Course detail

# Continuum Mechanics

FSI-S1KAcad. year: 2019/2020

The course deals with the following topics: Introduction, basic terminology, bodies, motions, configurations. Foundation of the theory of finite strains. General equation of balance. Cauchy's I. and II. law of continuum mechanics. Geometrical equations, compatibility conditions, boundary conditions. Thermodynamic background of the theory of constitutive relations. Models of elastic behaviour. Hyperelastic materials. Isotropic elasticity and thermoelasticity. Anisotropic elasticity. Classical formulation of an elastic problem using differential approach. Deformation theory and incremental theory of plasticity. Variational principles in the infinitesimal strain theory. Weak solution. Axisymmetric problems. Plane strain/plane stress. Solution of two-dimensional elasticity problems. Airy's stress function. Foundation of the theory of plates and shells. Fundamentals of linear fracture mechanics. Remarks on Ritz method and FEM in continuum mechanics problems.

Guarantor

Learning outcomes of the course unit

Prerequisites

Co-requisites

Recommended optional programme components

Literature

Ondráček, E., Vrbka,J., Janíček, P.: Mechanika těles- pružnost a pevnost II (CS)

Janíček, P., Petruška, J.: Úlohy z pružnosti a pevnosti II (CS)

Nečas, J., Hlaváček, I.: Úvod do teorie pružných a pružně plastických těles (CS)

Němec,J. Dvořák,J., Hoschl. C.: Pružnost a pevnost ve strojírenství (CS)

Novacki W.: Teorija uprugosti (CS)

Planned learning activities and teaching methods

Assesment methods and criteria linked to learning outcomes

Language of instruction

Work placements

Aims

Specification of controlled education, way of implementation and compensation for absences

#### Type of course unit

Lecture

Teacher / Lecturer

Syllabus

Mechanical quantities in the theory of finite deformations. Transport theorem. Euler-Cauchy laws in finite deformations. Piola-Kirchhoff and Cauchy stress tensors.

Introduction to the theory of constitutive equations, axioms and thermodynamical restrictions for constitutive equations.

Models of elastic materials. Hyperelastic material. Isotropic and anisotropic materials. Thermoelastic materials.

Basic equations of the mathematical theory of linear elasticity. Differential equations of equilibrium, geometrical equations, compatibility equations, Hooke law, boundary conditions, classical formulation of basic boundary-value problems of elasticity.

Variational principles of the theory of infinitesimal deformations. Variational formulation and solution of basic boundary-value problems of the theory of elasticity. Weak solution.

Basic elasticity problems in curvilinear coordinates.

2D problems in the theory of elasticity. Airy stress function. Solution to 2D problems in terms of stresses.

Introdution into the theory of plate bending.

Introduction into the theory of shells.

Deformation and incremental theory of plasticity. Mises yield condition. Associated theory of plastic flow. The rule of normality.

Deformation variant of the finite element method for a 2D problem.

Brief resume of the course, time reserve.

Exercise

Teacher / Lecturer

Syllabus

Stress tensors. Principal stresses, invariants. Equations of balance.

Constitutive equations in the continuum mechanics. Thermodynamic laws.

Hyperelastic material. Neo-Hooke law, Mooney-Rivlin law. Hooke law for isotropic and anisotropic bodies.

Selected 3D problems of the linear theory of elasticity.

Variational methods in the theory of infinitesimal deformations.

Basic quantities of the continuum mechanics in curvilinear coordinates.

Axial-symmetric problems of the linear elasticity.

Solution of plane problems using Airy stress function.

Circular and circular plate with concentric hole.

Cylindrical shell.

Axisymmetric membrane shell.

Selected simple problem form the theory of plasticity.

Numerical methods in the elasticity problems. Awarding course-unit credits.