In this book the real analytic solutions for the “Disc with Circular Inclusion” under normal- and shear force at plane-strain state (EVZ) are presented. The associated solution process, which was developed according to the principle of statically indeterminate systems, is documented extensively. The solutions are given in terms of mechanical quantities (deformations, strains and stresses). Due to the superposition of the solutions for normal force in x- and y-direction and shear force the plane strain-stress relation can be formulated. The validation of the real analytic solutions is carried out by numeric FEM solution results. Comparing the results of the finite and infinite disc there is, however, a very high correspondence of all mechanical quantities. Therefore it can be assumed the real analytical solutions are the exact solutions.
Author(s): Thomas Ranz
Series: SpringerBriefs in Applied Sciences and Technology
Publisher: Springer
Year: 2021
Language: English, German
Pages: 100
City: Cham
Foreword
Table of contents
Formula symbols, symbols and abbreviations
Abstract
1 Introduction
1.1 Overview of chapter
1.2 Literature survey
2 Initial position — Solutionprocess
3 Disc with circular inclusion — Plane strain condition
3.1 Unidirectional Force
3.1.1 Unidirectional Force σ_y
3.1.2 Procedure
3.1.3 Disc with hole under unidirectional force
3.1.4 Disc with hole under radial bearing load
3.1.5 Disc with hole under tangential bearing load
3.1.6 Circular disc under radial edge load
3.1.7 Circular disc under tangential edge load
3.1.8 Compatibility
3.1.9 Mechanical quantities for the disc with circular inclusion
3.1.10 Disc with hole under unidirectional force in x-direction
3.2 Shear force
3.2.1 Procedure
3.2.2 Disc with hole under shear load
3.2.3 Disc with hole under radial bearing load
3.2.4 Disc with hole under tangential bearing load
3.2.5 Circular disc under radial edge load
3.2.6 Circular disc under tangential edge load
3.2.7 Compatibility
3.2.8 Mechanical quantities for the disc with circular inclusion
3.3 Plane elasticity — disc with circular inclusion
3.3.1 Compliance — unidirectional load in x-direction
3.3.2 Compliance — unidirectional load in y-direction
3.3.3 Compliance — shear load
3.3.4 Elastic law for plane strain in matrix notation
3.4 Substitution at the constitutive level
4 Validation of the analytical solution
4.1.1 Disc with circular inclusion
5 Summery and outlook
6 Bibliography
