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Browse all 16 notes ›🧑🔬Mechanics / 🧊 Basics of Finite Element Method
2. Strong and Weak Form of Linear Elasticity Equivalence
The weak (variational) form follows from the strong equilibrium equations by testing with virtual displacements and integrating by parts. Use it as the blueprint of a finite-element implementation: it fixes the trial and test spaces, the bilinear form and the Neumann terms.
🧑🔬Mechanics / 🧊 Basics of Finite Element Method
1. Symmetric Stiffness Tensor and Voigt notation
Voigt notation packs symmetric stress and strain tensors into six-component vectors, so the elasticity tensor becomes a symmetric 6x6 matrix. Use it to read, write and implement constitutive laws compactly, including their FEniCSx form.
📐 Advanced Mathematics / random-process
4. Markov-decision-process
A Markov decision process formalizes sequential decision making with states, actions, rewards and transition probabilities. Use it to set up value and policy iteration, and as the base model that reinforcement learning methods optimize.
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