Upon completion of the course the students must have comprehended the basic principles of the Finite Element Method and apply it to the solution of common practical problems in mechanical components and structures (emphasizing in the automotive, aviation, elevator industries, etc.) using modern programing languages. They must be able to evaluate the results obtained in order to help the design process.
In particular, the student must be able to:
1. Define the boundary conditions of common practical problems, focusing on the design details at hand and the operational condition of the component/structure in order to achieve an accurate as possible simulation
2. Evaluate various analysis scenarios (mesh size, element type and order, boundary conditions, solution type, etc.) in order to select the optimum strategy to simulate the problem at hand more accurately.
3. Use and apply modern high-level programing languages for the solution of such problems,
4. Evaluate results
Course Content (Syllabus)
Introduction to the Finite Element Method: Areas of application focusing on the static analysis of structures. Brief historical review of the method’s foundations and modern evolution. Examples on simplified and complex mechanical structures from the automotive industry (suspension systems, frames, tires, belts, bearings, welds, etc.), the elevator industry (simulations of operation and compliance tests of components and the complete elevator car, wires, etc.) and the aviation industry (simulation of the skin of unmanned aerial vehicles made of metallic and composite materials).
Mathematical background and prerequisite knowledge: Mechanics of Materials and continuum mechanics. Matrix algebra and numerical analysis techniques. Elasticity theory and introduction to plasticity. Disk, plate, rods, trusses, beams and frames. Plane stress and plane strain with 1st, 2nd and higher order shell elements. Shape functions and coordinate systems (local and global). Creation of stiffness matrices for the elements and structures. 3D stress and 3D elements. Mathematical solution and introduction to explicit dynamics (transient and steady state) and thermal analysis.
Meshing of components and structures: Geometric simplifications, element size sensitivity and boundary conditions. Importance of choosing suitable element types and solution method for each problem. Evaluation of results in benchmark problems and comparison with the theoretical/analytical solutions. Results from complex structures and guidelines for evaluation results in common problems.
Development of a modular computer program for the design, meshing, boundary condition application, solving and results presentation of simple structures (1D elements, 2D and 3D trusses and frames and Plane stress problems).