Faculty of Science

Model (No 12)

Course Specification : نظرية المرونة (1) - ميكانيكا متقدمة

2010 - 2011

Farabi Quality Management of Education and Learning - 21/11/2024

University :Mansoura University

Faculty :Faculty of Science

Department :Mathematics Department

1- Course data :-

Code:	11304
Course title:	نظرية المرونة (1) - ميكانيكا متقدمة
Year/Level:	ثالثة رياضيات
Program Title:	Mathematics
Specialization:
Teaching Hours:	Theoretical:	4	Tutorial:	2	Practical:

2- Course aims :-

To introduce the dynamical equations of rotation.
To develop mathematical tools for the solution of simple problems in kinematics and dynamics.
To illustrate the idea of integrability.
This course will introduce governing equations of linear elasticity and will focus on solutions of boundary value problems in both two and three dimensions using several different methods

3- Course Learning Outcomes :-

4- Course contents :-

No	Topics	Week
1	Governing Equations of Linear Elasticity
2	Stress: Stress tensor and traction vector. Normal and shear stresses. Spherical, uniaxial and shear stresses. Balance of linear momentum. Symmetry of stress tensor.
3	Strain: Deformation and deformation gradient, material time derivative. Linear strain tensor and interpretations. Homogeneous deformations: uniform dilatation, simple extension, simple shear. Conservation of mass, dilatation.
4	Generalized Hooke’s Law of linear elasticity
5	Plane problems: Anti-plane strain. Plane strain and the Airy stress function. Plane stress.
6	Torsion: Torsion of circular, elliptical and triangular rods.
7	Elliptic integrals and Elliptic functions
8	Inertia tensor
9	Definition of a dynamical system – Motion of a rigid body around a fixed point description of rotation
10	Euler’s case
11	Lagrange’s case and the gyroscope
12	Kovalevskaya’s case – Motion of the top
13	The gyrostat

5- Teaching and learning methods :-

S	Method
	Two hours lecturer weekly with exercise sheets and solution sheets.
	Weekly one hour tutorials in groups.
	Using Internet facilities.

6- Teaching and learning methods of disables :-

7- Student assessment :-

A. Timing

B. Degree

8- List of books and references

S	Item	Type
1	Yehia H. M. Advanced mechanics , (in Arabic)
2	Leimanis E., The general problem of motion of coupled rigid bodies about a fixed point (Berlin: Springer) 1965.
3	Golubev V. V. Lectures on integration of the equations of motion of a rigid body about a fixed point, State Publishing house of theoretical technical Literature , Moscow 1953.
4	L D Landau & E M Lifshitz "Theory of Elasticity" (Pergamon, 1986)
5	R J Atkin & N Fox "An Introduction to the Theory of Elasticity" (Longman)
6	Landau, L.D.; Lifshitz, E. M. (1986). Theory of Elasticity (3rd ed.). Oxford, England: Butterworth Heinemann.
7	http://www.wordiq.com/definition/Elasticity_theory
8	http://en.wikipedia.org/wiki/Linear_elasticity

9- Matrix of knowledge and skills of the course

S	Content	Study week
	Governing Equations of Linear Elasticity
	Stress: Stress tensor and traction vector. Normal and shear stresses. Spherical, uniaxial and shear stresses. Balance of linear momentum. Symmetry of stress tensor.
	Strain: Deformation and deformation gradient, material time derivative. Linear strain tensor and interpretations. Homogeneous deformations: uniform dilatation, simple extension, simple shear. Conservation of mass, dilatation.
	Generalized Hooke’s Law of linear elasticity
	Plane problems: Anti-plane strain. Plane strain and the Airy stress function. Plane stress.
	Torsion: Torsion of circular, elliptical and triangular rods.
	Elliptic integrals and Elliptic functions
	Inertia tensor
	Definition of a dynamical system – Motion of a rigid body around a fixed point description of rotation
	Euler’s case
	Lagrange’s case and the gyroscope
	Kovalevskaya’s case – Motion of the top
	The gyrostat

Course Coordinator(s): -

Head of department: -

Ahmed Habeb Mohamed Nageb Elbassiony