University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM Coming Up... ASEN 6367 Term Projects Following Slides Outline Basic Rules, To be Posted Also on Course Website

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM ASEN 6367 Term Projects - Advanced FEM- Spring 2013 Group Composition Each term project should involve two (best) or (at most) three students. Teams of more than three are discouraged because workload distribution tends to get skewed. A project may also be carried out by a single, bright, hardworking but reclusive individual. Forming teams is primarily the responsibility of the students, but instructor can help. Teams may coordinate work by comparing results in related projects. Project groups need not be same as HW groups.

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM ASEN 6367 Term Projects - Advanced FEM- Spring 2013 Topic Submission Projects may be proposed by students or taken from the potential subjects list posted on web site. Project topics should be communicated to instructor by Tuesday class after Spring Break. submission OK. The description should name the participating students, project title, and one sentence that identifies the subject. Project rosters will be periodically handed out to class for verification.

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM ASEN 6367 Term Projects - Advanced FEM- Spring 2013 Topic Selection Projects should be related to the subject matter of the course as a starting point. Subjects involving nonstructural analysis (e.g., heat transfer or fluid mechanics), nonlinear structural analysis or structural dynamics & vibration are acceptable if proposers have had prior or collateral experience with such subjects; for example in ongoing thesis work. But in any case the subject must involve finite elements.

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM ASEN 6367 Term Projects - Advanced FEM- Spring 2013 Computer Programming Tools Instructor supplied programs may be modified or extended to meet the goals of a project. Use of Matlab may be more effective, however, to get quick numerical answers and produce graphical results. Use of computer algebra tools such as Mathematica is encouraged as help for analytically oriented projects that involve heavy algebraic manipulations.

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM ASEN 6367 Term Projects - Advanced FEM- Spring 2013 Instructor Help Instructor is available throughout the project timespan for technical discussion in his areas of expertise. Literature that may help with the work will be supplied on request to group if available to instructor. References to material on Web or in a CU Library may be also provided on request.

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM ASEN 6367 Term Projects - Advanced FEM- Spring 2013 Outcome A project does not have to be successful. However, participants should give it a serious try. Negative conclusions may be as valuable as positive ones. For example: of the six 2011 projects, only two were moderately successful. But all groups (except one) tried. Success rate seems to be going down since 1989 :-(

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM ASEN 6367 Term Projects - Advanced FEM- Spring 2013 Presentations Two presentations are required for each project. A 15-20’ in-progress presentation during the week of classes April These may be at class time (in this classroom) or outside it, depending on # of projects. They do not have to be on the same day. A 30-40' final presentation during the last week of classes April 29-May 3. May be done at class time or outside it, depending on the number of projects. A different classroom or conf room might be used off-class-hours if necessary. Multiperson teams chose a presenter or may time-share a presentation.

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM ASEN 6367 Term Projects - Advanced FEM- Spring 2013 Final Report Due Final reports in PDF are due on Wednesday May 8 by noon. They should be ed to by that deadline. The report should describe: objectives, formulation, implementation, results and conclusions. It should contain appropriate references to any literature used. The report should include a listing of key software developed to obtain results (example: an element formation module), but not generic software supplied by instructor or auxiliary software such as pre- or postprocessors written as part of the project.

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM ASEN 6367 Term Projects - Advanced FEM- Spring 2013 Project Result Posting Reports will be posted on the course web site, along with abstracts & presentation material, if files are of reasonable size. Project material for selective previous course offerings is available on the course web site.

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM Spring 2011 Possible Topics (To Be Updated) 1. Develop a 4-node quadrilateral elements for axisymmetric solids that perform better in bending than the standard iso-P 4-node quadrilateral element Quad4 (That is, has less shear locking.) Methods to be considered: Selective Reduced Integration (SRI) and Hellinger-Reissner. Compare with Quad4 and Quad8 on thin circular plates and axisymmetric shell benchmarks. Flavor: Analytical + computational. Symbolic computations required for SRI model. Requirements: medium programming ability, some physical insight 2. Develop an optimal mass matrix for the triangular membrane element with corner drilling freedoms. Flavor: Analytical + computational (heavy symbolic) Requirements: knowledge of computational dynamics & wave dispersion analysis. 3. Extend QuadSOR to do harmonic Fourier analysis in the circumferential direction. Test using a lateral point load on spherical shell moving it from pole to equator. Flavor: Computational (mostly numerical). Requirement: ability to do Fourier analysis in cylindrical coordinates, programming ability. 4. Modify QuadSOR to do thin shells of revolution. Flavor: Analytical + computational. Requirement: above average programming ability on a CAS.

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM Spring 2011 Possible Topics (cont’d) 5. Extend the shell element with 24 DOF to a stack element (using MFCs to represent offset links) for composite material analysis. Flavor: analytical + computational Requirement: understanding of MFCs, good programming ability, some physical insight 6. Develop a template for the 8-node solid brick element. Investigate optimal selection of higher order stiffness matrix for the rectangular geometry, using bending benchmarks. Flavor: Analytical + computational (mostly symbolic) Requirement: above average programming ability on a CAS. 7. Develop a template for the a triangular Kirchhoff plate bending element with 12 degrees of freedom: 9 corner freedoms and 3 midside rotations. Flavor: heavy symbolic computation. Requirement: above average ability in matrix algebra and symbolic computation. 8. Develop a template for the a quadrilateral Kirchhoff plate bending element with 12 degrees of freedom: 3 per corner. Flavor: heavy symbolic computation. Requirement: above average ability in matrix algebra and symbolic computation

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM

Curved Tets (e.g., Tet-10) Are Becoming Popular In Visualization

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM For Example, In Biomedical Imaging Fig 79. Iso-surface visualization from a deformed CT data set. A tetrahedral simulation mesh was adaptively refined along the surface and bone structures in the 3D medical data set. This mesh contains 1.1M tetrahedra Joachim Georgii, Rudiger Westermann A multigrid framework for real time simulation of deformable bodies Computers & Graphics, Vol 30, Issue 3,

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM Another Emerging Application: Dentistry

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM

Hex Elements Are Preferred For Regular Configurations As Well As Hand-Built Meshes

University of Colorado - Dept of Aerospace Engineering Sciences - ASEN 6367: Advanced FEM