Semester:

6

Course Code:

CE3110

Course Name:

Finite Element Methods in Solid Mechanics

Credit Value:

3 (Notional hours:150)

Prerequisites:

CE1130

Core/Optional

Core

Hourly Breakdown

Lecture hrs.

Tutorial hrs.

Practical hrs.

Assignment hrs.

Independent Learning & Assessment hrs.

30

5

-

20

95

Course Aim: To introduce numerical methods for solving engineering problems.

Intended Learning Outcomes:

On successful completion of the course, the students should be able to;

➢    explain numerical methods in solid mechanics and their limitations.

➢    analyze discrete and continuum structural systems using the displacement based Finite Element (FE) method.

➢    develop a general computer code for analysis of basic structural systems.

➢    predict the complex structural system response by using commercially available Finite Element (FE) codes.

Course Content:

➢    Introduction to approximate methods to solve basic engineering problems: Variational Formulations for 1D problems (weak formulations): Galerkin Method; Rayleigh-Ritz .

➢    Introduction of finite element methods: Displacement based finite element method and force based finite element method; discretization error, proof of convergence and convergence rate.

➢    Displacement based finite element formulation of truss element and its applications: 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; implementation using a computer code.

➢    Displacement based finite element formulation of frame element and its applications: Review of beam theory, derivation of stiffness matrix for frame element, shape (interpolation) functions, equivalent nodal forces, evaluation of stress resultants, implementation using a computer code.

➢    Finite element formulation of 2D plane stress/strain element: Basic equations; derivation of stiffness matrix for a 2D plane stress/strain element: constant strain triangular (CST) element, isoparametric formulation of 4-node quadrilateral element, and higher-order elements; equivalent nodal forces; Gaussian quadrature for numerical integration of 2D elements, reduced integration and Gauss points.

➢    Finite element formulation of 3D solid element: Isoparametric formulation of 8-node solid element, and higher-order elements; equivalent nodal forces; Gaussian quadrature for numerical integration of 3D elements, reduced integration and Gauss points.

➢    Modeling and analysis of complex structural systems using general purpose finite element programs: Pre-processor, input data, graphic interfaces, mesh generation, automatic renumbering for efficiency, processors, storage schemes, post-processors, output devices, graphic support, refining solution, use of finite element methods in CAD/CAE.

Teaching /Learning Methods:

Classroom lectures, computer based exercises, hands on experience with software

Assessment Strategy:

Continuous Assessment

50%

Final Assessment

50%

Details:

Assignments/Quizzes/Tutorials   25%

Mid Semester Examination        25%

Theory (%)

50

Practical (%)

-

Other (%)

-

Recommended Reading:

➢    Klaus-Jürgen Bathe. (2014). Finite Element Procedures, 2nd edition, Prentice Hall, Pearson Education, Inc.

➢    Logan, D. (2007). First Course in Finite Element Method, 4th edition, Nelson Engineering.

➢    Desai, C. (2005). Introduction to the Finite Element Method, 1st edition, CBS Publisher.

➢    Zienkiewicz, O. C., Taylor R.L., (1989/1990), The Finite Element Method in Structural and Continuum Mechanics, 4th edition, McGraw-Hill.