Computational Techniques in Mechanics and Bioengineering

Semester 1, 2020

Staff

- Justin Fernandez (director, coordinator)
- Samuel Rosset

Calendar notes

Theoretical and applied finite element and boundary element methods for static and time dependent problems of heat flow, bioelectricity, linear elasticity and non-linear mechanics.

Prerequisite: ENGGEN 131 or equivalent, and 15 points from ENGSCI 311, 313, 314

## Intended learning outcomes |
## Related graduate attributes |
## Related assessments |
---|---|---|

Boundary Element Methods: Integration: Calculation of Cauchy Principal Values; Development of the C computer code to numerically calculate integrals using variable order normal and logarithmic Gaussian quadrature schemes; Development of the C computer code to use element splitting methods to evaluating weakly singular integrals; Development of the C computer code to use row-sums to evaluate strongly singlar integrals. |
ENGA01: engineering knowledge (4) ENGA02: problem analysis (4) ENGA03: design and solution development (0) ENGA04: investigation (0) ENGA05: modern tool usage (4) ENGK01: theory of natural sciences (1) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) ENGK04: specialist knowledge (0) ENGK05: engineering design (0) ENGK06: engineering practice (0) ENGP01: depth of knowledge required (0) ENGP03: depth of analysis required (0) ENGP05: extent of applicable codes (0) UOA_1: Disciplinary Knowledge and Practice (3) UOA_2: Critical Thinking (2) |
No related assessments |

Boundary Element Methods: Comparison and Coupling with the Finite Element Method: Comparision and assessment of wether the Boundary Element or Finite Element method would be appropriate for a particular modelling situation; Use of the developed C program to solve the same problem in the FEM project with BEM. Evaulation and comparison of the results. |
ENGA01: engineering knowledge (4) ENGA02: problem analysis (4) ENGA03: design and solution development (0) ENGA05: modern tool usage (4) ENGA09: individual and team work (0) ENGA12: lifelong learning (0) ENGK01: theory of natural sciences (1) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) ENGK04: specialist knowledge (0) ENGK05: engineering design (0) ENGK06: engineering practice (0) ENGK08: research literature (0) ENGP01: depth of knowledge required (0) ENGP03: depth of analysis required (0) UOA_1: Disciplinary Knowledge and Practice (3) UOA_2: Critical Thinking (2) UOA_3: Solution Seeking (2) |
No related assessments |

Static linear elasticity: Construct FEM equations from first principles for 1D, small-strain static elasticity problems, including varying material properties and cross-sections. Use beam theory to formulate a FEM analysis for beam bending, including explanations of the assumptions made, the basis function type chosen, and the boundary conditions needed. |
ENGA01: engineering knowledge (4) ENGA02: problem analysis (4) ENGA03: design and solution development (0) ENGA05: modern tool usage (4) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) ENGK05: engineering design (0) ENGP07: interdependence (1) UOA_3: Solution Seeking (2) |
No related assessments |

Boundary Element Methods: Green's functions: Derivation of adjoint operators; Derivation of the freespace Green's function for Laplace's equation in 2 and 3 dimensions. |
ENGA01: engineering knowledge (4) ENGK01: theory of natural sciences (1) ENGK02: mathematical modelling (4) ENGP01: depth of knowledge required (0) UOA_1: Disciplinary Knowledge and Practice (3) |
No related assessments |

Basis functions: Derive basis functions for a given element, including 1D, 2D quadrilaterals as well as 2D linear and quadratic triangular elements, apply them to interpolation and FEM problems, formulate computer code in C for their application within FEM code |
ENGA05: modern tool usage (4) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) UOA_1: Disciplinary Knowledge and Practice (3) UOA_3: Solution Seeking (2) |
No related assessments |

Boundary Element Methods: Application and Numerics: Derive the boundary element system of equations Au = Bq for Laplace's equation in 2 and 3 dimensions; Development of a C computer program to solve Laplace's equation in 2 dimensions; Use of the developed computer program to calculate a domain solution. |
ENGA01: engineering knowledge (4) ENGA03: design and solution development (0) ENGA05: modern tool usage (4) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) ENGK04: specialist knowledge (0) ENGK08: research literature (0) ENGP05: extent of applicable codes (0) UOA_1: Disciplinary Knowledge and Practice (3) UOA_2: Critical Thinking (2) |
No related assessments |

Boundary Element Methods: Boundary Integral Equations: Derive the boundary integral equation for Laplace's equation in 2 and 3 dimensions. |
ENGA01: engineering knowledge (4) ENGK01: theory of natural sciences (1) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) ENGK04: specialist knowledge (0) UOA_1: Disciplinary Knowledge and Practice (3) |
No related assessments |

