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Sep 07, 2024
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ME 4602 - Transient and Nonlinear Finite Element Methods3 lecture hours 0 lab hours 3 credits Course Description This course is a mechanical engineering technical elective whose purpose is to introduce students to the finite element method applied to structural and thermal problems of both a transient dynamic nature and a nonlinear nature. In the lecture portion of the course, students will be instructed in formulation of a finite element procedure for solving any differential equation in space or time. Also, students will be taught how time integration algorithms are used in conjunction with distributed modeling and how nonlinearities are handled by the finite element method. A laboratory portion of the course will be planned using a commercial software code for the purposes of extending the one-dimensional algorithms for more complex applications. (prereq: ME 460 ) Course Learning Outcomes Upon successful completion of this course, the student will be able to: • have reviewed the procedural steps involved in FEA analysis
• derive a finite element formulation from a governing differential equation
• understand and implement time integration of dynamic systems with inertia
• understand step-wise linearization of nonlinear systems
• understand and implement iterative solution techniques for nonlinear systems
• be familiar with use of a commercial general-purpose FEA software package for transient and nonlinear applications
• understand how to validate results for problems involving systems design Prerequisites by Topic • Mechanics of materials, statics, dynamics, heat transfer, linear algebra, integral and differential calculus Course Topics • Review of the method (1 class)
• Method of weighted residuals (3 classes)
• Comparison with energy methods (1 class)
• Modal analysis (2 classes)
• Modeling inertia and mass distribution using FEA (2 classes)
• Modeling damping in continuous systems using FEA (1 class)
• Understanding and implementing time integration algorithms for dynamic FEA analysis (2 classes)
• Implementing nonlinear FEA solutions as a set of iterative, quasi-linearized sub-problems (3 classes)
• Use commercial general-purpose FEA software package for transient and nonlinear applications (3 classes)
• Review of static analysis (1 class)
• Modal analysis and transient analysis (1 class)
• Nonlinear structural analysis (1 class)
• Transient, nonlinear thermal conduction, convection, and radiation
• Validate results for real design of an engineering system (4 week course project)
Coordinator Vince Prantil
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