By Michael Schäfer
This booklet is an advent to trendy numerical equipment in engineering. It covers functions in fluid mechanics, structural mechanics, and warmth move because the such a lot correct fields for engineering disciplines corresponding to computational engineering, clinical computing, mechanical engineering in addition to chemical and civil engineering. The content material covers all elements within the interdisciplinary box that are crucial for an ''up-to-date'' engineer.
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This publication is an advent to trendy numerical tools in engineering. It covers purposes in fluid mechanics, structural mechanics, and warmth move because the such a lot suitable fields for engineering disciplines reminiscent of computational engineering, clinical computing, mechanical engineering in addition to chemical and civil engineering.
Extra resources for Computational engineering: introduction to numerical methods
In the following we will consider some of these special cases, which often can be found in applications. 2 Bars and Beams The simplest special case of a linear elasticity problem results for a tensile bar. We consider a bar with length L and cross-sectional area A = A(x1 ) as shown in Fig. 8. 4 Structural Mechanics Problems 31 x3 ✻ x3 ✻ ✲ x1 ✛ ✲ ✲ fl ✲ ✲ kL ✲ ✲ A(x1 ) ✲ L ✲ x2 Cross-sectional area Fig. 8. Tensile bar under load in longitudinal direction forces only act in x1 -direction, the cross-section remains plane and moves only in x1 -direction.
9). We will focus here on the shear-rigid beam (or Bernoulli beam). This approximation is based on the assumption that during the bending along one main direction, plane crosssections remain plane and normals to the neutral axis (x1 -axis in Fig. 9) remain normal to this axis also in the deformed state. Omitting the latter assumption one obtains the shear-elastic beam (or Timoshenko beam). x3 ✻ ❄ ❄ ❄ fq ❄ ❄ x3 ❄ ❄ ❄ ❄ ✲ x1 QL ✛ ✲ L ❄ ✻ A(x1 ) ✲ x2 Cross-sectional area Fig. 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 .
Thermally coupled ﬂuid-solid problem: conﬁguration and boundary conditions (left), streamlines, displacements, and global temperature distribution (right) Multi-Coupled Problem Finally, as an example with multiple ﬂuid-solid coupling mechanisms, we consider the multi-ﬁeld problem determining the functionality of a complex antenna structure as they are employed, for instance, in space applications for tracking satellites and space probes (see Fig. 27). 6 Coupled Fluid-Solid Problems 55 Fig. 27. 28 schematically illustrates the problem situation and the interactions.