Boundary Element Methods: Linear elasticity and other equations: Describe the pro's and con's on using the Boundary Element Method for Linear Elasticity. |
ENGA02: problem analysis (4) ENGA05: modern tool usage (4) ENGK01: theory of natural sciences (1) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) ENGK04: specialist knowledge (0) ENGP01: depth of knowledge required (0) UOA_1: Disciplinary Knowledge and Practice (3) UOA_2: Critical Thinking (2) |
No related assessments |

Computational assembly of FEM algorithms: Reformulate governing equations in terms of appropriate matrices for the creation of a linear system to solve an FEM problem, include appropriate boundary conditions, describe the sources of error and convert the theory into C functions. |
ENGA05: modern tool usage (4) ENGK02: mathematical modelling (4) UOA_1: Disciplinary Knowledge and Practice (3) UOA_3: Solution Seeking (2) |
No related assessments |

Finite Elements for Time Dependent Problems: Students will be able to demonstrate comprehension of Partial Differential Equations (PDEs) by recognising and classifying various PDE's. Students will be able to demonstrate their ability to apply PDE theory by deriving PDE's for some elementary engineering problems. Students will be able to demonstrate their ability to apply the FEM to solve PDE's by working through ab initio from a time-dependent PDE and deriving the FEM equations. |
ENGA01: engineering knowledge (4) ENGA02: problem analysis (4) ENGK02: mathematical modelling (4) ENGK08: research literature (0) |
No related assessments |

Finite Elements for non Linear problems: Students will be able to demonstrate their proficiency with basis functions, Finite Element analysis and non-linear analysis as follows: they will be presented with a non-linear partial differential equation and they will be able to work through the FEM analysis, reducing the equation to a system of non-linear algebraic equations, which can then be solved approximately using the Newton-Raphson algorithm. |
ENGA01: engineering knowledge (4) ENGA02: problem analysis (4) ENGK02: mathematical modelling (4) UOA_2: Critical Thinking (2) UOA_3: Solution Seeking (2) UOA_5: Independence and Integrity (1) |
No related assessments |

Boundary Element Methods: Integration: Calculation of Cauchy Principal Values; Development of the C computer code to numerically calculate integrals using variable order normal and logarithmic Gaussian quadrature schemes; Development of the C computer code to use element splitting methods to evaluating weakly singular integrals; Development of the C computer code to use row-sums to evaluate strongly singlar integrals. |
ENGA01: engineering knowledge (4) ENGA05: modern tool usage (4) ENGK01: theory of natural sciences (1) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) ENGK08: research literature (0) ENGP01: depth of knowledge required (0) UOA_1: Disciplinary Knowledge and Practice (3) |
No related assessments |

Boundary Element Methods: Comparison and Coupling with the Finite Element Method: Comparision and assessment of wether the Boundary Element or Finite Element method would be appropriate for a particular modelling situation; Use of the developed C program to solve the same problem in the FEM project with BEM. Evaulation and comparison of the results. |
ENGA01: engineering knowledge (4) ENGA02: problem analysis (4) ENGA03: design and solution development (0) ENGA04: investigation (0) ENGA05: modern tool usage (4) ENGK01: theory of natural sciences (1) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) ENGK08: research literature (0) ENGP05: extent of applicable codes (0) UOA_1: Disciplinary Knowledge and Practice (3) UOA_2: Critical Thinking (2) |
No related assessments |

Static linear elasticity: Construct FEM equations from first principles for 1D, small-strain static elasticity problems, including varying material properties and cross-sections. Use beam theory to formulate a FEM analysis for beam bending, including explanations of the assumptions made, the basis function type chosen, and the boundary conditions needed. |
ENGA01: engineering knowledge (4) ENGA02: problem analysis (4) ENGA03: design and solution development (0) ENGK02: mathematical modelling (4) ENGP07: interdependence (1) UOA_1: Disciplinary Knowledge and Practice (3) |
No related assessments |

Boundary Element Methods: Green's functions: Derivation of adjoint operators; Derivation of the freespace Green's function for Laplace's equation in 2 and 3 dimensions. |
ENGA01: engineering knowledge (4) ENGA05: modern tool usage (4) ENGK01: theory of natural sciences (1) ENGK02: mathematical modelling (4) ENGK04: specialist knowledge (0) ENGK08: research literature (0) ENGP01: depth of knowledge required (0) UOA_1: Disciplinary Knowledge and Practice (3) |
No related assessments |

