In this lecture, we'll cover the following:

• Solving for nodal displacements using the reduced stiffness matrix and force vector
• Reconstructing the full global displacement vector including restrained degrees of freedom
• Computing reaction forces from the full stiffness matrix and global displacements
• Applying corrections for self-weight at restrained nodes
• Validating results through equilibrium checks and expected physical behaviour (e.g. corner uplift)
• Extracting and interpreting maximum displacement and its location
• Visualising reaction forces in 3D for qualitative validation

In this lecture, we work through the complete solution phase of the finite element model. We begin by solving for the unknown displacements using the reduced stiffness matrix and corresponding reduced force vector, ensuring consistency by removing restrained degrees of freedom from both. Once obtained, we reconstruct the full global displacement vector by reinserting zero displacements at restrained locations, allowing us to move back to the full system representation.

We then compute reaction forces using the original (unreduced) stiffness matrix and the global displacement vector, making an important correction to account for self-weight at restrained nodes. From there, we carry out several validation steps: we check global equilibrium by comparing total reactions with applied loads, and we confirm expected structural behaviour such as the characteristic corner uplift in simply supported plates. Finally, we extract the maximum vertical displacement and verify its location.

Next up

Next, we will visualise the computed displacements using contour plots, providing a clear graphical check of the structural response.