FEM and PDE: Solving a Simple Falling Mass Differential Equation

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Discussion Overview

The discussion revolves around understanding the finite element method (FEM) through the application of a simple differential equation related to a falling mass. Participants explore the relevance of this equation for learning FEM, boundary conditions, and initial conditions, while also expressing interest in more complex problems and nodal analysis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses a desire to understand FEM using the differential equation d²y/dx² = force/mass, emphasizing the need to grasp boundary and initial conditions.
  • Another participant suggests that the falling mass problem is too simple for understanding FEM and mentions its applications in various boundary value problems (BVP) and initial value problems (IVP).
  • There is a request for relevant problems in nodal analysis, indicating a search for practical applications of FEM.
  • A participant points out that the conventional representation of acceleration should be d²y/dt² = F/m = g, noting that the equation can be solved analytically or numerically.
  • One participant seeks a basic explanation of FEM and partial differential equations (PDE), indicating confusion despite having read multiple articles.
  • A later reply challenges the expectation of a comprehensive teaching session, suggesting that specific questions would yield more targeted answers.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the suitability of the falling mass problem for learning FEM, with some arguing it is too simplistic while others believe it can serve as a starting point. The discussion remains unresolved regarding the best approach to understanding FEM and PDE.

Contextual Notes

Participants express varying levels of familiarity with FEM and PDE, indicating a range of assumptions and knowledge gaps. The discussion includes references to both analytical and numerical solutions without resolving the complexities involved in each approach.

Who May Find This Useful

This discussion may be useful for individuals interested in learning about finite element methods, particularly those seeking to understand the application of FEM in solving differential equations and exploring boundary conditions.

chandran
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i want to understand finite element method by solving the simple differential equation of falling mass

d2y/dx2=force/mass

eventhough this equation contains derivative of only one variable i want to understand fem using this

Or some one can give a somemore difficult pde and solve using fem

with this DE how can i understand boundary condition and initial condition. i
 
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FEM is used in various boundary value problems (BVP), and BVP-IVP (initial value problems), both static and dynamic.

The falling mass is a simple one dimensional problem and would be rather poor for understanding FEM.

FEM is used to calculate stresses and strain in various mechanical (static and dynamic) problems, fluid mechanics, computational fluid dynamics, heat transfer problems, and combinations thereof.
 
i want some relevant problem in nodal analysis
 
i want to understand finite element method by solving the simple differential equation of falling mass

d2y/dx2=force/mass
Well, first of all, the convention is to right acceleration as d2y/dt2 = F/m = g. Of course this can be solved analytically, although one could do it numerically.

i want some relevant problem in nodal analysis
Say, Please. :biggrin: Let me see what I can do.

Basically, FEM involves the numerical solution to differential equations (ordinary or partial), and these are generally those equations which are applied to 2D (areas) or 3D (volumes) elements. The boundaries of 2D areas are lines (1D), and the boundaries of volumes are areas (2D).

The key to FEA/FEM is the "mesh discretization of a continuous domain into a set of discrete sub-domains."

Here is some background -
FEA - http://en.wikipedia.org/wiki/Finite_element_analysis

FEM - http://en.wikipedia.org/wiki/Finite_element_method

I work with two guys who were FEM pioneers at Berkeley during the 1960's.
 
can anyone teach me what is fem and pde? i am newbie on it.. I've read so many article about it.. but I'm still confuse.. can anyone give me explanation about it? thanks a lot..
 
So you want someone to teach you a full course? I don't think that's going to happen. Ask specific questions and you will get specific answers.
 

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