Recent content by blue24

Thank you, this is helpful!

Ok, so this question is still lingering in my mind - where do the PDE's come in for structural analysis? FEAnalyst says that FEA programs don't solve PDE's directly. I think I understand that part. But what is the PDE that is being "indirectly" solved? Is it the strain displacement equations?

Thanks both of you. I know the strain displacement equations are PDE's. Is that where the PDE's come in? So in general, for a dynamic structural analysis, Step 1 - Solve an ODE for displacements, based on applied boundary conditions and applied loading Step 2 - Solve PDE's for strain from...

I am a mechanical an engineer with a few years of experience. Most of the work I do is transient, structural finite element analysis. I have gotten reasonably competent at building models and pumping out results, but I regularly come across gaps in my fundamental knowledge. I have been doing...

Thank you. That is a really helpful answer. So when I am looking at equations which are written in index notation, I should treat the elements of the equation as numbers, not matrices. For me, that begs a new question. In order to arrive at the final solution (see first attached image)...

Thanks for the reply. That was my understanding before I got the textbook for this class and started reading through it. However, this textbook seems to use a notation where ##a_{ij}## represents a matrix. See the image below. Also, in order to calculate the solution, we get to...

Good idea. The book I am using is Elasticity: Theory, Applications, and Numerics; Third Edition; by Martin Sadd.

Sorry, yes, Eqs 1 and 2. Thanks. I am definitely confused on this point. I thought the terms were matrices, not numbers. If you look at the book solution (my post from yesterday at 12:46), it appears that they are matrices. And I thought that order matters for matrix multiplication.

The given equation from the book is: ##a^{'}_{ij}=Q_{ip}Q_{jq}a_{pq}## (Eq 1) Per strangerrep's post from Yesterday at 1:55PM, this "turns into ##a^{'}_{ij}=Q_{ip}a_{pq}Q_{jq}##..." (Eq 2) He does not introduce the transpose until after shifting the ##a_{pq}## term before the ##Q_{jq}##...

I don't understand how you got from ##Q_{ip} Q_{jq} a_{pq}## to ##Q_{ip} a_{pq} Q_{jq}##. Why did the order of the terms change?

Thank you for the feedback. This is exactly what I am trying to figure out. This class is going to be a heavy lift for me, and so I need to figure out what the gaps are in my understanding and start working on addressing those. I have not taken a linear algebra class (was optional in my...

Ok, so I'd like to zoom out here and get a better understanding of ##Q_{ij}##. I'm trying to do a basic example problem where the solution is given in the book (see attached image). I can calculate the transformation matrix, ##Q_{ij}## (did it without looking at the solution, woot!), and do...

My apologies! The book defines ##Q_{ij}## as the cosine of the angle between the ##x^{'}_{i}## and ##x_j## axes. See attachment.

Thank you for the reply. Unfortunately those terms, "covariant" and "contravariant", are not in my textbook. I have a pdf (legally purchased) and I searched for them. I will do some searching online. What is throwing me is that the textbook literally says, "[referring to isotropic tensors]...

Thank you for the response. The book defines ##Q_{ij}## as the angle between the ##x^{'}_i## and ##x_j## axes.