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 enable to model and solve some reological problems. Through understanding the reological processes they will be able to use computer programs in this field.

- By negotiation of this program, students will master some methods and procedures of theory of elasticity and tensor method. - They will be able to calculate stress components on the base of balance equations and to form appropriate tensors of stress and strain for an 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 plates.

Cauchy's principle. Stress components in Cartesian and cylindrical coordinate system. Stress tensor. Equilibrium equations in Cartesian and cylindrical coordinate system. 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. Lame's constants. Thin plates.

Determination of the stress components on the base of equilibrium equations. Determination of the stress components in oblique plane - transformation of stress tensor. Principal stresses, the intensity, the position. The maximum shear stress, intensity and position. Stress invariants. Calculation of the main strains. Application of material failure theories. Tensors of stress and strain for an 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: 65

New material: 40
Elaboration and examples (recapitulation): 10

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

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 10
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 5

Activity during lectures: 0
Test/test: 0
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 50
Project: 0
Final exam: 50
Requirement for taking the exam (required number of points): 50

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.; T. Maneski, V. Milosevic-Mitic, D. Ostric, Sets of the structural strength, University of Belgrade, 2002. ISBN 86-70803-435-9 (in Serbian); Hlitčijev J., Chapters from the calculation of ship structures, Faculty of Mechanical Engineering Belgrade, 1973.