Finite element analysis node displacement

In summary: There are a few reasons why we use polynomial functions to estimate the displacement of the center of an element. The first reason is that these functions are easy to calculate. Polynomial functions involve only the displacement at the nodes, so they are very efficient in terms of computation. Additionally, these functions are consistent with the physical experiment that we are trying to model. If we were to use another function to estimate the center of an element, the results would likely be inaccurate.The second reason is that these functions are accurate. Polynomial functions are able to accurately model the physical phenomenon involved in the displacement of the center of an element. Other functions might not be able to do this as accurately.The third reason
  • #1
mertcan
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upload_2017-12-15_10-16-38.png


Hi, I would like to ask why center of element displacement is always estimated with polynomial equation involving nodes displacement (like in attachment/picture)? Also I know that if nodes' number increase for an element then displacement of center of element is estimated with higher order polynomial, why do we always include polynomial equation to estimate center of element?? why don't we use logarithmic or exponential function or other kind of function to model the displacement of center of element?? Does the application of polynomial equation to estimate the displacement of center of element give better real results ?? if it gives then why ??
 

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  • #2
Hi everyone I have been waiting for 2 days but nobody has responded to my question is there a in comprehensible situation in thread?
 
  • #3
My FEA is a bit rusty so maybe others will have to chime into confirm or deny what I'm saying, but I'm replying for the sake of starting the discussion.

In classical finite element theory (really the Galerkin method), we discretize the geometry by placing nodes and connecting them with elements. We are calculating the displacement of the nodes under certain boundary conditions and elements are there to restrict the nodes to be displaced consistent with physical experiment. In the end, the only result we get back are the displacement at the nodes. We have to interpolate to get the displacement at what we're calling the center of the element. In your above image, this just looks like a formulation of a point in barycentric coordinates. I think the exact formulation for interpolation needs to be consistent with the basis functions used for the FEA calculation.

(Note for FEA gurus: this is a really simplistic explanation and not intended to be thorough, so be gentle when ripping this apart :-) )
 
  • #4
thanks for return @timthereaper , but whenever I want to learn how the center of element displacement is estimated what I see is always it is estimated involving polynomial functions not other functions, so I am really eager to know why only polynomial function is used?
 

FAQ: Finite element analysis node displacement

1. What is finite element analysis (FEA) node displacement?

Finite element analysis node displacement is a numerical method used to solve engineering problems by dividing a larger system into smaller, more manageable elements. It calculates the displacement of each node in the system, allowing engineers to analyze stress, strain, and other properties of the system under different conditions.

2. How is FEA node displacement calculated?

FEA node displacement is calculated using mathematical equations and algorithms that take into account the properties and behavior of the system's elements. These equations are solved iteratively to determine the displacement of each node in the system.

3. What factors can affect FEA node displacement?

There are several factors that can affect FEA node displacement, including the type and properties of the elements used, the boundary conditions applied, and the loading conditions on the system. The accuracy of the material properties and the mesh density can also impact the results.

4. How is FEA node displacement used in engineering?

FEA node displacement is commonly used in engineering to analyze the behavior of complex systems and structures. It can be used to predict stresses, strains, and deformations in a variety of applications such as structural design, heat transfer, fluid flow, and more. It allows engineers to optimize designs and identify potential failure points before physical prototypes are built.

5. What are the advantages of using FEA node displacement?

FEA node displacement offers several advantages over traditional analytical methods, including the ability to handle complex geometries and material properties. It also allows for more accurate and detailed analysis of systems, leading to improved designs and cost savings. Additionally, FEA node displacement can be easily integrated with computer-aided design (CAD) software, making it a powerful tool for modern engineering design and analysis.

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