Finite Element Analysis
The theory and practice of finite element analysis: the direct stiffness method, bar, truss, beam and frame elements, energy and Galerkin formulations, triangles, isoparametric quadrilaterals, solids and shells, mesh convergence and singularities, heat transfer, modal analysis, and verification and validation, applied to a heavier-duty pump at a pump manufacturer in Moncton.
MEC-450 Year 4 3 credits 12 lessons · 4 h 23 min ▶ Video lessons coming soon
Offered by HSM University · Mechanical Engineering
This is the Canadian version of this course. See the American version.
What you'll learn
- Explain the finite element workflow from idealization to recovery, assemble spring models by the direct stiffness method, apply supports and recover reactions, and check results for equilibrium.
- Derive and apply bar elements with consistent nodal loads and thermal initial strains, and explain why nodal displacements converge faster than element stresses.
- Analyse plane trusses with transformed bar elements, verify member forces by the method of joints, and recognize what a linear truss model leaves out, including buckling.
- Build beam and plane frame models with Hermite elements, choose appropriate support conditions for shafts and brackets, and interpret nominal stresses and deflections.
- Derive element equations from minimum potential energy and Galerkin's weighted-residual method, and predict how displacement and strain errors fall with element size.
- Choose between plane stress, plane strain and axisymmetric idealizations, formulate the constant-strain triangle and explain shear locking in low-order elements.
- Formulate isoparametric quadrilaterals with Gauss quadrature, interpret the Jacobian, and judge element quality and integration choices.
- Plan and interpret mesh convergence studies with Richardson extrapolation and the grid convergence index, and identify and handle stress singularities.
- Plan three-dimensional solid and shell models with appropriate symmetry, bolt, gasket and contact representations, and bound results with hand calculations.
- Solve steady and transient heat conduction problems with convection by finite elements, and apply temperature fields as loads in thermal stress analysis.
- Form consistent and lumped mass matrices, solve for natural frequencies and mode shapes, and check modal models against hand estimates and tests.
- Verify and validate finite element analyses using benchmarks, manufactured solutions, convergence studies and test data, and document them as a professional engineer's record.
Course content
12 lessons · 4 h 23 min total · final exam
- 1 The finite element method and the direct stiffness approach 25 min · quiz
- 2 Bar elements and assembly 22 min · quiz
- 3 Plane trusses and coordinate transformation 22 min · quiz
- 4 Beam and frame elements 22 min · quiz
- 5 Energy and weighted-residual formulations 21 min · quiz
- 6 Two-dimensional elements: the constant-strain triangle 21 min · quiz
- 7 Isoparametric elements and numerical integration 22 min · quiz
- 8 Meshing, convergence and stress singularities 20 min · quiz
- 9 Solids, shells and practical model building 21 min · quiz
- 10 Heat transfer by finite elements 23 min · quiz
- 11 Dynamics: mass matrices and modal analysis 23 min · quiz
- 12 Verification, validation and the baseplate capstone 21 min · quiz
- E Final exam 20 questions
Requirements
Recommended background. You can start any course at any time.
Description
The theory and practice of finite element analysis: the direct stiffness method, bar, truss, beam and frame elements, energy and Galerkin formulations, triangles, isoparametric quadrilaterals, solids and shells, mesh convergence and singularities, heat transfer, modal analysis, and verification and validation, applied to a heavier-duty pump at a pump manufacturer in Moncton.
Part of the Engineering stream, typically taken in year 4.