FEM and PDE: Solving a Simple Falling Mass Differential Equation

In summary, the conversation discusses the desire to understand finite element method (FEM) by solving a simple differential equation of a falling mass. The equation is d2y/dx2=force/mass and the goal is to gain a better understanding of FEM using this equation. The conversation also touches on the use of FEM in various boundary value problems and initial value problems. The conversation then shifts to discussing the relevance of nodal analysis and the basics of FEA and FEM. The conversation ends with the suggestion to ask specific questions in order to gain a better understanding of FEM and PDE.
  • #1
chandran
139
1
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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  • #2
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.
 
  • #3
i want some relevant problem in nodal analysis
 
  • #4
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.
 
  • #5
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..
 
  • #6
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.
 

1. What is a PDE?

A PDE (partial differential equation) is a mathematical equation that involves multiple independent variables and their partial derivatives. It is commonly used to model physical systems in fields such as physics, engineering, and finance.

2. What is FEM?

FEM (finite element method) is a numerical technique used to solve PDEs by dividing the domain into smaller elements. These elements are then approximated using simpler functions, making it easier to solve the equation and obtain a numerical solution.

3. How are PDEs and FEM used in real-world applications?

PDEs and FEM are used in a wide range of real-world applications, such as predicting weather patterns, designing structures and buildings, simulating fluid flow, and analyzing financial markets. They allow scientists and engineers to model complex systems and make predictions about their behavior.

4. What is a simple example of PDE and FEM?

A simple example of PDE and FEM is the heat equation, which describes the distribution of heat in a given space over time. FEM can be used to solve this equation by dividing the space into smaller elements and approximating the temperature at each point. This allows us to predict how the temperature will change over time.

5. What are the advantages of using FEM to solve PDEs?

FEM has several advantages over other methods of solving PDEs. It can handle complex geometries and boundary conditions, it can provide accurate solutions with a relatively small number of elements, and it can easily incorporate different types of physical phenomena into the same model. Additionally, FEM is a versatile tool that can be applied to a wide range of problems in various fields.

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