BVPs留学生辅导、讲解Electronic留学生、辅导Python程序设计、Python编程语言调试
辅导R语言程序|调试Matlab程序
April 5, 2019
Assignment Ten: BVPs
Assigned: 5 April Submission: Electronic
Due Date: 19 April Collaboration Type: Individual
Due Time: before 11:59 pm Grading: 50 points
Assignment Purpose:
The purpose of this assignment is to help further your understanding in how to
solve ordinary differential equations (ODEs) posed as boundary value problems
(BVPs). Most physical laws are expressed in terms of ODEs, and many are solved
over a spatial domain with conditions specified along its boundaries; consequently,
this type of problem pervades engineering applications, e.g., finite elements.
Submission Instructions: Electronic submission only. Create a zip archive
containing all your py-files and pdf documents, as appropriate, and submit the
archive via your eCampus homework link. Right next to the SUBMIT button is a
SAVE DRAFT button. You can save a draft as many times as you like. Once it
is in a form you want, then submit it. If you find your submission to be wanting,
for some reason or another, a second submission is permitted, but no more than
that. If there are two submissions, we will only grade the second submission. Use
the following naming convention: A10_Spring_2019_lastName_firstName.zip.
Please do not use nick names, as it can at times become difficult to discern who to
assign the grade to. FAILURE TO USE THIS FILE NAMING CONVENTION
WILL RESULT IN YOU RECEIVING HALF CREDIT.
Submission Note: Submit the solutions to all non-Python program problems as
pdf files, e.g., as exported from a document editor like Microsoft Office, Apple
iWorks, Linux Libre Office, a.k.a. Open Office, LaTeX, etc.
Submission Note: Not all versions of doc and docx files can be read by someone
else’s particular version of Word, which is why only pdf files are accepted.
Submission Note: pdf documents made from scanned hand-written answers will
receive half their otherwise earned points.April 5, 2019
Grading Policy: All Python programs that you write for this homework
assignment will be graded using a grading script written by your professor that
your TA will execute. This grading script will run the software that you write.
How your code executes will determine your grade.
Grading Note: You will receive 0 points for this assignment if your submission is
late by more than a week, loosing 15% per day late as determined by the time
stamp that eCampus assigns to your file upon its submission. Being 1 second late
equates with being 1 day late. Being a day late may be a better option than not
completing a task altogether.
Script File Format:
In the various tasks for this homework assignment you will be asked to write script
files that run (i.e., execute) your programs. The script file that you write, viz.,
a10task1.py, will contain a procedure with the following basic format:
# any imports you use
def runTask<#>():
# execute the problem assigned in task <#>
# print to the command window in Spyder the requested results in
# the requested format, including figures
runTask<#>():
Any functions that you create, which are to be used by your script file(s), are to be
cited/used through imports into your script file(s). Do not forget to include these
function files in your list of files that you zip up as an archive for submission.
For the most part, naming conventions for your imported functions are not strictly
enforced (unless stated otherwise); however, naming conventions for your script
files are strictly enforced. As a rule of thumb, if the grading script has to call
something that you write, then the naming convention must be strictly adhered to.April 5, 2019
Grading your Source and Script Files:
There is only one task for which files are to be supplied for this homework
assignment that will be run by the Grader. Points will be assigned accordingly (36
of 50 points):
36 pts) File/script executes, answers are correct, printout is in the
correct format
27 pts) File/script executes, answers are correct, printout is NOT in
the correct format
18 pts) File/script executes, at least one answer is NOT correct,
printout is in the correct format
9 pts) File/script executes, at least one answer is NOT correct,
printout is NOT in correct format
0 pts) File/script does NOT execute
Visual inspection of the code (14 of 50 points):
14 pts off) If you solve the problem using a method other than as
assigned.
8 pts off) If there are any error symbols (bullets) in the editor.
6 pts off) If you do not incorporate reasonable comment statements into
your code.
4 pts off) If there are any ‘style’ errors (yellow triangles) in the editor.
2 pts off) If you use cryptic variable names (a judgment call)
else Full creditApril 5, 2019
In this homework you will be analyzing the following beam problem.
Here x and y form your coordinate frame. The beam has a length L and is made of
a material whose Young’s modulus is E with a geometry that has a moment of
inertia I. The beam is subjected to an uniformly distributed loading of q and an
axial compression loading of p. The beam is simply supported.
The differential equation that governs this boundary value problem is
which you can use to verify your software.April 5, 2019
Task 1:
Write a solver that uses a finite difference engine to solve for the deflection of this
beam, i.e., y (x). This solver is to have an interface of
runTask1(EI, L, p, q, nodes)
and is to be called as
x, y = runTask1(EI, L, p, q, nodes)
where EI is the product of a Young’s modulus E with a moment of inertia I, L is
the length of the simply support beam, p is the compressive force, q is the
distributed loading, and nodes is the number of integration nodes (there will be
nodes–1 intervals of integration) that the algorithm is to employ when solving from
0 to L. The returned values x and y are arrays of length nodes that contain the
displacements y[i] at locations x[i], i = 0 .. nodes-1.
Note: Error will diminish with increasing numbers of nodes. Running analyses
with different nodal densities allows one to study the convergence properties of a
solver, which is an import topic when seeking reliable numerical solutions.
Submit this script as file a10task1.py