Development and Application of the Finite Element Method based on MatLab
1st Edition
Published on 10. May 2010
X, 64 pages
978-3-642-13153-0 (ISBN)
Description
The intention of this booklet is a brief but general introduction into the treatment of the Finite Element Method (FEM). The FEM has become the leading method in computer-oriented mechanics, so that many scienti?c brancheshavegrownup besides overthelastdecades. Nevertheless,theFEM today is a question of economy. On the one hand its industrial application is forced to reduce product development costs and time, on the other hand a large number of commercial FEM codes and a still growing number of software for e?ective pre- and postprocessors are available in the meantime. Due to that, today it is a quite challenging task to operate with all these di?erent tools at the same time and to understand all handling and so- tion techniques developed over the last years. So, we want to help in getting a deeper insight into the main "interfaces" between the "customers of the FEM" and the codes itself by providing a totally open structured FE-code based on Matlab, which is a very powerful tool in operating with matrix based formulations. That idea and conditions forced us some years ago to initiateDAEdalon as a tool for general FE developments in research appli- tions. In spite of still existing high sophisticated - mostly commercial - FE codes, the success and the acceptance of such a structured tool justify that decision afterwards more and more.
Reviews / Votes
From the reviews:
"The book is written for students of applied mechanics, mechanical and civil engineering sciences, and engineers interested in computer-aided technologies." (IEEE Control Systems Magazine, Vol. 30, December, 2010)
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05/2010
1st Edition
Springer
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Content
A Quick Start into DAEdalon.- Fundamentals of Solid (Continuum) Mechanics.- Constitutive Behavior.- FEM Implementation within Matlab.- Applications and Examples.- What Does DAEdalon Mean ? - Background for Computational System - and Greek Mythology.
"3 Constitutive Behavior (p. 27-28)
3.1 The Materials Point of View
The description of any material behavior within a ?nite element simulation requires a clearly structured interface within an element formulation. As stated before in (2.36), in Sec. 2.6.4 and in (2.53), the (local) material behavior is respected and needed for at the integration points while the integration loop on element level. According to the presented modular structure of DAEdalon, we intend to de?ne any constitutive model by the function MATMOD, where the deformation gradient F and the history database is given as input and the material response is given out in terms of the stress tensor and the material (tangent) modulus.
In that sense, linear or nonlinear material behavior is treated in the same way. So, the user has all possibilities in de?ning any deformation measure as function of the deformation gradient F and the history and take care for the conjugated stress tensor and its derivative. Please note, that the overall convergence behavior of a ?nite element solution procedure depends dramatically on the right formulation of the stress response and its derivative in form of the material modulus.
3.1.1 Stress Response
Basically, one has the free choice in formulating the material behavior with respect to any con?guration. There are many discussions on that topic, each with advances and each with negative aspects, but the overlaying element formulation has to be respected to take care on the energy turn over expressed by the tensors given by the material model, see Sec. 2.4.
3.1.2 The Material Modulus
The crucial task in the formulation and assembly of Kmat in (2.53) is the representation of the derivative of the stress response with respect to the applied deformation measure in the algorithmic setting. We illustrate here the results of that procedure for two typical material behaviors, namely hyperelasticity in its simplest form and ?nite plasticity, in the following. Generally, we have a look on the structure and the implementation of typical representations of forth order tensors like."
3.1 The Materials Point of View
The description of any material behavior within a ?nite element simulation requires a clearly structured interface within an element formulation. As stated before in (2.36), in Sec. 2.6.4 and in (2.53), the (local) material behavior is respected and needed for at the integration points while the integration loop on element level. According to the presented modular structure of DAEdalon, we intend to de?ne any constitutive model by the function MATMOD, where the deformation gradient F and the history database is given as input and the material response is given out in terms of the stress tensor and the material (tangent) modulus.
In that sense, linear or nonlinear material behavior is treated in the same way. So, the user has all possibilities in de?ning any deformation measure as function of the deformation gradient F and the history and take care for the conjugated stress tensor and its derivative. Please note, that the overall convergence behavior of a ?nite element solution procedure depends dramatically on the right formulation of the stress response and its derivative in form of the material modulus.
3.1.1 Stress Response
Basically, one has the free choice in formulating the material behavior with respect to any con?guration. There are many discussions on that topic, each with advances and each with negative aspects, but the overlaying element formulation has to be respected to take care on the energy turn over expressed by the tensors given by the material model, see Sec. 2.4.
3.1.2 The Material Modulus
The crucial task in the formulation and assembly of Kmat in (2.53) is the representation of the derivative of the stress response with respect to the applied deformation measure in the algorithmic setting. We illustrate here the results of that procedure for two typical material behaviors, namely hyperelasticity in its simplest form and ?nite plasticity, in the following. Generally, we have a look on the structure and the implementation of typical representations of forth order tensors like."
