estimate the number of degrees of freedom. In the COMSOL Multiphysics ® software, the number of degrees of freedom (DOFs) in a model have a significant correlation to, and effect on, the computation of a model. On the other hand, if you actually are interested in the tension in the string (will it break?) you use the Newtonian method, or maybe work backwards from the Lagrangian solution.How to Estimate the Number of Degrees of Freedom in a Model
![calculate degree of freedom mechanics calculate degree of freedom mechanics](https://i.ytimg.com/vi/p114nu1fgdo/maxresdefault.jpg)
Notice, though, that these forces never do any work. This force doesn’t even appear in the Lagrangian approach! Other constraint forces, such as the normal force for a bead on a wire, or the normal force for a particle moving on a surface, or the tension in the string of a pendulum-none of these forces appear in the Lagrangian. This is definitely less work than the Newtonian approach, which involves constraint forces, such as the tension in the string. It’s usually pretty easy to figure out the kinetic energy and potential energy of a system, and thereby write down the Lagrangian.
![calculate degree of freedom mechanics calculate degree of freedom mechanics](https://media.cheggcdn.com/study/501/5017ec14-812b-4a20-bd79-71964bcbf769/DC-162V4.png)
Gives the equation of motion in just one step.