Applied Structural Mechanics: Fundamentals of Elasticity, by Prof. Dr.-Ing. H. Eschenauer, Prof. Dr. techn. N. Olhoff,

By Prof. Dr.-Ing. H. Eschenauer, Prof. Dr. techn. N. Olhoff, Prof. Dr. Dr.-Ing.E.h W. Schnell (auth.)

In view of the transforming into value of product legal responsibility and the call for for success of maximum standards for brand spanking new items, this e-book presents the fundamental instruments for setting up version equations in structural mechanics. also, it illustrates the transition and interrelation among structural mechanics and structural optimization. these days, this new course is intensely very important for extra potency within the layout process.
The e-book is split into 4 components overlaying the basics of elasticity, aircraft and curved load-bearing constructions and structural optimization. each one half comprises various difficulties and recommendations, so as to give you the scholar with the elemental instruments from the sector of elasticity thought and help the pro engineer in fixing problems.
Fachgebiet: Mechanical Engineering Zielgruppe: examine and Development

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Extra resources for Applied Structural Mechanics: Fundamentals of Elasticity, Load-Bearing Structures, Structural Optimization

Example text

1) with the position vector r ( t i ) and the displacement vector v ( t i ) of the same material point P of the undeformed body B. 2) dv = dF - dr = V dr , where V is the tensor of the displacement derivatives. 25) the base vectors gj and gi result from the total differential of the respective position vectors dr ar j =aC. dt = r ' l' dt j = g. dt j 1 _ ~ dti _ ~ dti d r~ -- a F. dti <, - r. <, - g. :Jb) These infinitesimal changes of the position vectors lead to the points Q and to P and P (see Fig.

E) The theorem of mass conservation ( dV = dV) and the volume forces in the deformed and undeformed bodies (f == f) are equal. 2 Energy expressions First, we consider the uniaxial state of stress of a rod subjected to a single force F. The relation between force and displacement can be assumed to be nonlinear as well as linear (Fig. 1). The external work done by the normal force F against the displacement 0 u is given by oW = Foil. g. deformation differentials, strain differentials. For these quantities it is assumed that they are virtual (not existing in reality), infinitesimally small and geometrically compatible.

1 X Kinematics of a deformable body 27 1 Fig. 1: Kinematics of a deformable body Position vector r of the material point P of the deformed body 13 (Fig. 1) with the position vector r ( t i ) and the displacement vector v ( t i ) of the same material point P of the undeformed body B. 2) dv = dF - dr = V dr , where V is the tensor of the displacement derivatives. 25) the base vectors gj and gi result from the total differential of the respective position vectors dr ar j =aC. dt = r ' l' dt j = g.

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