Goals: Computer models are being increasingly used for the solution of many complex problems in Engineering. This course will give the students an insight on how computer models based on numerical methods are applied in Mechanical and Energy Engineering. Students will be required to complete mini projects in each of the applications that will be discussed in this course.
Course Objectives:
- To learn basic principles of finite element analysis procedure
- To learn the theory and characteristics of finite elements that represent engineering structures
- To learn and apply finite element solutions to structural, Static, dynamic problem to develop the knowledge and skills needed to effectively evaluate finite element analyses
- To interpret and evaluate the quality of the results (know the physics of the problems)
- To have a basic understanding of the theory used to solve a FE problem;
Course Learning Outcomes
Upon successful completion of this course, students should be able to:
- Understand the concepts behind formulation methods in FEM.
- Identify the application and characteristics of FEA elements such as, springs, bars, beams, Trusses plane and iso-parametric elements.
- Develop an element characteristic equation and the generation of global equation.
- Able to apply suitable boundary conditions to a global equation for bars, trusses, beams, mechanical structures, Static and dynamic problems and solve them displacements, stress and strains induced.
- Understand the main implications of the approximate nature of computational methods in engineering design and analysis
- Recognize the character of computation and simulation as future mechanical engineers
Inductive Content
1. Introduction: Structural analysis, objectives, static, Dynamic and kinematics analyses, Skeletal and continuum structures, modeling of infinite degree of freedom(DOF) system into finite DOF system, Basic steps in finite element problems formulation, general applicability of the method.
2. Element types and characteristics: Discretization of the domain, Basic element shapes, Aspect ratio, shape function, generalized co-ordinates and nodal shape functions, 2d rectangular and triangular elements, Axisymmetric elements.
3. Finite Element Formulation Techniques
Finite Element Method: Displacement Approach, Stiffness Matrix and Boundary Conditions
4. Assembly of elements and matrices: Concept of element assembly, Global and local coordinate system, band width and its effects, Banded and skyline assembly, Boundary conditions, solution of simultaneous equations, Guassian elimination methods, one and 2D applications Higher order and isoparametric elements
5. Static analysis: Analyses of Bars, trusses and frames, analyses of machine subassemblies, Use of commercial software packages, advantages and limitations
6. Applications of Finite element method (FEM)/ Finite element analysis ( FEA)
1. Use of software(computer modeling and simulation) lab practice: Introduction, Linear and non-linear models
2. Dynamic analysis: Determination of natural frequencies and mode shapes, Application to stress analysis and vibration problems. Use of commercial software packages.
Computer lab: Introduction to practical problems of FE modeling in Solidworks/ 2D and 3D linear stress analysis/ Static analysis of simple shell structure/Discretization error and adaptive meshing
Grading:
Homework/Assignments (at least 2) 10%
Project (1) 5%
Quizzes (more than 5) 5%
CATs (at least 2) 30%
Final comprehensive examination (Theories + Practical's) 50%
Assessment method: Assessment based on tests and results of computer lab work (reports).
Practical work: Project/laboratory classes, where students will build and analyze the results of simple FE models of elastic structures
Abilities: After completing the course, the students will be able to build simple FE models and will know the possible applications and limitations of the method in mechanics of structures.