كلية العلوم

نموذج رقم(12)

توصيف مقرر دراسي : نظرية المرونة (1) - ميكانيكا متقدمة

2010 - 2011

الفارابى لإدارة جودة التعليم والتعلم - 23/11/2024

الجامعة :جامعة المنصورة

الكلية :كلية العلوم

القسم :الرياضيات

1- بيانات المقرر :-

الرمز الكودى:	11304
اسم المقرر:	نظرية المرونة (1) - ميكانيكا متقدمة
الفرقة:	ثالثة رياضيات
عنوان البرنامج:	Mathematics
التخصص:
عدد الساعات:	نظري:	4	فصل:	2	عملى:

2- أهداف المقرر :-

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- نواتج التعلم المستهدفة للمقرر :-

4- محتويات المقرر :-

م	الموضوع	الأسبوع
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- أساليب التعليم والتعلم :-

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

6- أساليب التعليم والتعلم للطلاب ذوى القدرات المحدودة :-

7- تقويم الطلاب :-

أ- التوقيت

ب- توزيع الدرجات

8- قائمة الكتب الدراسية والمراجع

م	العنصر	النوع
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- مصفوفة المعارف والمهارات المستهدفة من المقرر الدراسي

م	المحتوى	أسبوع الدراسة
	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

اساتذة المادة: -

رئيس مجلس القسم العلمى: -

أحمد حبيب محمد نجيب البسيونى