Special Numerical Techniques to Joint Design

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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 as 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 postcomputational 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 chapter 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.

Keywords

Numerical method Finite element method Boundary element method Finite difference method Substructure Submodel Static condensation Superelement Internal forces Enforced displacement Weighted residual method Weighting function Strong formulation Weak formulation Inverse formulation Residuum Partial differential equation Fundamental solution Representation formula Load point 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Esslingen University of Applied SciencesFaculty of Mechanical EngineeringEsslingenGermany

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