It’s physics for computers, specifically the Direct Stiffness Method. The formal definition of what you send into a computer for stress analysis involves a whole lot of matrixes. You turn a structure into tiny little nodes not unlike pixels or voxels. Each point can be connected to other elements, and these connections have unique internal linear or twisting “stiffness”, like a spring has. Think how a spring and a stick of wood resist squishing and bending. They can be expressed as one massive square (important!) matrix. The equation in the third panel is essentially a mega version of Hooke’s law:
F = ku
“The vector of forces on the nodes = the matrix containing all information of the stiffness of the connections * the vector of positions of the nodes”.
This is a linear algebra problem, the easiest type of problem for a computer with a GPU. We can insert the known positions and forces on the bridge and solve for all unknown positions. If a truss on a bridge is calculated to experience too much force than it can handle, you can say that the bridge will fail under those conditions.
Is this physics?
It’s physics for computers, specifically the Direct Stiffness Method. The formal definition of what you send into a computer for stress analysis involves a whole lot of matrixes. You turn a structure into tiny little nodes not unlike pixels or voxels. Each point can be connected to other elements, and these connections have unique internal linear or twisting “stiffness”, like a spring has. Think how a spring and a stick of wood resist squishing and bending. They can be expressed as one massive square (important!) matrix. The equation in the third panel is essentially a mega version of Hooke’s law:
F = ku
“The vector of forces on the nodes = the matrix containing all information of the stiffness of the connections * the vector of positions of the nodes”.
This is a linear algebra problem, the easiest type of problem for a computer with a GPU. We can insert the known positions and forces on the bridge and solve for all unknown positions. If a truss on a bridge is calculated to experience too much force than it can handle, you can say that the bridge will fail under those conditions.
Oh I should have guessed.
It’s the matrix