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cvnaditya
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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.cvnaditya said:how to solve the large deflection of the beam, i have tried using finite element method but unable to find it.
cvnaditya said: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.
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.SteamKing said: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.
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.Nidum said:Please post a clear drawing showing all the details of the problem .
As I mentioned in a previous post, using a linear FEM will probably not get you anywhere. You say you are also using Matlab.cvnaditya said: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
The deflection of a cantilever beam can be determined using the Euler-Bernoulli beam theory, which takes into account the beam's length, material properties, and applied load. This theory can be solved using mathematical equations or through finite element analysis.
The maximum deflection limit for a cantilever beam is typically defined as the point where the beam becomes unstable or fails. This limit depends on the material, size, and loading conditions of the beam. In general, a maximum deflection limit of 1/1000 of the beam's length is considered acceptable for most applications.
Non-uniform loading can be accounted for by breaking the beam into smaller sections and analyzing each section separately. The deflections of each section can then be summed to determine the overall deflection of the beam. This method is known as the method of superposition and is commonly used in engineering calculations.
The material of the beam plays a significant role in its deflection. A stiffer material, such as steel, will have a smaller deflection compared to a more flexible material, such as wood. The material's Young's modulus, which is a measure of its stiffness, is a key factor in determining the deflection of a cantilever beam.
There are several methods for reducing the deflection of a cantilever beam, including increasing the beam's cross-sectional area, using a stiffer material, or adding supports along the beam's length. Additionally, incorporating structural reinforcements, such as trusses or cables, can help reduce deflection and increase the beam's overall strength.