Summary
In this lecture, we'll cover:
- How to construct the bending and shear stiffness matrices for an element,
- How the bending and shear contributions fit alongside the membrane contribution to form the full element stiffness matrix,
The lecture focuses on completing the remaining parts of the element stiffness matrix calculation. We first repeat the established Gauss quadrature-based process for bending, using a different constitutive matrix and a different strain-displacement matrix, whilst keeping the sampling, weighting, Jacobian handling, and numerical integration structure the same.
We then do the same for shear: the constitutive matrix now includes the shear correction factor and shear modulus, and the shear strain-displacement matrix has a different shape, with negative shape function terms appearing in the relevant positions rather than derivatives.
Next up
The next step will be to wrap these calculations into a function and move it into a utilities file for easier reuse.
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Finite Element Analysis of Plate and Shell Structures: Part 2 - Shells
Expanding from plate to shell elements - build a workflow that unlocks the behaviour of 3D shell structures
After completing this course...
- You will understand how we make the leap from Reissner-Mindlin plate elements to shell elements and what extra modelling fidelity that provides.
- You will be comfortable using a combination of GMSH and the open-source 3D modelling software, Blender, to generate custom finite element meshes.
- You will be able to use OpenSeesPy to model shell structures, as an alternative to your own custom finite element solver.
- You will have a much greater understanding of what commercial finite element packages are doing, behind the UI, allowing you to authoritatively interrogate their results.