By Michael Schäfer
This e-book is an creation to fashionable numerical equipment in engineering. It covers purposes in fluid mechanics, structural mechanics, and warmth move because the such a lot correct fields for engineering disciplines comparable to computational engineering, medical computing, mechanical engineering in addition to chemical and civil engineering. The content material covers all points within the interdisciplinary box that are crucial for an ''up-to-date'' engineer.
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Additional info for Computational Engineering — Introduction to Numerical Methods
6 Coupled Fluid-Solid Problems 55 Fig. 27. 28 schematically illustrates the problem situation and the interactions. The key parameters for the ﬂow are the wind velocity and the site topography. The temperature distribution is inﬂuenced by the sun radiation, the ambient temperature, as well as by the ﬂow. The structural deformation is aﬀected by the antenna weight, the temperature gradients, and the ﬂow forces. From the deformation of the structure, the pointing error describing the deviation of the axis of the reﬂector from the optical axis can be determined.
In principle, for structural mechanics problems one distinguishes between linear and non-linear models, where the non-linearity can be of geometrical and/or physical nature. Geometrically linear problems are characterized by the linear strain-displacements relation (see Sect. 25) whereas physically linear problems are based on a material law involving a linear relation between strains and stresses. 4 the diﬀerent model classes are summarized. 4. 4 Structural Mechanics Problems 27 elasticity, which can be used for many typical engineering applications.
27. Sun radiation Ambient temperature Antenna weight Thermal analysis Tem pera ture Structural analysis Flow analysis rces d fo Flui Deformation Wind velocity Site topography Surface accuracy Pointing error Fig. 28. Multi-ﬁeld analysis of antennas 56 2 Modeling of Continuum Mechanical Problems Exercises for Chap. 1. Given is the deformation x(a, t) = (a1 /4, et (a2 +a3 ) + e−t (a2 −a3 ), et (a2 +a3 ) − e−t (a2 −a3 )) . (i) Compute the Jacobi determinant of the mapping x = x(a, t) and formulate the reverse equation a = a(x, t).