In this lecture, we'll cover:

• How to express the global force–displacement relationship for the structure
• How to solve for nodal displacements using the global stiffness matrix
• The role of the applied force vector in determining structural response
• How matrix inversion is used in a coding environment to obtain displacements

In this lecture, we move on to determining the nodal displacements of the structure using the global force–displacement relationship. We begin by revisiting the full system equation, identifying the structure stiffness matrix and the vector of unknown nodal displacements. We focus on how these components interact with the externally applied force vector to define the structural response.

We then discuss how to solve this system of equations, emphasising that in a coding environment the process is relatively straightforward: we invert the global stiffness matrix and multiply it by the force vector. We highlight that the force vector contains only the externally applied loads, in this case, a 200 kN vertical load applied at node one, corresponding to a specific degree of freedom. By carrying out this matrix operation, we obtain the numerical values of the nodal displacements, completing the solution step for the unknown degrees of freedom.

Next up:

In the next lecture, we compute the support reactions by substituting the known displacements back into the full force–displacement relationship.