Syllabus

Module I: Mathematical background required for Finite Element Method:
Vector Matrix tensor rank of matrix transpose of force-displacement Vector Basic matrix operations difference between Matrix and Determinate Multiplication of Matrix, Inversion of Matrix Solution of linear equations, Properties of Stiffness matrix, Flexibility Matrix ill- condition matrix, Rigid body motion etc. [6 hours]

Module II: Approximate Solution: Introduction, Boundary value problems and solution methods, Direct approach – example, advantage and limitations. Strong form and weak form, Method of weighted residuals, Rayleigh-Ritz method, etc. [6 hours]

Module III: Finite Element Formulation of Truss and Beam Element, Stiffness Matrix of Spring and Bar Element Energy Approach Derivation of Shape Functions for a truss element and Beam element [6 hours]

Module IV: Finite Element Formulation of Plate Element, Plane Stress Elements CST and LST Elements Rectangular Plane Stress Elements Area Coordinates Isoparametric Elements Plate Bending Elements etc., Finite element formulation for static, dynamic and buckling analysis, Modal analysis, Transient Analysis and buckling of structure in finite element framework [8 hours]

Module V: Use of Finite Element for Computer Application, Implementations of ABAQUS for all finite element program-related homework and projects. Static Analysis of Beam, modal Analysis, buckling of a structural member, etc. The modelling of composite structure, stress concentration, etc., will be done in ABAQUS. [8 hours]

Students will learn some Basic terminology and basic theory approximate solutions used widely in engineering practice

Students will learn the theory of Truss, beam, and derivation of the force-displacement relationship

Students will capitalize on the knowledge of plane stress, plane strain and other 2D modelling problem

Students will be able to model various real life structural elements by using standard Software based FEM Theory

I. Understand the Mathematical Foundation & Matrix Operations required for finite element method
II. Approximate Solution Methods & Variational Approaches
III. Finite Element Formulation for Structural Elements and understanding the role of 1D element, CST, and Isoparametric elements in structural modelling.
IV. Structural Analysis using FEM will be able to perform static, dynamic analysis using FEM principles
V. Computational Implementation using Software such as ABAQUS

D. L. Logan, A First Course in the Finite Element Method, Thomson

A. J. M. Ferreira, Matlab Codes for Finite Element Analysis, Springer

J.N. Reddy, Introduction to the Finite Element Method, McGraw-Hill Education, 4th Edition (2019)

laus-Jürgen Bathe, Finite Element Procedures, Prentice Hall, 2nd Edition (2006)