Engineering Mechanics: Statics Theory | Cartesian Vector Notation (CVN)

[@nasosskaltsas9890]

Hello! Your videos have helped me a lot! Is there a video where you explain Lagrange shape functions and serendipity elements?

[@ClaytonPettit]

Hi! Glad the videos have helped :) I mainly discuss shape functions in the recorded lectures 4 and 5 of my graduate class (kzbin.info/aero/PLLSzlda_AXa3yQEJAb5JcmsVDy9i9K_fi) but plan to make a standalone theory video soon as they have been asked about quite extensively haha as for serendipity elements I have yet to discuss them yet but plan to in the future (probably a while out though as I am focusing on statics and solid mechanics at the moment). Hope this answers your questions :)

[@nasosskaltsas9890]

@@ClaytonPettit Yeah i've seen already those vids. So... my professor has given us a solid finite element problem where the element belongs to the Lagrange family (the displacement approach is quadratic with respect to ξ and cubic with respect to η), and we have to figure out each node's position and numbering. I'm really confused and i dont know what i should search on youtube to find the matching explanation. Thanks for your time !

[@ClaytonPettit]

Ah I see haha unfortunately I am not sure you will find such a video as this would be a niche problem specifically designed for an academic setting as for simplicity the same approximation function is used for both directions in typical scenarios. It is not hard to expand the theory of shape functions to accommodate this as one element edge direction would simple have more nodes compared to the other edge direction (e.g. 3 nodes along the horizontal edge and 4 along the vertical edge). From there you can solve for the shape functions by using the identity that for a particular node the shape function must be 1 for that node and 0 for the remaining nodes. Other factors however such as element type (quadrilateral, triangular, etc.) and node spacing (typically evenly distributed along the element edge) would be a factor however so the question wording would be quite important. Hope this helps guide you a bit and I'm sorry my videos couldn't help more!

[@lifebred4763]

amazing video, it was a huge help