Course Description:
The finite element method is a widely used numerical procedure that can be applied to obtain solutions to a large class of engineering problems. A robust understanding of the finite element method assures that analyses are performed correctly, confidently and efficiently. This course presents the fundamentals of the finite element method and modeling techniques for structural analysis applications.
Theory of the finite element method, using several approaches is covered throughout the course. The direct method is mostly covered, but the Principle of Minimum Potential Energy is also mentioned. The direct method, the Principle of Minimum Potential Energy, various methods of Weighted Residual and a Variational approach are introduced. The formulations of several element types are discussed. The isoparametric formulation of the elements stiffness matrices and numerical integration are covered.
This demonstrates how software solves large scale problems and provide an understanding which aids with setting up analyses and post processing results, and sets the basis for more advanced uses. An introduction to nonlinear finite element analyses and modal analyses is provided at the end of the course. The concepts covered in this course are enforced with practical problems and examples, and discussion on common errors and typical use of the finite element method in the aerospace industry. Lastly, the concepts of verification and validation, their requirements and methods are presented throughout the course.
Course Includes:
 A course notebook prepared by your instructors
 Supplemental material to enhance the subject matter
Course Textbook:
Logan, Daryl L., A First Course in the Finite Element Method, Cengage Learning Global Engineering Publisher, Sixth Edition, 2016
Course Outline:
Day 1 (7 Hours)
 Theoretical component
 Introduction – 1.5 Hrs.
 Review of Mathematical Fundamentals – Linear Algebra – 1 Hr.
 Introduction to Finite Element Method – 1.5 Hrs.
 Finite Element Analysis Using Direct Method – 1.5 Hrs.
 Rod and springs Element – 1.5 Hrs.
 Application component
 Use of FEM to solve statically indeterminate problems and examples – 1 Hr.
 Assignment
 Selected truss problems to be solved by hand
Day 2 (7 Hours)
 Theoretical component
 Finite Element Analysis Using Minimum Potential Energy – 1.5 Hrs.
 Introduction of the concept
 Derivation of the stiffness matrix for a bar/rod element
 Example
 Introduction to Beam Element – 3 Hrs.
 Bernoulli and Timoshenko formulations
 Extending the concept of minimum potential energy to a beam element
 Examples with FEMAP, show orientations
 Finite Element Analysis Using Minimum Potential Energy – 1.5 Hrs.
 Application component
 Design and analysis of bolted joints – 2.5 Hrs.
 Assignment 2
 Load transfer of a bolted joint using FEM (by hand or with software)
Day 3 (7 Hours)
 Theoretical component
 Introduction of 2D Solid Elements – 3 Hrs.
 Triangle element
 Constant strain elements
 Element limitations
 Quadrilateral element
 Examples and inclass demo
 Triangle element
 Isoperimetric Formulation – 2 Hrs.
 Mapping of coordinate systems from physical to natural and vice versa
 Numerical integration (integration points) – Midpoint Rule, Simpson Rules, Newton Cotes, Gaussian Quadrature, and Gaussian Points
 Examples
 Introduction of 2D Solid Elements – 3 Hrs.
 Applications component
 Stress concentrations, intro to fatique, and use of the FEM in conjunction with SN Curves – 2 Hrs.
 Assignment 3
 Calculation of stress concentrations using FEM (requires use of software)
Day 4 (8 Hours)
 Theoretical component
 3D Solid Elements – 1 Hr.
 Show element types and formulations and shape functions
 Solve example problems
 Class exercise
 Introduction to Shell Elements – 1 Hr.
 Introduce and discuss element types and formulations and shape functions
 Kirchhoff and Mindlin formulations
 Examples and inclass demo
 Introduce and discuss element types and formulations and shape functions
 Higher Order Elements – 1 Hr.
 Introduction to Nonlinear Analyses – 1.5 Hrs.

 Sources of nonlinearity
 Quick mathematical background
 FEMAP/ANSYS/ABAQUS demonstration

 Introduction to dynamic FEM – 1 Hr.
 3D Solid Elements – 1 Hr.
 Applications component
 How to go from CAD to FEM – 0.5 Hr.
 Demo of nonlinear analyses with FEM – 1 Hr.
 Demo of implicit / explicit fem – 1 Hr.
 Assignment 4
 Analysis of bulkhead undergoing pressure loading (requires use of software)
Day 5 (8 Hours)
 Theoretical component
 Modal Analysis – 1.5 Hrs.
 Introduction to Natural Frequency
 Computation techniques using FEM
 Introduction to buckling
 Computation techniques using FEM
 Examples and inclass demo
 Introduction to Natural Frequency
 Modal Analysis – 1.5 Hrs.
 Applications component
 Introduction to FEM as a tool in fracture mechanics – 2 Hrs.
 Linear Elastic Fracture Mechanics
 ElastoPlastic Fracture Mechanics
 Examples and inclass demo
 Closing – 0.5 Hr
 Introduction to FEM as a tool in fracture mechanics – 2 Hrs.
Course Project:
Beam bending modeled with beam elements, rods and plates, shells, solid elements. Comparison with close form solution and computational cost.