339-0501/01 – Theory of Elasticity (TP)
| Gurantor department | Department of Mechanics of Materials | Credits | 6 |
| Subject guarantor | doc. Ing. Leo Václavek, CSc. | Subject version guarantor | doc. Ing. Leo Václavek, CSc. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2003/2004 | Year of cancellation | 2014/2015 |
| Intended for the faculties | FS | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
Educate students in basic procedures which are applied for a definition and solving of more exciting engineering technical problems in the sphere of mechanics of solid elastic deformable bodies. Ensure understanding of teaching problems. To learn the students apply gained theoretical peaces of knowledge in praxis.
Teaching methods
Lectures
Tutorials
Summary
Transformation properties of vectors and tensors. Analysis of strain at a point in a deformable body. Strain-displacement relations. The Green-Lagrange strain tensor, Cauchy`s small (linear) strain tensor. Small strain tensor invariants. Principal strains. Principal axes of strain. Spherical tensor, strain deviator tensor. Octahedral normal and shear strains. Compatibility of strain conditions. The state of stress at a point in a body. Stress tensor. Invariants of the stress tensor. Principal stresses, principal planes, principal directions of the stress tensor at a point. Spherical tensor and stress deviator. Normal and shear stresses on the octahedral plane. The method of Mohr`s circles. Cauchy`s differential equations of equilibrium. Physical equations for anisotropic, orthotropic, transversely isotropic and isotropic, linearly elastic homogeneous solid. Boundary conditions. Solution of the elastic problem, formulation in terms of displacements - Lamé (Navier) equations, formulation in terms of stresses - Beltrami-Michell equations. Planar problems of the theory of elasticity, plane stress and plane strain. Airy`s stress function, biharmonic differential equation in orthogonal Cartesian coordinates. The planar problem in polar coordinates. Planar axial-symmetric problem. The stress concentration due to a circular hole in an infinite plate of constant thickness. Pure bending of the circular curved bar. Bending of the circular curved bar with the force at the free end. The stress field around an edge dislocation. Line uniform continuous traction on the boundary of the elastic half-space – Flamant`s problem.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Test, example solutions
E-learning
no
Other requirements
Requirements to the students are solved in exercise
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Transformation properties of vectors and tensors. Analysis of strain at a point in a deformable body. Strain-displacement relations. The Green-Lagrange strain tensor, Cauchy`s small (linear) strain tensor. Small strain tensor invariants. Principal strains. Principal axes of strain. Spherical tensor, strain deviator tensor. Octahedral normal and shear strains. Compatibility of strain conditions. The state of stress at a point in a body. Stress tensor. Invariants of the stress tensor. Principal stresses, principal planes, principal directions of the stress tensor at a point. Spherical tensor and stress deviator. Normal and shear stresses on the octahedral plane. The method of Mohr`s circles. Cauchy`s differential equations of equilibrium. Physical equations for anisotropic, orthotropic, transversely isotropic and isotropic, linearly elastic homogeneous solid. Boundary conditions. Solution of the elastic problem, formulation in terms of displacements - Lamé (Navier) equations, formulation in terms of stresses - Beltrami-Michell equations. Planar problems of the theory of elasticity, plane stress and plane strain. Airy`s stress function, biharmonic differential equation in orthogonal Cartesian coordinates. The planar problem in polar coordinates. Planar axial-symmetric problem. The stress concentration due to a circular hole in an infinite plate of constant thickness. Pure bending of the circular curved bar. Bending of the circular curved bar with the force at the free end. The stress field around an edge dislocation. Line uniform continuous traction on the boundary of the elastic half-space – Flamant`s problem.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction