At this stage, we have a minimum viable code - our solver performs an iterative analysis that tries to converge on the final state of the structure, and we’ve implemented an extensive structure visualisation. This section acts as a validation of sorts for our solver so far.
In this section, we’ll close the circle, so to speak, and compare our code’s results with the linear cable solution we developed at the start of the course. We’ll be able to closely approximate the linear solution we derived previously but also observe the emergence of non-linear behaviour as the axial stiffness of our cable is progressively reduced, leading to larger and larger self-weight deflections.
We’ll also compare the behaviour of our new non-linear solver with the linear truss analysis solver we developed in the pre-requisite course. Again highlighting the advantage offered by a non-linear solver when deflections start to become large by comparison to the scale of the structure.
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Non-linear Finite Element Analysis of 2D Catenary & Cable Structures using Python
Build an iterative solution toolbox to analyse structures that exhibit geometric non-linearity due to large deflections.
After completing this course...
- You will understand the concept of geometric non-linearity and when it should be considered.
- You will understand how to modify the axially loaded element stiffness matrix to account for large deflections and changes in geometry.
- You will have implemented a Newton-Raphson iterative solution algorithm that seeks to converge on the deformed state of the structure.
- You will have a workflow that leverages open-source modelling tools in Blender to quickly generate the initial structural geometry.