Finite Element newbie question

In summary, the conversation involves a person seeking assistance with implementing boundary conditions in their finite element program. They have successfully built and assembled the GLOBAL stiffness matrix and load vector, but are unsure of how to apply the boundary conditions using the elimination approach. They have found a book on FEM with an algorithm for transient heat conduction using a LUMPED capacity matrix, but are unsure of one step in the algorithm - correcting the nodal heat vector for boundary conditions. They are seeking help and guidance from the community.
  • #1
dinaharchery
24
0
Hello all,

I am trying to create a simple finite element program in C++ and have been able to build and assemble the GLOBAL stiffness matrix as well as the load vector. I want to apply the boundary conditions using the elimination approach, can anyone tell me how to do this?

I am sorry for the simplicity of the problem but I have been unable to find any information on this particular issue. Thanks in advance.
 
Engineering news on Phys.org
  • #2
Well, I figured out the boundary "elimination" approach to the GLOBAL stiffness matrix as well as the vector Load/Heat-Rate:smile: (I finally got a book on FEM)

The book has a section on transient heat conduction using a LUMPED capacity matrix - complete with algorithm. However, there is one step in the algorithm that I am not sure about.

The last step before iterating the time-loop again is to "correct" the just determined nodal heat vector (i.e. solution vector at current time) for boundary conditions. Can anyone please explain what is meant by correcting the solution vector for boundary conditions, I thought the bounds were set-up before entering the Time-Loop?

BTW, the algorithm is explicit forward difference for LUMPED capacity matrix. I really need some help if anyone has a hint?

Thank you
 
  • #3
Anyone?

I just need some kind of hint in the direction to go for the application of boundary corrections at each time step. I am not an engineer but am trying to learn finite element for a program.

Once again, thank you.
 

What is the Finite Element Method and how does it work?

The Finite Element Method (FEM) is a numerical method used to solve complex engineering problems by dividing a continuous domain into smaller finite elements. It uses a system of equations to approximate the behavior of the entire domain, making it easier to analyze and solve complex problems.

What are the advantages of using the Finite Element Method?

The Finite Element Method offers several advantages, including the ability to handle complex geometries, the ability to model physical phenomena with high accuracy, and the ability to analyze a wide range of problems in various engineering disciplines.

What are the limitations of the Finite Element Method?

While the Finite Element Method is a powerful tool, it also has some limitations. These include the need for a high level of expertise to set up and interpret results, the potential for errors due to simplifications and assumptions, and the high computational cost for solving large-scale problems.

What are some common applications of the Finite Element Method?

The Finite Element Method is widely used in various engineering fields, including structural analysis, heat transfer, fluid mechanics, and electromagnetics. It is also applied in other areas such as biomedical engineering, geotechnical engineering, and aerospace engineering.

How can I learn and improve my skills in using the Finite Element Method?

To become proficient in using the Finite Element Method, it is essential to have a strong understanding of the underlying principles and equations. Additionally, practicing on different problems, attending workshops and conferences, and using software and online resources can help improve skills in using this method.

Similar threads

  • Mechanical Engineering
Replies
9
Views
2K
Replies
4
Views
767
Replies
3
Views
812
  • Mechanical Engineering
Replies
2
Views
896
Replies
6
Views
2K
  • Differential Equations
Replies
12
Views
3K
  • Mechanical Engineering
Replies
3
Views
9K
  • Mechanical Engineering
Replies
2
Views
3K
  • Mechanical Engineering
Replies
7
Views
4K
Back
Top