Project Assignment

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Project Assignment

• Projects can be done individually or in teams of
  no more than two students. Each project can be
  one of two general types of projects
• 1) Perform a finite element simulation of a
  problem for which either an analytical solution
  or experimental data is available. The analysis
  must include a mesh convergence study to verify
  accuracy.
• 2) Code development Develop and validate source
  code using Matlab or other programming language
  to implement some aspect of finite element
  analysis.

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Project Deadlines

• Submit proposal (approx 1-2 pages) via e-mail to
  taggart_at_uri.edu by 3/27. Students submitting
  ideas already submitted will be asked to submit
  an alternate topic. Early submission of ideas is
  therefore encouraged. Proposal shall include 1)
  a brief description of the problem to be solved,
  2) Discussion of background information including
  relevant analytical solutions, experimental data,
  and/or procedure to be implemented (be sure to
  include references) and 3) preferred date of
  presentation.
• Progress reports showing preliminary results,
  modeling questions, etc. are due Thursday 4/9.
  Students are encouraged to see me with project
  questions.
• In-class presentations (including submission of
  Powerpoint presentations) are planned for 4/23
  4/28. Powerpoint presentations will be posted on
  the course web page.
• Project reports are due 4/29 (last day of
  classes). Please submit both hard copy printouts
  and electronic copies (MS Word or pdf) of your
  report. The quiz during finals week will
  include questions related to selected projects.

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Potential Project Topics

• Axial and transverse shear stresses in laminated
  beams plates under bending
• Code development implement a particular element
  formulation in Matlab (or other programming
  language)
• Comparison of available 3-D mesh generation
  algorithms (Abaqus, Cosmos, Hypermesh)
• Comparison of tetrahedral vs. hexahedral element
  performance
• Contact stresses between two cylinders (Hertzian
  contact)
• Elastic-plastic beam bending
• Elastic-plastic torsion
• Evaluation of column buckling formulas using 2-D
  3-D solid elements (Euler / Johnson)

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Potential Project Topics (cont.)

• Evaluation of transverse properties of fiber
  reinforced composites
• Free-edge interlaminar stresses in composite
  laminates
• Heat conduction (steady state or transient)
• Literature review and implementation of a mesh
  generation algorithm
• Study of shear coupling effects in composite
  laminates
• Thermal stress effects
• Torsion of non-circular shafts
• Vibrating string and/or plate
• Wave propagation

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Potential Project Topics (cont.)

• Sources of other project ideas texts on
  Mechanics of Materials (CVE 220), Machine Design
  (MCE 301 / 302), Advanced Mechanics of Materials
  (MCE 426), Mechanics of Composite Materials (MCE
  440), Heat and Mass Transfer (MCE 448)

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Step 4 Derive Element Equations
Chapter 6. Plane Stress / Plane Strain (cont.)
which will be used to derive
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Derive Element Equations (cont.)

• Strain energy

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Derive Element Equations (cont.)

• Potential energy of applied loads

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Derive Element Equations (cont.)

• Potential energy

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Derive Element Equations (cont.)

• Substitute
• to yield

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Derive Element Equations (cont.)

• Apply principle of minimum potential energy
• To obtain

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Derive Element Equations (cont.)

• Element stiffness matrix

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Steps 4-7

• 4. Assemble global equations
• 5. Solve for nodal displacements
• 6. Compute element stresses (constant within each
  element)

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Example CST element stiffness matrix
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CST Element Stiffness Matrix

• where
• B depends on nodal coordinates
• D depends on E, ?
• See text for details

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Body and Surface Forces

• Replace distributed body forces and surface
  tractions with work equivalent concentrated
  forces.

fs
fb
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Work Equivalent Concentrated Forces Body Forces

• For a uniformly distributed body forces Xb and
  Yb

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Work Equivalent Concentrated Forces Surface
Forces
For a uniform surface loading, p, acting on a
vertical edge of length, L, between nodes 1 and
3
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Example 6.2
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Example 6.2 - Solution
Element 2
Element 1