Explicit Finite difference scheme on spreadsheet

In summary, the conversation is about a problem involving a steel bar being struck by a heavy mass, causing a compression wave to travel through it. The density and elasticity of the bar are given, and the person is asking for guidance on how to solve the problem using a spreadsheet with specific time steps. They are also seeking clarification on the boundary conditions at the two ends of the bar.
  • #1
seraphi
1
0
I know this is really stupid and it looks like i haven't tried at all but i am genuinely confused about this so any guidance at all would help big time. so here is the question.


A steel bar, 70mm long is struck at one end by a heavy mass moving at 20m/s. The impact causes a compression wave to travel to the end of the bar whihc is kept fixeed. density of bar is 7900kg/m and E=200Gpa.

a)what are boundary consitions at the two ends.

b)construct a spreadsheet to solve problem using explicit FD scheme with 8 nodes. time step= 1E-6s. plot results for displacement w at times t=1E-5s and t=2E-5s.


I assume the boundary conditions to be 20 and 0 but the problem for me is what exactly do i program each cell to do.
 
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  • #2
Hi i know this is an answer to your question, but i was just wondering, which university do you go to?
 

1. What is an explicit finite difference scheme on spreadsheet?

An explicit finite difference scheme on spreadsheet is a numerical method used to solve partial differential equations on a spreadsheet. It involves discretizing the equation into smaller time and space intervals, and then using a set of finite difference equations to approximate the solution at each point in the grid. The explicit part refers to the fact that the solution at each point is only dependent on the values at previous time steps.

2. What are the advantages of using a spreadsheet for explicit finite difference schemes?

One advantage of using a spreadsheet for explicit finite difference schemes is that it allows for easy visualization of the solution. The grid can be easily represented as cells in the spreadsheet, and the values at each point can be easily updated and tracked. Additionally, spreadsheets have built-in functions and tools that can be used to perform calculations and analyze the solution.

3. What types of problems can be solved using explicit finite difference schemes on spreadsheet?

Explicit finite difference schemes on spreadsheet can be used to solve a variety of problems in fields such as physics, engineering, and finance. Some examples include heat conduction, diffusion, and option pricing. Essentially, any problem that can be described by a partial differential equation can be solved using this method.

4. What are the limitations of using explicit finite difference schemes on spreadsheet?

One limitation of using explicit finite difference schemes on spreadsheet is that it can be computationally expensive for problems with a large number of grid points. This is because the calculations for each time step depend on the values at previous time steps, and the spreadsheet may need to be recalculated for each time step. Additionally, the accuracy of the solution may be affected by the size of the time and space intervals used.

5. Are there any alternatives to using explicit finite difference schemes on spreadsheet?

Yes, there are other numerical methods that can be used to solve partial differential equations, such as implicit finite difference schemes and finite element methods. These methods may have different advantages and limitations compared to explicit finite difference schemes on spreadsheet, and the choice of method will depend on the specific problem being solved.

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