{"id":81,"date":"2020-08-07T21:09:54","date_gmt":"2020-08-07T19:09:54","guid":{"rendered":"http:\/\/alma-consulting.eu\/?p=81"},"modified":"2022-05-28T13:49:17","modified_gmt":"2022-05-28T11:49:17","slug":"working-wonders-with-apdl-math-ep-01-thermal-modal-analysis","status":"publish","type":"post","link":"https:\/\/alma-consulting.eu\/index.php\/2020\/08\/07\/working-wonders-with-apdl-math-ep-01-thermal-modal-analysis\/","title":{"rendered":"Working wonders with APDL Math – Ep 01 : Thermal Modal Analysis"},"content":{"rendered":"\n

As Times Goes By<\/strong><\/h3>\n\n\n\n

Do you remember the moment you first heard about ANSYS introducing APDL Math?<\/p>\n\n\n\n

I, for one, do, and I have a vivid memory of thinking \u201cWow, that can be a powerful tool, I\u2019m dead sure it won\u2019t be long before an opportunity arises and I\u2019ll start developing pretty useful procedures and tools\u201d. Well, that was half a decade ago, and to my great shame, nothing quite like that has happened so far. Reasons for this are obvious and probably the same for most of us:  lack of time and energy to learn yet another set of commands, fear of the ever present risk of developing procedures that are eventually rejected as nonstandard use of the software and therefore error-prone (those of you working under quality assurance, raise your hand!), anxiety of working directly under the hood on real projects with little means to double check your results, to name a few.<\/p>\n\n\n\n

That said, finally an opportunity presented itself, and before I knew it, I was up and running with APDL Math. The objective of this article is to showcase some simple yet insightful applications and hopefully remove the prevention one can have regarding using these additional capabilities.<\/p>\n\n\n\n

For the sake of demonstration, I will begin with a somewhat uncommon analysis tool that should nevertheless ring a bell for most of you, that is: modal analysis (and yes, the pun is intended). You may wonder what is the purpose of using APDL Math to perform a task that is a standard ANSYS capability since say revision 2.0, 40 years ago? But wait, did I mention that by modal analysis, I mean thermal modal Analysis?<\/p>\n\n\n\n

Thermal Modal Analysis at a Glance<\/strong><\/h3>\n\n\n\n

Although scarcely used, thermal modal analysis is both an analysis and a design validation tool, mostly used in the field of precision engineering and or optomechanics. Specifically, it can serve a number of purposes such as in the following Q&A:<\/p>\n\n\n\n

Q: Will my system settle fast enough to fulfill design requirements?<\/p>\n\n\n\n

A: Compute the system Thermal Time Constants<\/p>\n\n\n\n

Q: Where should I place sensors to get information rich \/ robust measurements?<\/p>\n\n\n\n

A: Compute Thermal modes and place your sensors away from large thermal gradients<\/p>\n\n\n\n

Q: Can I develop a reduced model to solve large transient thermal mechanical problems?<\/p>\n\n\n\n

A: Working on a modal basis rather than with the full problem allows for the construction of such reduced model effectively converting a high-order coupled system to a low order, uncoupled set of equations.<\/p>\n\n\n\n

Q: How to develop a reduced order state-space matrices representation of my thermal system (equivalent to SPMWRITE command)?<\/p>\n\n\n\n

A: Modal analysis provides every result needed to build those matrices directly within ANSYS.<\/p>\n\n\n\n

Although you might only be vaguely familiar with many or all of those topics, the idea behind this article is really to show that APDL Math does exactly what you need it to do: allow the user to efficiently address specific needs, with a minimal amount of additional work. Minimal? Let\u2019s see what it looks like in reality, and you will soon enough be in a position to make your own opinion on the matter.<\/p>\n\n\n\n

 Thermal Modal Analysis using APDL Math<\/strong><\/h3>\n\n\n\n

To begin with, it is worth underlining the similarities and differences between structural (vibration) modes and thermal modes. Mathematically, both look very much the same, i.e. modes are solutions of the dynamics equation in the absence of forcing (external) term:<\/p>\n\n\n\n

<\/p>\n\n\n\n

Domain<\/td>Equation solved<\/td>Terms Explained <\/td><\/tr>
Structural<\/td> \"([K]-\lambda [M]) \Phi=0\"<\/td>\"[K] = {stiffness \quad matrix}\"
\"[M]= {mass \quad matrix}\" <\/td><\/tr>
Thermal<\/td>\"([K]-\lambda [C]) \Phi=0\" <\/td>\"[K] = {conductivity \quad matrix}\"
\"[C] = {capacitance \quad matrix}\"<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Now, the fundamental difference is that the eigenvalues have completely different physical interpretations:<\/p>\n\n\n\n