How to solve the large deflection of the cantilever beam

[cvnaditya]

how to solve the large deflection of the beam, i have tried using finite element method but unable to find it.

 

[SteamKing]

how to solve the large deflection of the beam, i have tried using finite element method but unable to find it.

I'm afraid your post is too vague to be able to respond to.

How large a deflection are you talking about?

Does the beam stress go beyond yield for the material of construction?

What type of finite element method was used?

What do you mean "unable to find it"?

 

[cvnaditya]

Steamking before i also have the same doubt but when going through project i got to know there will be large defelction. according to strength of material we find deflection for slope angle of 0.5 when load acting at the end point. But when the load is increasing and the slope angles changes from 0.5-80 and goes on till the beam has its ability without break which depends on flexural rigidity. after certain value example when the slope is 85 degree the beam may break.

In strength of material we use the formula Pl3/3EI it is just to find out one maximum deflection but when we use finite element method we use sinx or cosx expansion n solve it. i am getting trouble near this some logic or basic parameter i am missing.

 

[SteamKing]

Steamking before i also have the same doubt but when going through project i got to know there will be large defelction. according to strength of material we find deflection for slope angle of 0.5 when load acting at the end point. But when the load is increasing and the slope angles changes from 0.5-80 and goes on till the beam has its ability without break which depends on flexural rigidity. after certain value example when the slope is 85 degree the beam may break.

In strength of material we use the formula Pl3/3EI it is just to find out one maximum deflection but when we use finite element method we use sinx or cosx expansion n solve it. i am getting trouble near this some logic or basic parameter i am missing.

First, you should be aware that the standard beam formulas, like δ = PL³ / 3EI, are only valid when the slopes of the deflected shape are very small. Is a slope of 0.5° small enough for your particular beam? Only you know the answer to that. Certainly, when the slopes increase to 5° or 10°, let alone 80°, linear elastic beam theory no longer applies.

It appears that you are trying to calculate the elastica of this beam, which is how most large-deflection situations are treated.

https://en.wikipedia.org/wiki/Elastica_theory

If you are using finite elements to find such a solution, make sure solving this problem is one which your software can handle. Generally, you would use a non-linear, rather than a linear, FEM.

 

[cvnaditya]

First, you should be aware that the standard beam formulas, like δ = PL³ / 3EI, are only valid when the slopes of the deflected shape are very small. Is a slope of 0.5° small enough for your particular beam? Only you know the answer to that. Certainly, when the slopes increase to 5° or 10°, let alone 80°, linear elastic beam theory no longer applies.

It appears that you are trying to calculate the elastica of this beam, which is how most large-deflection situations are treated.

https://en.wikipedia.org/wiki/Elastica_theory

If you are using finite elements to find such a solution, make sure solving this problem is one which your software can handle. Generally, you would use a non-linear, rather than a linear, FEM.

I am using MATLAB for analysis, and this is my final analysis of the project. unable to get the equation and right method to get the result. Can you help me.

 

[Nidum]

Please post a clear drawing showing all the details of the problem .

 

[cvnaditya]

Please post a clear drawing showing all the details of the problem .

As shown below figure. my cantilever is of two different rigidity modulus. At the end point of the beam, load is applied. As the load increase the beam tends deflects more, where θ value will be from 1° to 80°. i have to use finite element method to solve the problem.

 

[SteamKing]

As shown below figure. my cantilever is of two different rigidity modulus. At the end point of the beam, load is applied. As the load increase the beam tends deflects more, where θ value will be from 1° to 80°. i have to use finite element method to solve the problem.

View attachment 90539

As I mentioned in a previous post, using a linear FEM will probably not get you anywhere. You say you are also using Matlab.

At the bottom of the article linked below, there is a large-deflection theory described for uniform cantilever beams:

https://en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

Having a non-homogeneous beam like you do will only add complexity to the solution.

You can do a web search for more articles which may return hits for analyses which more closely resemble your particular beam.

 

[Hysteresis]

In order to solve this problem use the Euler-Bernoulli principle for simple bending theory, it does also appear from your drawing that you have a "point end load" in oppose to uniformly distributed load.
This does make the answer somewhat easier to interpret