Weighted Residual (1/5): Intro & Process

[@danielbadel1226]

Maybe you do not have a lot of views because people do not know the power of this video. I'm coursing my master in Aeronautical engineering and i'm greatly thankful for this video, thank you! PVW is sooo clear now!

[@mariajaen1795]

MASTER?! i am in my second year mech eng and my teacher decided it was an amazing idea to teach us this in mechanical vibrations course. I KNEW this was an advanced topic

[@danielbadel1226]

@@mariajaen1795 yes, typically this is tought in mechanical vibrations. The principle of virtual work is basically a weak formulation of the static or dynamic equilibrium equations This meas that we are not finding the exact solution but a pretty close one. So using It you can obtain the same equations of motion for dynamic systems. So, why to learn it? Because is by default the method used to impose equilibrium in finite element models and solve structural problems. Try to study weak formulations of ODE is really useful

[@mariajaen1795]

​@@danielbadel1226 I did study weak formulations of ODEs througt variational formulation and therefore i studied how to make them "strong", thank you for answering. Its interesting how the governing equation tends to change depending on what youre looking for, in my case, lowest mode shapes or natural frequencies. Sadly my governing equation changes so the formulation of a solution is more complex but your answer and this video ended up being extremely useful, thanks for answering

[@DM-pm8hr]

This is so great! Thank you!

[@yeisoncastellanos5816]

Hi, Mike. Thanks for this video. it is fantastic and powerful

[@Rashidiill]

You saved my 2 hours.

[@eamona708]

Videos helping me out, cheers bro

[@carbon273]

how do you know what shape to assume? Thats where im stuck at. What about cases where its not obvious to predict the shape of the solution?

[@amritkshetri5528]

what is the textbook you are refering to?

[@jorgealejandroaguirrelara]

Hi, I have a big doubt. In this case, the solution equation was assumed easily as the bending moment of a beam is "easy" to predict. However, what if I can´t predict the system's behavior at all. How can I propose a solution equation for a problem of which I've got no idea how is it going to behave?

[@Rashidiill]

Leave it to computer.

[@william19155]

Hello. I have a specific problem in which I have to compute the integral of the residual, R, along the entire length of a beam example. I was wondering if you could walk me through it and answer any questions I have. I would be willing to compensate accordingly. Thanks

[@husnainhyder6713]

Dear Mr Fosters Great Lecture no dought But there are some book in which they are choosing a trail function or supposed function regardless of the fact that they satisfy all the boundry conditions suppose heat diffusion equation (d^2 T)/(dx^2 )=T0 , and they say lets take trail function T(x)=ax^3+bx^2+cx+d with BC’s that doesn’t satisfy the trail function such as T(0)=25 and q(x=L)=0 Please Explain Thanks

[@danielbadel1226]

Hi Husnain, to propose a solution as you said always has to satisfy the essential boundary conditions (this are the conditions with not derivatives as you have), but not necessarily the natural one. Even is the final answer is to find the the coefficients a-d the in the proposed solution you can know the values of some coefficients before starting, for example d=25, otherwise the first homogeneous boundary condition is not satisfied. The solution you are proposing is general and need to be adapted to your specific problem to find the coefficients that satisfy the BC. Was that helpful?

[@AryaArald]

Very helpful.

[@AryaArald]

My question is, why do we assume a solution, when we already have the exact one (Bending equation)?

[@danielbadel1226]

Hi, because you do not only use this method for structural problems when you already know the solution, also for thermal of any other physical problem. Bon the other hand, you can use it to solve any ODE and not only in 1 dimension as the beam case but also for 3D systems of ODE as for solid elements. This is basically what the computer inside a FE simulation requires

[@徐捷耀]

so, I still do not understand why do we assume the form of the solution like "Y=Asin(pi*x / L)". Would you tell me why if you know the answer ? thanks

[@Torq123]

Great.