The course provides advanced knowledge on the application of finite element analysis to engineering applications in linear structural mechanics and heat transfer problems. The course analyses critically problems involving one, two- and three-dimensional idealizations. The topics covered include steps in finite element modelling process, behaviour of spring, truss, beam, plane stress/strain and three dimensional finite element modelling approaches in structural mechanics. The heat transfer part of the course examines the conduction and convection behaviour and analyzing these mechanisms using finite element analysis.
COURSE LEARNING OUTCOMES (CLO)
CLO: 1. Formulate and Solve 1D, 2D problems by using Bar, truss, beam, triangle and quadrilateral elements. C3
CLO: 2. Analyze and interpret FE analysis results for solid mechanics and heat transfer problems.C4
Introduction- Two Lectures
• Introducing the basic notion of FEM and related domain discretization strategies for solving problems of continuum mechanics.
• Introducing the FEM concepts of idealization, element formulation, domain discretization, mesh generation, assembly, solution and recovery of derived quantities.
Introduction to the Stiffness (Displacement) Method – Ten Lectures
• Development of truss equation
• Development of beam equation
• Development of frame and grid equations
Variational formulation of linear bar/truss element – Eight Lectures
• Formulation of 1D linear bar element using principle of minimum potential energy and through Galerkin approach.
• Introduction to Shape/interpolation functions and demonstration of linear shape function.
• Application of formulated element to problems with distributed loads and varying cross-sectional geometry
Development of the Plane Stress and Plane Strain Stiffness Equations – Six Lectures
• Constant-Strain Triangular Element Stiffness Matrix and Equations
• Linear-Strain Triangular Element Stiffness Matrix and Equations
Finite Elements in Thermo-Fluid Analysis – Four Lectures
• Steady state problems.
• Thermal transient problems.
Practical Considerations in Modeling, Interpreting Results – Two Lectures
• Equilibrium and Compatibility of Finite Element Results
• Convergence of Solution