• Mechanics, Semester 2, position 1

The purpose of this course is that students understand and learn the basic concepts of the theory of elasticity. They will acquire the basis of the tensor method, too. Students will be enabled to model and solve some rheological problems. Through understanding the rheological processes, they will be able to use computer programs in this field.

- By negotiation of this program, students will master some basic methods and procedures of the theory of elasticity and of the tensor method. - They will be able to calculate stress components on the base of the equilibrium equations and to form appropriate tensors of stress and strain for an ideal elastic body. - They will be introduced with principal stresses (intensity, position) and with maximum shear stress. - They will be able to calculate main strains. - Students will master application of material failure theories. - They will understand elasticity and stiffness matrixes. - They will be able to solve some real problems related to thin simply supported plates.

Introduction. The concept of stress. Cauchy's principle. Stress components in Cartesian and cylindrical coordinate system. Stress tensor. Equilibrium equation in Cartesian and cylindrical coordinate system. Stresses in an arbitrary plane - transformation of stress tensor. Principal stresses. Stress invariants. Volume and deviator components. The maximum shear stress. Plane state of stress. Deformation, Lagrange's strain. Small deformation. Geometric interpretation. Compatibility equations. The main deformations. Volume and deviator components. Material failure theories. Plane state of strain. The rate of strain. Linear elasticity. Hooke's law. Modulus of sliding. Lame's constants. Poisson's ratio. Thin plates. Rheological models and modeling.

Determination of the stress components on the base of balance equations. Determination of the stress components in oblique plane - transformation of stress tensor. Principal stresses, the intensity, the position. Maximum shear stress, intensity and position. Stress invariants. Deformation by Lagrange and Euler. Calculation of the main strains. Application of failure theories. Tensors of stress and strain for an ideal elastic body. Thin simply supported plates.

Set by the Curriculum of the study program

Handouts from the website of the Department for Strength of the constructions

Total assigned hours: 75

New material: 20
Elaboration and examples (recapitulation): 10

Auditory exercises: 20
Laboratory exercises: 0
Calculation tasks: 5
Seminar paper: 5
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 3
Review and grading of lab reports: 0
Review and grading of seminar papers: 3
Review and grading of the project: 0
Test: 4
Test: 0
Final exam: 5

Activity during lectures: 10
Test/test: 40
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 10
Project: 0
Final exam: 40
Requirement for taking the exam (required number of points): 40

T. Atanacković, Theory of elasticity, FTN University of Novi Sad, 1993. (in Serbian); S. Tymoshenko, J. N. Gudier, Theory of elasticity, Građevinska knjiga - Beograd, 1962. (in Serbian); T. Maneski, V. Milosevic-Mitic, D. Ostric, Sets of the structural strength, University of Belgrade, 2002. ISBN 86-70803-435-9; Hlitčijev J., Chapters in Theory of elasticity, Naučna knjiga Beograd, 1950. (in Serbian)