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 Course Number: ENGRG 7540 Course Name: Advanced Finite Element Method (Online) Course Description: This course introduces the finite element method. It emphasizes beam and frame analysis, plane stress and plane strain, axisymmetric and three-dimensional stress analysis. It includes dynamic analysis and field problems, such as heat transfer. The course utilizes readily available finite element computer programs to solve stress analysis, heat transfer, thermal stresses, etc. P: BS in Civil or Mechanical Engineering or related field. Prerequisites: None Level: Graduate Credits: 3 Format: Online Program: Master of Science in Engineering

NOTE: The information below is representative of the course and is subject to change.  The specific details of the course will be available in the Desire2Learn course instance for the course in which a student registers.

Learning Outcomes
Upon completion of this course, you should be able to

• Demonstrate a working knowledge of computational methods in the finite element method that allow for the solution of stress analysis and heat-transfer problems.
• Select which element(s) to use and what model to construct for a specific problem in stress analysis and heat transfer.
• Assess practical situations where the finite element method is applicable.
• Develop skills that enable you to define and solve open-ended engineering design problems with the aid of a finite element computer program.

Unit Descriptions

Unit 1: Preliminary and Basic Concepts
Overview
The finite element method involves the effective use of matrix algebra and the setup and solution of simultaneous linear algebraic equations. To better understand the discussions, derivations, notations, and formulations of equations to follow in later units, it is imperative that you understand matrix algebra and solution procedures for simultaneous linear algebraic equations. Along with background material, Unit 1 presents a brief history of the finite element method, as well as some significant references for those wanting to examine the development of this method. Unit 1 outlines the general steps in a finite element formulation. It shows numerous applications of the finite element method. Finally, it introduces basic concepts on which the primary method, called the direct stiffness method, is based.

Unit 2: Line Elements - Bar (Truss), Beam (Frame) - and Flowchart of Computer Program for Truss Analysis
Overview
Line elements form the basis for the stress analysis of real structures. Such structures as two- and three-dimensional trusses, statically indeterminate beams, and two- and three-dimensional frames can be analyzed quite easily with the line elements introduced in this unit. Unit 2 then develops the stiffness matrices for bar, truss, beam, and frame elements. This unit also introduces concepts of transformation matrices, inclined or skewed supports, use of symmetry, distributed loading, and beam element with nodal hinge. Finally, Unit 2 describes a flowchart that is a basis for a computer program for the analysis of trusses.

Unit 3: Two-Dimensional Elements for Plane Stress/Strain and Axisymmetric Problems and Computer Program Analysis
Overview
Two-dimensional or plane elements are used for plane stress/strain analysis where the loading is applied in the plane of each element. These elements are used to analyze plates with holes, fillets, or other changes in geometry for stress concentration problems. An example would be a hydraulic cylinder rod end used in a piece of heavy equipment such as a backhoe tractor. Axisymmetric elements allow a simple method to model three-dimensional solids that are actually axisymmetric in their geometry. An example is a steel die used in the plastic film industry. Unit 3 then develops the stiffness matrices for the plane stress/strain and axisymmetric elements. This unit also introduces various concepts that should be considered when modeling any problem for solution using these elements. Further extension of the computer program to solve problems with these elements is also described. Numerous examples are included.

Unit 4
Overview
Three-dimensional elements are used for three-dimensional (3-D) stress analysis where the loading is applied anywhere in space. These elements are either tetrahedral (4-sided) or hexahedral (6-sided or brick-type) elements and are used to model such bodies as engine blocks, thick-walled dams, foot pedals, and other truly 3-D structures. Unit 4 first develops the stiffness matrix for the tetrahedral element and describes how the hexahedral element stiffness matrix is developed. It goes on to develop the stiffness matrix for 1-D and 2-D heat transfer due to both conduction and convection, allowing the determination of temperature variation and heat transfer throughout a body. Then, for bodies subjected to variations in temperature, the unit examines how thermal stresses occur. Finally, Unit 4 formulates the equations necessary for a time-dependent loading problem, such as when a blast load is applied to a building frame.

The approximate breakdown of possible points for each longhand assignment and computer program assignment is as follows:

 Longhand Assignments Computer Assignments Appendices A & B 90 points Chapter 1 10 points Chapter 2 40 points Chapter 3 100 points 100 points Chapter 4 70 points 100 points Chapter 5 100 points 100 points Chapter 6 50 points Chapter 7 20 points 100 points Chapter 9 50 points 100 points Chapter 10 70 points Chapter 11 40 points 100 points Chapter 13 60 points 50 points Chapter 15 60 points Chapter 16 60 points Total: 820 points 650 points

Note: Longhand assignments may be done in Mathcad, Matlab or any similar computer algebra program. Also the total number of points earned from longhand and computer program homework will be adjusted on the basis indicated under Course Requirements described above. That is, longhand homework is worth 20% of your grade and computer program homework is worth 15% of your grade.

Each of the four exams is worth 100 points for a total of 400 exam points (40% of your grade). Each of the two design reports is worth 100 points for a total of 200 points (20% of your grade). Also remember that discussion participation is worth 5% of your grade.