# Computational engineering. Introduction to Numerical Methods by Michael Schäfer

By Michael Schäfer

This ebook is an creation to fashionable numerical tools in engineering. It covers purposes in fluid mechanics, structural mechanics, and warmth move because the so much correct fields for engineering disciplines similar to computational engineering, clinical computing, mechanical engineering in addition to chemical and civil engineering. The content material covers all features within the interdisciplinary box that are crucial for an ''up-to-date'' engineer.

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Thermally coupled problem As an example of a thermally coupled ﬂuid-solid problem we consider a hollow thick walled massive pipe coaxially surrounded by another pipe conveying a ﬂuid. The pipes are assumed to be inﬁnitely long such that plane strain conditions for the solid part can be applied. The (two-dimensional) problem conﬁguration with boundary conditions is sketched in Fig. 26 (left). The inner 54 2 Modeling of Continuum Mechanical Problems Fig. 25. Streamlines and horizontal ﬂuid velocity for ﬂow around cylinder with ﬂuidstructure interaction boundary of the solid pipe is ﬁxed and imposed with a constant temperature T = Th .

9. Beam under vertical load Under the assumptions for the shear-rigid beam, the displacement u1 can be expressed by the inclination of the bending line u3 (deﬂection parallel to the x3 -axis): u1 = −x3 ∂u3 . ∂x1 In the strain tensor, just as for the tensile bar, only the component ε11 = ∂u1 ∂ 2 u3 = −x3 ∂x1 ∂x21 is diﬀerent from zero. 41) where fq = fq (x1 ) denotes the continuous lateral load (uniform load) of the beam in x3 -direction. For instance, to take into account the self-weight of the beam one has again fq = ρAg, where the acceleration of gravity g now is acting in x3 -direction.

Aeroelasticity of bridges or airplanes, injection systems, valves, pumps, airbags, . . ). , heat exchangers, cooling of devices, thermal processes in combustion chambers, chemical reactors, . . ). In the following we will address some special modelling aspects which arise due to the coupling. Afterwards we will give a couple of exemplary applications for the above mentioned problem classes. Fluid (vi , p, T ) Fluid properties ✻ ✲ Forces ✛ Deformations Convective heat transfer Thermal stresses ❄ Solid (ui , T ) ✻ Mechanical dissipation ❄ Temperature T Fig.