Special Numerical Techniques to Joint Design
 Prof. Andreas Öchsner
 … show all 1 hide
Abstract
The aim of this chapter is to introduce special numerical techniques. The first part covers special finite element techniques which reduce the size of the computational models. In the case of the substructuring technique, internal nodes of parts of a finite element mesh can be condensed out so that they do not contribute to the size of the global stiffness matrix. A post computational step allows to determine the unknowns of the condensed nodes. In the case of the submodel technique, the results of a finite element computation based on a coarse mesh are used as input, i.e., boundary conditions, for a refined submodel. The second part of this chapters introduces alternative approximation methods to solve the partial differential equations which describe the problem. The boundary element method is characterized by the fact that the problem is shifted to the boundary of the domain and as a result, the dimensionality of the problem is reduced by one. In the case of the finite difference method, the differential equation and the boundary conditions are represented by finite difference equations. Both methods are introduced based on a simple one‐dimensional problem in order to demonstrate the major idea of each method. Furthermore, advantages and disadvantages of each alternative approximation methods are given in the light of the classical finite element simulation. Whenever possible, examples of application of the techniques in the context of adhesive joints are given.
 Banerjee, PK (1994) Boundary element methods in engineering. McGraw‐Hill, London
 Bathe, KJ (1996) Finite element procedures. Prentice‐Hall, Upper Saddle River
 Beer, G, Smith, I, Duenser, C (2008) The boundary element method with programming. Springer, Wien
 Brebbia, CA, Felles, JCF, Wrobel, JCF (1984) Boundary element techniques: theory and applications. Springer, Berlin CrossRef
 Bushnell, D, Almroth, BO, Brogan, F (1971) Finite‐difference energy method for nonlinear shell analysis. Comput Struct 1: pp. 361387 CrossRef
 Collatz, L (1966) The numerical treatment of differential equations. Springer, Berlin
 Cook, RD, Malkus, DS, Plesha, ME, Witt, RJ (2002) Concepts and applications of finite element analysis. Wiley, New York
 Crocombe, AD, Bigwood, DA (1992) Development of a full elasto‐plastic adhesive joint design analysis. J Strain Anal Eng 27: pp. 211218 CrossRef
 Dohrmann, CR, Key, SW, Heinstein, MW (2000) A method for connecting dissimilar finite element meshes in two dimesions. Int J Numer Meth Eng 48: pp. 655678 CrossRef
 Fish, J, Belytschko, T (2007) A first course in finite elements. Wiley, Chichester CrossRef
 Forsythe, GE, Wasow, WR (1960) Finite‐difference methods for partial differential equations. Wiley, New York
 de G Allen, DN (1955) Relaxation methods. McGraw‐Hill, New York
 Gaul, L, Kögl, M, Wagner, M (2003) Boundary element methods for engineers and scientists. Springer, Berlin
 Gmür, TC, Kauten, RH (1993) Three‐dimensional solid‐to‐beam transition elements for structural dynamics analysis. Int J Numer Meth Eng 36: pp. 14291444 CrossRef
 Groth, HL (1986) Calculation of stresses in bonded joints using the substructuring technique. Int J Adhes Adhes 6: pp. 3135 CrossRef
 Knight, NF, Ransom, JB, Griffin, OH, Thompson, DM (1991) Global/local methods research using a common structural analysis framework. Finite Elem Anal Des 9: pp. 91112 CrossRef
 Love, AEH (1944) A treatise on the mathematical theory of elasticity. Dover Publications, Mineola
 Mackerle, J (1995) Fastening and joining: finite element and boundary element analyses – a bibliography (1992–1994). Finite Elem Anal Des 20: pp. 205215 CrossRef
 Mackerle, J (1995) Some remarks on progress with finite elements. Comput Struct 55: pp. 11011106 CrossRef
 Mitchell, AR, Griffiths, DF (1980) The finite difference method in partial differential equations. Wiley, New York
 Raamachandran, J (2000) Boundary and finite elements – theory and problems. Alpha Science International, Pangbourne
 Raghu, ES (2009) Finite element modeling techniques in MSC.NASRAN and LS/DYNA. Arup, London
 Sokolnikoff, I (1956) Mathematical theory of elasticity. McGraw‐Hill, New York
 Southwell, RV (1946) Relaxation methods in theoretical physics. Clarendon Press, Oxford
 Stratford, T, Cadei, J (2006) Elastic analysis of adhesion stresses for the design of a strengthening plate bonded to a beam. Constr Build Mater 20: pp. 3445 CrossRef
 Chapter 5: Differential equations. Visual Numeric, Houston
 Vable, M, Maddi, JR (2010) Boundary element analysis of adhesively bonded joints. Int J Adhes Adhes 30: pp. 191199 CrossRef
 Wahab, MMA, Ashcroft, IA, Crocombe, AD (2004) A comparison of failure prediction methods for an adhesively bonded composite beam. J Strain Anal 39: pp. 173185 CrossRef
 Wang, RX, Cuia, J, Sinclair, AN, Spelt, JK (2003) Strength of adhesive joints with adherend yielding: I. analytical model. J Adhesion 79: pp. 2348 CrossRef
 Wang, ZY, Wang, L, Guo, W, Deng, H, Tong, JW, Aymerich, F (2009) An investigation on strain/stress distribution around the overlap end of laminated composite single‐lap joints. Compos Struct 89: pp. 589595 CrossRef
 Xu, W, Li, G (2010) Finite difference three‐dimensional solution of stresses in adhesively bonded composite tubular joint subjected to torsion. Int J Adhes Adhes 30: pp. 191199 CrossRef
 Zhao, C, Hobbs, BE, Mühlhaus, HB, Ord, A (1999) A consistent point‐searching algorithm for solution interpolation in unstructured meshes consisting of 4‐node bilinear quadrilateral elements. Int J Numer Meth Eng 45: pp. 15091526 CrossRef
 Zienkiewicz, OC, Taylor, RL (2000) The finite element method – volume 1: the basis. Butterworth‐Heinemann, Oxford
 Title
 Special Numerical Techniques to Joint Design
 Reference Work Title
 Handbook of Adhesion Technology
 Reference Work Part
 Part E
 Pages
 pp 661688
 Copyright
 2011
 DOI
 10.1007/9783642011696_26
 Print ISBN
 9783642011689
 Online ISBN
 9783642011696
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors

 Lucas F. M. da Silva ^{(100)}
 Andreas Öchsner ^{(101)}
 Robert D. Adams ^{(102)}
 Editor Affiliations

 100. Department of Mechanical Engineering (DEMec), Faculty of Engineering of the University of Porto (FEUP)
 101. Faculty of Mechanical Engineering, Universiti Teknologi Malaysia
 102. Emeritus Professor of Applied Mechanics, University of Bristol Queen's Building University Walk
 Authors

 Prof. Andreas Öchsner ^{(1)} ^{(2)}
 Author Affiliations

 1. Faculty of Mechanical Engineering, Technical University of Malaysia, 81310 UTM, Skudai, Johor, Malaysia
 2. The University of Newcastle, Callaghan, New South Wales, 2308, Australia
Continue reading...
To view the rest of this content please follow the download PDF link above.