Phenomena occurring during a contact of two bodies are encountered in everyday life. In reality almost every type of motion is related to frictional contact between a moving body and a ground. Moreover, modeling of simple and more complex processes as nailing, cutting, vacuum pressing, movement of machines and their elements, rolling or, finally, a numerical simulation of car crash tests, requires taking contact into account. Therefore, its analysis has been a subject of many research efforts for a long time now. However, it is author’s opinion that there are relatively few efforts related to contact between structural elements, like beams, plates or shells. The purpose of this work is to fill this gap. It concerns the beam-to-beam contact as a specific case of the 3D solids contact. A numerical formulation of frictional contact for beams with two shapes of cross-section is derived. Further, a couple of effective methods for modeling of smooth curves representing beam axes are presented. A part of the book is also devoted to analyze some aspects of thermo-electro-mechanical coupling in contact of thermal and electric conductors. Analyses in every chapter are illustrated with numerical examples showing the performance of derived contact finite elements.
Author(s): Przemyslaw Litewka
Edition: 1st Edition.
Publisher: Springer
Year: 2010
Language: English
Pages: 159
Tags: Математика;Вычислительная математика;Метод конечных элементов;
front-matter.pdf......Page 1
From the Ancient Egypt to the Computer Era......Page 11
Frictionless Contact between Solids......Page 13
Methods of Introduction of Contact Constraints......Page 15
The Finite Element Method in Contact Analysis......Page 17
Friction Constraints......Page 19
Assumptions......Page 22
Penetration Function......Page 24
Contact Search......Page 28
Weak Form and Kinematic Variables for Contact......Page 33
Discretisation of Kinematic Variables......Page 36
Residual Vector and Tangent Stiffness Matrix......Page 38
Introduction......Page 40
Example 1......Page 41
Example 2......Page 43
Example 3......Page 44
Friction Model......Page 47
Kinematic Variables for Friction......Page 51
Weak Form Components due to Friction......Page 55
Discretization of Friction Terms Present in Weak Form......Page 57
Residual Vector and Tangent Stiffness Matrix for Friction......Page 60
Introduction......Page 65
Example 1......Page 66
Example 2......Page 69
Example 3......Page 71
Example 4......Page 74
Example 5......Page 76
General Remarks on Smoothing of Contact Facets......Page 78
Inscribed Curve Algorithm......Page 79
Node-Preserving Algorithm......Page 83
Inscribed Curve Elements......Page 86
Node-Preserving Elements......Page 88
Introduction......Page 90
Example 1......Page 91
Example 2......Page 93
Example 3......Page 95
Example 4......Page 98
Example 5......Page 100
Example 6......Page 102
Electro-mechanical Variables for Contact......Page 105
Weak Formulation of Electro-mechanical Contact......Page 109
Beam Finite Element for the Electric Current Flow......Page 111
Discretisation and Electro-mechanical Contact Finite Element......Page 112
Introduction......Page 115
Example 1......Page 116
Example 2......Page 117
Example 3......Page 119
Example 4......Page 122
Example 5......Page 123
Introduction......Page 126
Thermo-mechanical Beam Finite Element......Page 127
Variables for Thermo-mechanical Contact......Page 130
Weak Form for Thermo-mechanical Contact......Page 131
Discretisation and Thermo-mechanical Contact Beam Finite Element......Page 132
Example 1......Page 136
Example 2......Page 139
Summary and Outlook......Page 140
back-matter.pdf......Page 142
