What are the best methods for analyzing structural loads using Wolfram?

Questions
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1

Hi everyone,

I’m currently working on an engineering project where I need to analyze the structural loads for a building design. I’ve been using Wolfram Mathematica for some basic calculations, but I’m looking for more advanced techniques to simulate and analyze the distribution of forces across beams, columns, and supports.

Specifically, I’m interested in using Mathematica to calculate stress, strain, and moment distribution. Are there any built-in functions or packages in Mathematica that can simplify this process? How can I use it to visualize the results, and are there any tips for ensuring the accuracy of the calculations when working with complex structures?

Thanks!

www.concretesrichmondva.com

2

Hi
It depends on what you want to do. Writing a routine for solving continuous beams or trusses is quite straightforward. Plane frames is doable with effort but if you want 3D space frames I would suggest that you use commercial software.
Some links - https://demonstrations.wolfram.com/StressPropagationInATrussBridge/
Analysis of Trusses and Other Engineering Structures with Mathematica -- from Wolfram Library Archive
However, if you need finite elements to design slabs, concrete structures or other structures that lend themselves to finite elements, then the Wolfram finite element package is excellent and relatively easy to use.
Finite Element Method User Guide—Wolfram Documentation
Solid Mechanics—Wolfram Documentation

3

Perhaps 1D finite elements – such as beams and the like – could one-day be incorporated into the Wolfram Finite Element Package?

4

Yes. It seems a strange omission. Maybe because other methods may be more efficient?

5

Have you looked at the Documentation pages on PDE modelling? And, in particular, the section on Solid Mechanics?

6

Leo,

You may find the following link to “An introduction to Mathematica for Civil Engineers” of assistance. Whilst not specifically for structural work, it does cover the use of subscripts, units, load tracing, beam design, and many other tasks common to civil engineers. Including an example of finite elements.
It is available, for free, at https://notebookarchive.org/2025-03-cx2tujb https://notebookarchive.org/2025-03-cx2tujb

7

The finite element library that comes with WL provides functionality for performing solid mechanics. This means analysis on solid objects, like I-beams etc. The functionality provided is for 2D, 2D axisymmetric and 3D cases. There is no 1D or 1D axisymmetric functionality or solid mechanics. The main reason for this is that it is not very useful for solids.

What you are looking for, as far as I understand, are modeling trusses. This is from the domain of structural (not solid) mechanics. If you want to model this, you can use NDSolve directly; but you’d have to set up the equations yourself. There is no pre-packaged functionality available, that I am aware of. An alternative choice for modeling trusses would then be to use system modeler. See for example this post

So, as Malcolm pointed out, it depends a bit on what exactly you want to do. If you want to do solid mechanics then you’d used SolidMechanicsPDEComponent and if you want to model trusses then system modeler is a possible choice unless you want to get your hands dirty and use NDSolve.

A third option might be to use the third party product Timo Structural

https://www.wolfram.com/products/applications/timostructural/

Though I have not used this I am not sure about the scope of it.

8

You may also find my notebook “An Introduction to Mathematica for Civil Engineers” useful. It covers a lot of ground with examples relevant for civil engineering, including some on structural design. It is available, for free, on Wolfram’s Notebook Archive at https://notebookarchive.org/2025-03-cx2tujb