Problem 2779. Rule of mixtures (composites) - weighted bound

Created by goc3

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Rule_of_mixtures\"><w:r><w:t>rule of mixtures</w:t></w:r></w:hyperlink><w:r><w:t> is used in the mechanical design of composite structures to estimate the elastic modulus (Ec) based on the following properties:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Ef: elastic modulus of the fiber material</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Em: elastic modulus of the matrix material</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>ff or fm: volume fraction of the fiber or matrix material (ff = 1 – fm)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Based on these values, the lower-bound estimate of elastic modulus is calculated by:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Ec = 1 / (ff / Ef + (1 – ff) / Em).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>On the other hand, the upper-bound (linear) estimate of elastic modulus is calculated by:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Ec = ff * Ef + (1 – ff) * Em.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Write a function to calculate the weighted Ec between both bounds, based on the provided weighting (wt) of the upper bound. (The lower bound will have the remainder of the weighting, or 1–wt.)</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

73 Solutions
47 Solvers

Last Solution submitted on Sep 22, 2023

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers47

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 2779. Rule of mixtures (composites) - weighted bound

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers47

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Problem 2779. Rule of mixtures (composites) - weighted bound

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers47

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Players