Elasticity 1

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Materials

Synopsis:

The course represents an introduction for several another lectures on continuum mechanics and the strength of materials. The first part contains a detailed theory of stress, small strains and linear elasticity. The second one represents a logical descent from the continuum mechanics to the practical engineering solution of simple problems on tension, bending, shearing and torsion in the cross section of bars and beams.

Requirements:

Technical mechanics (14TEM) - Statics

Syllabus of lectures:

1. Tenzors 2. Strain: Lagrangian and Eulerian coordinates, finite strain tenzor, small strain tensor, rotation tensor, compatibility equations 3. Stress: internal forces, stress vector, Cauchy's stress tensor, equilibrium equations, principal stresses, octahedral shear stress, Mohr's circles. 4. Basic of elasticity theory: generalized Hook's law, linear equations of mathematical theory of elasticity and boundary conditions, Saint-Venant's principle, superposition principle, Beltrami-Michell equations, Lame's equations, potential and complementary strain energy of internal and external forces, variational principles of elasticity, Castigliano's theorems, principle of finite element method, elasticity equations in polar coordinates 5. Mathematical vs. engineering solutions of elasticity problems, plasticity conditions, fatigue fracture, brittle and ductile fracture.

6. Bars and beams: geometric characteristics of the cross sestion, forces and moments in the cross section, load and supports and fixations, statically determinate and indeterminate problems. 7. Tension and compresion: statically indeterminate cases, thin-walled pressure vessel, sudden changes in geometry and in the load. 8. Flexural loading of straight beams - stress: pure bending, transverse loading, load and shear and moment relationship, stresses in symmetrical and thin-walled cross sections under the shear force. 9. Flexural loading of straight beams - deflections: curvature of neutral axis, differential equation of the elastic curve, energy methods. 10. Statically indeterminate straight beams, theorem of three moments. 11. Curved beams: flexural stresses and changes in curvaturte, thin curved beams, frames. 12. Torsion of circular shaft: shear stress distribution, geometry of deformation.

Syllabus of tutorials:

Strain and stress tensor, axial load, bending of beams, analysis of a pressurized thick-walled cylinder.

Study Objective:

Knowledge: Basic theoretical problem of linear elasticity - terms, assumptions, formulation, methods of solution and possible simplifications. Connection between theoretical continuum mechanics and conventional concepts of engineering elasticity. Standard methods of stress and strain calculations for bars and beams.

Skills: Calculations of deflection, strains and stresses in bars and beams. Understanding of formulations and methods of solution in more general model problems of elasticity.

Study materials:

Key references:

[1] Oliva, V.: Aplikovaná mechanika kontinua I - Elastomechanika. [University textobook FJFI]. ČVUT v Praze 1982.

[2] Oliva, V.: Elastomechanika I. [Written materials for lectures P-KMAT-805/10]. Praha, ČVUT-FJFI-KMAT, 2010, 90 s.

Recommended references:

[1] Brdička, M. - Samek, L. - Sopko, B. : Mechanika kontinua. Academia 2005, ISBN: 80-200-1344-X.

[2] Šejnoha, J. - Bittnarová, J.: Pružnost a pevnost 10. [University textbook FS]. Vydavatelství ČVUT, 2000.

[3] Michalec a kol.: Pružnost a pevnost I. [University textbook FSI] Ediční středisko ČVUT 2001.

[4] Servít, R. - Doležalová, E. - Crha, M.: Teorie pružnosti a plasticity I. SNTL/ALFA, Praha 1981.

[5] Sochor, M.: Strength of Materials. [University textbook FSI]. Vydavatelství ČVUT 2000.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• BS Diagnostika materiálů (compulsory course of the specialization)