Basis functions: Derive basis functions for a given element, including 1D, 2D quadrilaterals as well as 2D linear and quadratic triangular elements, apply them to interpolation and FEM problems, formulate computer code in C for their application within FEM code |
ENGA05: modern tool usage (4) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) UOA_1: Disciplinary Knowledge and Practice (3) UOA_3: Solution Seeking (2) |
No related assessments |

Boundary Element Methods: Application and Numerics: Derive the boundary element system of equations Au = Bq for Laplace's equation in 2 and 3 dimensions; Development of a C computer program to solve Laplace's equation in 2 dimensions; Use of the developed computer program to calculate a domain solution. |
ENGA01: engineering knowledge (4) ENGA02: problem analysis (4) ENGA03: design and solution development (0) ENGA04: investigation (0) ENGA05: modern tool usage (4) ENGK01: theory of natural sciences (1) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) ENGK04: specialist knowledge (0) ENGK08: research literature (0) ENGP01: depth of knowledge required (0) UOA_1: Disciplinary Knowledge and Practice (3) UOA_2: Critical Thinking (2) |
No related assessments |

Boundary Element Methods: Boundary Integral Equations: Derive the boundary integral equation for Laplace's equation in 2 and 3 dimensions. |
ENGA01: engineering knowledge (4) ENGA05: modern tool usage (4) ENGK01: theory of natural sciences (1) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) ENGK04: specialist knowledge (0) ENGK08: research literature (0) ENGP01: depth of knowledge required (0) UOA_1: Disciplinary Knowledge and Practice (3) UOA_2: Critical Thinking (2) |
No related assessments |

Boundary Element Methods: Linear elasticity and other equations: Describe the pro's and con's on using the Boundary Element Method for Linear Elasticity. |
ENGA01: engineering knowledge (4) ENGA02: problem analysis (4) ENGA05: modern tool usage (4) ENGK01: theory of natural sciences (1) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) ENGK04: specialist knowledge (0) ENGK08: research literature (0) ENGP01: depth of knowledge required (0) ENGP05: extent of applicable codes (0) UOA_1: Disciplinary Knowledge and Practice (3) UOA_2: Critical Thinking (2) |
No related assessments |

Computational assembly of FEM algorithms: Reformulate governing equations in terms of appropriate matrices for the creation of a linear system to solve an FEM problem, include appropriate boundary conditions, describe the sources of error and convert the theory into C functions. |
ENGA05: modern tool usage (4) ENGK02: mathematical modelling (4) UOA_1: Disciplinary Knowledge and Practice (3) UOA_3: Solution Seeking (2) |
No related assessments |

Finite Elements for Time Dependent Problems: Students will be able to demonstrate comprehension of Partial Differential Equations (PDEs) by recognising and classifying various PDE's. Students will be able to demonstrate their ability to apply PDE theory by deriving PDE's for some elementary engineering problems. Students will be able to demonstrate their ability to apply the FEM to solve PDE's by working through ab initio from a time-dependent PDE and deriving the FEM equations. |
ENGA01: engineering knowledge (4) ENGA02: problem analysis (4) ENGK02: mathematical modelling (4) |
No related assessments |

Boundary Element Methods: Integration: Calculation of Cauchy Principal Values; Development of the C computer code to numerically calculate integrals using variable order normal and logarithmic Gaussian quadrature schemes; Development of the C computer code to use element splitting methods to evaluating weakly singular integrals; Development of the C computer code to use row-sums to evaluate strongly singlar integrals. |
No related attributes |
No related assessments |

Static linear elasticity: Construct FEM equations from first principles for 1D, small-strain static elasticity problems, including varying material properties and cross-sections. Use beam theory to formulate a FEM analysis for beam bending, including explanations of the assumptions made, the basis function type chosen, and the boundary conditions needed. |
No related attributes |
No related assessments |

Basis functions: Derive basis functions for a given element, including 1D, 2D quadrilaterals as well as 2D linear and quadratic triangular elements, apply them to interpolation and FEM problems, formulate computer code in C for their application within FEM code |
ENGA05: modern tool usage (4) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (4) UOA_1: Disciplinary Knowledge and Practice (3) UOA_3: Solution Seeking (2) |
No related assessments |

Computational assembly of FEM algorithms: Reformulate governing equations in terms of appropriate matrices for the creation of a linear system to solve an FEM problem, include appropriate boundary conditions, describe the sources of error and convert the theory into C functions. |
ENGA05: modern tool usage (4) ENGK02: mathematical modelling (4) UOA_1: Disciplinary Knowledge and Practice (3) UOA_3: Solution Seeking (2) |
No related assessments |

Coursework

No description given

Exam rules

No description given

Inclusive learning

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Other assessment rules

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