Unit 1

Introduction to FEM – equilibrium condition, strain-displacement relation, linear constitutive relations – domain discretization, types of elements, assembly procedures, boundary conditions- Formulations: Potential energy method, Variational formulation, Weighted residual, Galerkin and Rayleigh-Ritz methods.

Unit 2

Coordinate systems, convergence criteria, 1D Elements: Axial elements basic formulations, formations of shape functions, problems using 1D elements, Beam (bending) element: formulations and formation of shape function and problems – 2D elements: Plane stress and Plane strain element formulation, shape function development, problems using 2D elements – axi-symmetric elements- iso-parametric formulation of elements.

Unit 3

3D element formulations – Introduction to FE formulation of Plate bending and shell elements – Numerical integration – Solution techniques of the numerical equations- Introduction to FE software- FE modeling of aircraft and spacecraft components- Application of boundary conditions and loadings on FE models- Analysis of subcomponents like wings, fuselage, motor casing, etc.

Objectives

• Understand the concepts of mathematical modeling of engineering problems by introducing the Finite Element Methods and to help the students use this method and commercial software package to solve simple aerospace structures.

Course Outcomes

• CO1: Understand the concepts behind variational methods and weighted residual methods in FEM.
• CO2: Identify the application and characteristics of FEA elements such as bars, beams, plane and Iso parametric elements, and 3-D element.
• CO3: Develop element characteristic equation procedure and generation of global stiffness equation will be applied.
• CO4: Able to apply Suitable boundary conditions to a global structural equation, and reduce it to a solvable form
• CO5: Able to identify how the finite element method expands beyond the structural domain, for problems involving dynamics, heat transfer, and fluid flow.

CO – PO Mapping

Textbook(s)

• Daryl L. Logan, “A First Course in the Finite Element Method”, CL, New Delhi, 2007

Reference(s)

• C. S. Krishnamoorthy, “Finite Element Analysis” , Tata McGraw-Hill Publishing Company Limited, New Delhi, 1999.
• David V. Hutton, “Fundamentals of Finite Element Analysis”, Tata McGraw-Hill Publishing Company Limited, New Delhi.
• Megson, T. H. G., “ An introduction to aircraft structural analysis”, Butterworth-Heinemann, USA, 2010.
• Tirupathi R. Chandrapatla and Ashok D. Belegundu, “Introduction to Finite Element in Engineering”, Prentice Hall of India, New Delhi.

Evaluation Pattern