Solving PDEs via FEM: A Gut Check of the Procedure

Click For Summary
SUMMARY

The discussion focuses on the process of solving Partial Differential Equations (PDEs) using Finite Element Analysis (FEA) and Finite Element Method (FEM). The author, a high school student, seeks to understand the underlying procedures before utilizing software tools for FEA/FEM. They have created a document summarizing their understanding and are requesting feedback to clarify any misconceptions. The discussion emphasizes the importance of grasping the theoretical aspects of FEA/FEM to effectively apply software solutions.

PREREQUISITES
  • Basic understanding of Partial Differential Equations (PDEs)
  • Familiarity with Finite Element Analysis (FEA)
  • Knowledge of Finite Element Method (FEM) principles
  • Proficiency in reading technical documentation
NEXT STEPS
  • Study the theoretical foundations of Finite Element Method (FEM)
  • Explore software tools for FEA, such as ANSYS or COMSOL Multiphysics
  • Learn about mesh generation techniques in FEA
  • Investigate common applications of FEA in engineering problems
USEFUL FOR

This discussion is beneficial for students, engineers, and researchers interested in understanding the principles of Finite Element Analysis and Method, particularly those new to the field or seeking to enhance their theoretical knowledge before applying software tools.

Vanilla Gorilla
Messages
78
Reaction score
24
TL;DR
I want to understand the process computers goes about solving PDES in FEM, and/or how people solve PDES in FEM without the aid of software.
I basically just want to check if my understanding of the method - described in the Google Doc - is correct, before I use software.
Hi, I am a newcomer to FEA/FEM. I am aware that for any practical purpose, software is used to solve problems. However, before I utilize software, I want to understand the process the computer goes about doing. This document is simply an attempt to summarize the solving procedure in a concise manner, according to my understanding. Because I am new, this understanding should have flaws, and I would just like someone to check it over to make sure everything looks right, and/or to clear up some of the confusions I have, which are specified in the document.

https://docs.google.com/document/d/...uKhTJV43hpqS4B30Q/edit#heading=h.d4e1rnx82ic6

I know it's 12 pages, but it's not actually very long to read, most of the pages are taken up by pictures.Any help is much appreciated!
P.S., I'm not always great at articulating my thoughts, so my apologies if this question isn't clear. Also, I know this isn't high school material, but I am currently in high school, which is why I made my level "Basic/high school level."

Note to moderators: I think that is the most appropriate forum for this post. However, if not, apologies, and please feel free to move at your own discretion. :)
 

Similar threads

High School Incorporating boundary conditions in the Finite Element Method (FEM)
  • · Replies 4 ·
Replies
4
Views
3K
Graduate FEM for Solving PDEs: Beginner Textbooks & Fluid Flow
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Deriving the FEA formulation using triangular elements
  • · Replies 2 ·
Replies
2
Views
2K
Discussions about Finite Element Analysis (PDFs)
  • · Replies 15 ·
Replies
15
Views
2K
Engineering Current density calculation in anisotropic ferromagnetic film
  • · Replies 7 ·
Replies
7
Views
2K
Confidence in FEA stress values?
  • · Replies 9 ·
Replies
9
Views
3K
Superposition of loadcases in FEA software (with SPC+inrel)
  • · Replies 1 ·
Replies
1
Views
2K
FEM for Gearbox Design: Key Input Data for Finite Element Method Analysis
  • · Replies 10 ·
Replies
10
Views
7K
High School Solving for the Nth divergence in any coordinate system
  • · Replies 41 ·
2
Replies
41
Views
4K
High School Array Representation Of A General Tensor Question
  • · Replies 2 ·
Replies
2
Views
2K