Unit 1

Basic Concepts, applicability and applications, basic equations of solid mechanics, boundary and initial conditions, Euler Lagrange equation, Generalization of finite element concepts.

Discretization, Interpolation models, weighted residual and variational approaches, Principle of minimum potential energy, principle of virtual work.

Unit 2

Element types– Line element (bar, truss, beam and frame element), Plane elements- Triangular, rectangular, quadrilateral, sector, Solid elements – tetrahedron and hexahedron.

Curved andiso-parametric elements, coordinate systems and numerical integration, Mesh generation.

Unit 3

Structural applications -line elements, two-dimensional stress analysis (Plane stress, plane strain and axisymmetric analysis),three dimensional stress analyses.

Application to field Problems – heat transfer, dynamics and fluid flow problems.

Laboratory Sessions: Introduction to Finite Element packages and its application to solid mechanics, fluid and heat transfer problems.

Course Objectives

• Familiarize with the fundamental concepts of finite element method
• Inculcate the formulation of finite element models by selecting a suitable element, developing element matrices & vectors, and incorporating boundary conditions
• Familiarize with finite element procedures to solve structural, thermal, and fluid flow problems using commercial finite element packages

Course Outcomes

• CO1: Understand the fundamental concepts of finite element method to solve engineering problems
• CO2: Formulate finite element models using appropriate element selection, development ofstiffness & force matrices, and application of boundary conditions
• CO3: Solve structural, thermal, and dynamic problems using the developed finite element formulations
• CO4: Demonstrate the ability to create models for structural, thermal, and fluid flow applications using commercial finite element packages
• CO5: Interpret the analysis results to improve product and system design

CO – PO Mapping

Textbook(s)

• Rao, S.S., “The Finite Element Method in Engineering”, 6/e, Butterworth-Heinemann Publisher, 2018
• Logan, D.L., “A First Course in the Finite Element Method”, 5/e, Cengage Learning, 2012
• Moaveni, Saeed. “Finite element analysis theory and application with ANSYS”, 3/e. Pearson Education India, 2011.

Reference(s)

• Chandrupatla, T.R., and Belegundu, A.D., “Introduction to Finite Element in Engineering”, 4/e, Prentice Hall of India Pvt. Ltd.’, New Delhi, 2012
• Hutton, D.V., “Fundamentals of Finite Element Analysis”, McGraw-Hill, 2017
• Cook, R.D., Malkus, D.S., and Plesha, M.E., “Concepts and Application of Finite Element Analysis”, 4/e, John Wiley & Sons, 2007
• Reddy J.N, “An Introduction to Finite Element Method”, McGraw-Hill International Education, 3/e., 2005

Evaluation Pattern