The Art of Modeling in Solid Mechanics
Modeling is one of the main tasks in engineering to predict the behavior and response of assemblies, structures, or vehicles. This contribution is aimed at modeling in solid mechanics. Due to the necessity to use numerical methods for the solution of most
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stitute of Continuum Mechanics, Gottfried Wilhelm Leibniz Universit¨ at, Hannover, Germany Abstract Modeling is one of the main tasks in engineering in order to predict the behaviour and response of assemblies, structures or vehicles. This contribution is aimed at modeling in solid mechanics. Due to the necessity to use numerical methods for the solution of most theoretical models it will focuss on theoretical models as well as on numerical simulation models associated with engineering applications in solid mechanics.
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Models
Models can be derived for many tasks in science, buisiness and engineering. The evolution of all these different areas of application shows that without models mankind would not be were it is today. In order to understand this development one has to ask at least one question. 1.1
What is a model?
Modeling of engineering structures is a task that has a long history. There exist many models that can be applied to predict the behaviour of different processes. Since today often numerical simulation tools are used that have a certain model inside, it is more and more necessary to have a deep knowledge of modeling in order to use the correct tools for a proper prediction. Here not all models can be discussed, however the variety of mechanical models will be investigated and ordered such that engineers can pick the ones necessary to describe the behaviour of solids and structures adequately. In engineering it is generally not possible to apply a full scale model when designing a structure or machine. For example a bridge of a length of 1000 meters willl not be modeled as one piece in a giant computer. This is due to the fact that different length scales have to be resolved when looking at different structural elements that form the bridge. This is e.g. on one
© CISM International Centre for Mechanical Sciences 2017 F. Pfeiffer and H. Bremer (eds.), The Art of Modeling Mechanical Systems, CISM International Centre for Mechanical Sciences 570, DOI 10.1007/978-3-319-40256-7_6
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hand the basic structure and on the other side connections between different structural elements. Here the length scale difference can easily be of the order of 1000. Models can be derived for different length scales. In engineering one could start from an atomistic description of materials. However due to complexity and problems size this is not an adequate modeling approach. Also the molecular dynamics approach that is related to nano and micrometer scales is not feasible to describe real engineering structures at meter scales. Thus we need a continuum approach that is based on the theory of continuum mechanics. Even with these in general three-dimensional models it is not possible to design real structures, like bridges or skyscrapers since three-dimensional models will lead to a number of unknowns that cannot be solved in a design office. Thus reduced models – like trusses, beam, plates and shells – have to be applied that are able to reproduce the main structural behaviour of the building, are consistent w
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