Explicit Finite difference scheme on spreadsheet

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SUMMARY

The discussion focuses on implementing an explicit finite difference scheme on a spreadsheet to analyze the behavior of a steel bar subjected to a compression wave. The steel bar is 70mm long, with a density of 7900 kg/m³ and Young's modulus (E) of 200 GPa. Participants address the boundary conditions, which are identified as fixed at one end and free at the other, and provide guidance on constructing a spreadsheet model with 8 nodes and a time step of 1E-6 seconds to plot displacement results at specified times.

PREREQUISITES
  • Understanding of explicit finite difference methods
  • Familiarity with spreadsheet software (e.g., Microsoft Excel)
  • Knowledge of wave propagation in materials
  • Basic principles of mechanics and material properties (density, Young's modulus)
NEXT STEPS
  • Learn how to implement explicit finite difference schemes in spreadsheets
  • Research boundary conditions in wave propagation problems
  • Explore plotting techniques for displacement over time in spreadsheet software
  • Study the effects of varying time steps on numerical stability and accuracy
USEFUL FOR

Students and professionals in engineering, particularly those focusing on mechanical or civil engineering, as well as anyone interested in numerical methods for solving wave propagation problems.

seraphi
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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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Hi i know this is an answer to your question, but i was just wondering, which university do you go to?
 

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