Department of Civil Engineering

Finite Element Methods in Solid Mechanics- CE307

Credits : 3

Prerequisites :CE201

Compulsory/Optional : Compulsory

Aim(s)
To introduce approximate methods used in analysing civil engineering problems.
Intended Learning Outcomes
On successful completion of the course, the students should be able to;

1. Explain the different approximate methods and their limitations for analysis of civil engineering problems.
2. Analyse basic 1D and 2D civil engineering problems by developing a computer program based on finite element method.
3. Model and analyse engineering problems by using commercially available Finite Element (FE) software.
Course content/Course description
1. Introduction to approximate methods to solve basic engineering problems: Variational methods: Rayleigh-Ritz; finite difference method; finite element method
2. Displacement based finite element formulation for truss structures: Derivation of element stiffness matrix for a spring/bar element referring local coordinate system; shape (interpolation) functions; 2D transformation of element stiffness matrix from local to global coordinate system; assembly of element stiffness matrices into global stiffness matrix; boundary conditions; solution techniques; evaluation of member forces; computer implementation using a computer program
3. Displacement based finite element formulation for frame structures: Review of beam theory, derivation of stiffness matrix for frame element, shape (interpolation) functions, equivalent nodal forces, evaluation of stress resultants, computer implementation using a computer program
4. Finite element formulation for 2D plane stress/strain problem: Basic equations; derivation of stiffness matrix for a 2D plane stress/strain elements: constant strain triangular (CST) element, bi-linear rectangular element, isoperimetric formulation and 4-node quadrilateral element, and higher-order elements; equivalent nodal forces; Gauss quadrature numerical integration and Gauss points, convergence criteria, discretization error and convergence rate
5. Introduction to general purpose finite element programs: Pre-processor, input data, graphic interfaces, mesh generation, renumbering for efficiency, processors, storage schemes, post-processors, output devices, graphic support, refining the solution, use of finite element methods in CAD/CAE, applications of general purpose finite element programs
Recommended Texts
1. Logan, D 2007, First Course in Finite Element Method, 4th edn, Nelson Engineering.
2. Desai, C 2005, Introduction to the Finite Element Method, 1st edn, CBS Publisher.
3. Weaver, W and Gere, JM 2004, Matrix Analysis of Framed Structures, 2nd edn, Springer.
Time Allocation Hours
Lectures 36
Tutorials 4
Practical -
Assignments 10
Assessment Percentage Marks
In-course
Assignments/Quizzes 20
Mid Semester Examination 30
End-semester 50

Department of Civil Engineering