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Structural Mechanics is a classical application of the Finite Element Method (FEM). This FEniCS video tutorial is on the deflection of a beam under its own weight with a visualization in Paraview. Here is the code: https://github.com/Ceyron/machine-learning-and-simulation/blob/main/english/fenics/cantilever_beam_linear_elasticity.py The easiest scenario of Structural Mechanics using Continuum Mechanics is the solution to the elliptic PDE given by Cauchy's equation of motion together with linear elasticity. Let's build a numerical solver for this. Why it has to be nabla_grad instead of grad: This is a really interesting question and goes deep into conventions in matrix/tensor calculus. For the discussion within FEniCS, consult the red info box here https://fenicsproject.org/pub/tutorial/html/._ftut1009.html#ftut1:NS:varform . I can also recommend checking out the Matrix Calculus Wikipedia page: https://en.wikipedia.org/wiki/Matrix_calculus . Particularly interesting is the difference between numerator and denominator layout. ------- 📝 : Check out the GitHub Repository of the channel, where I upload all the handwritten notes and source-code files (contributions are very welcome): https://github.com/Ceyron/machine-learning-and-simulation 📢 : Follow me on LinkedIn or Twitter for updates on the channel and other cool Machine Learning & Simulation stuff: https://www.linkedin.com/in/felix-koehler and https://twitter.com/felix_m_koehler 💸 : If you want to support my work on the channel, you can become a Patreon here: https://www.patreon.com/MLsim ------- Timestamps: 00:00 Introduction 00:53 Equations and Constitutive Relations 02:47 Clamped Cantilever Beam 03:37 Weak Form 04:50 Alternative Weak Form 05:39 von-Mises stress 06:30 Imports & Parameters 08:00 Some Boilerplate 08:17 Mesh & Vector Function Space 09:47 Boundary Conditions 12:23 Strain & Stress 15:58 Implement Weak Form 20:33 Compute solution 21:58 Compute von-Mises stress 24:41 Save fields to disk (for Paraview) 26:51 Executing and Discussing created files 27:19 Paraview Visualization 30:41 Outro Key Highlights & Overview: Understanding <strong>Fenics Tutorial</strong> requires clear step-by-step guidance and practical hands-on visual demonstrations. Follow along with top-rated video tutorials from industry experts today on <strong>TutorTube</strong>.