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#10 — The Eiffel Tower
I’ve decided to take the next step in my FEM study: building a structural model of the Eiffel Tower.
The challenge is not simply to reproduce its geometry, but to formulate an engineering model: geometry, materials, …
#9 — Solving the System
Consider a steel frame subjected to external loads.
After defining its stiffness matrix, boundary conditions, and load vector, the unknowns are the nodal displacements and rotations:
\[
\mathbf K\mathbf u=\mathbf f
…
#8 — Loads & Equilibrium
How do loads enter a finite element model?
Consider a beam-to-column connection in a steel frame. The forces and moments acting at the connection must satisfy equilibrium:
\[
\sum \mathbf F = 0,
\qquad
\sum \mathbf…
#7 — Boundary Conditions
A structural model needs more than elements and connectivity. It also needs constraints.
For example, an ideal fixed support can impose:
\[
u_x=u_y=u_z=\theta_x=\theta_y=\theta_z=0
\]
These boundary conditions rest…
#6 — Connectivity
If degrees of freedom describe how a node can move, how does an element connect the motion of two nodes?
For a structural element, the nodal degrees of freedom are gathered into an element vector:
\[
\mathbf d^{(e)} =
\be…
#5 — Degrees of Freedom
What does a degree of freedom actually represent in a structural model?
For a 3D structural node, the displacement vector can be written as:
\[
\mathbf d_i =
\begin{bmatrix}
u_x & u_y & u_z & \theta_x & \theta_y & \…
#4 — Global Assembly
So, how do individual element stiffness matrices become the stiffness matrix of the whole structure?
Consider a 3D structural element connecting two nodes. Each node has three translations and three rotations, giving t…
Exposición: Le Corbusier 150 + maquetas
"Considerado el padre de la arquitectura moderna, Le Corbusier —o Charles-Édouard Jeanneret— (1905-1980), fue el primer arquitecto de alcance global, construyendo más de 75 edificios en doce países …
#3 — Finite Element
Where does the element stiffness matrix come from?
For a simple 1D axial element, the stiffness matrix is:
\[
\mathbf{k}^{(e)}
=
\frac{EA}{L}
\begin{bmatrix}
1 & -1\\
-1 & 1
\end{bmatrix}
\]
Here, \(E\) is Young’s modul…
#2 — Algebraic System
One question I’m exploring in my study of the Finite Element Method:
How does a mechanical model become a system of algebraic equations?
For a simple elastic structure, the formulation leads to:
\[
\mathbf{K}\mathbf{u…
#1 — Physical Principle
I’ve recently started studying the mathematical foundations of the Finite Element Method.
One concept that caught my attention is the Principle of Virtual Work:
\[
\delta W_{\mathrm{int}} - \delta W_{\mathrm{ext}} =…
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