Download e-book for kindle: 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.)

ISBN-10: 3540612327

ISBN-13: 9783540612322

ISBN-10: 3642592058

ISBN-13: 9783642592058

In view of the turning out to be value of product legal responsibility and the call for for success of utmost necessities for brand spanking new items, this publication 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 very vital for extra potency within the layout process.
The e-book is split into 4 elements masking the basics of elasticity, aircraft and curved load-bearing constructions and structural optimization. every one half comprises a number of difficulties and suggestions, for you to give you the scholar with the elemental instruments from the sphere of elasticity concept and support the pro engineer in fixing problems.
Fachgebiet: Mechanical Engineering Zielgruppe: study and Development

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

Example text

Curvilinear coordinates Base vectors - metric tensor In the three - dimensional space a vector r can be presented in Cartesian coordinates xi and in curvilinear coordinates indicated by ~i (i = 1,2,3) (Figs. 4). ~2 ~3 X 3 X 2 Fig. 4: Curvilinear coordinates and base vectors Fig. 24) (xi) Base vectors ei or = 0 xi = r,; gi or = if" = r,i . 25) Relation between base gi ( ~i) and orthonormalized base e i gk = oxi o~kei . 26) Length of a line element ds 2 = dr . dr -----+ First fundamental form of a surface.

36b} Divergence of a vector v · V d lV = nv . V = V jl . = J 1 -c) . ({i r;; g v j) . 38} LAPLACE operator 6. iP 1 = V2 iP =. dlV grad iP = iP Iii = {i (r;; Yg gjk iP ,k ) ,j . 41} 16 2 Tensor algebra and analysis Example: Application of the previous formulas to cylindrical coordinates Single-valued relations between Cartesian coordinates xi and cylindrical coordinates i read as follows (see Fig. 4a) For example: g22 = g2 . 22 ) sm e + (e12) cos 22e = (12 e) . 5c), because of ---+ for i =f. 5c) g (ii) g(ii) = 1 -+ ( ii) g 1 =-g( ii) Fig.

IP 1 = V2 iP =. dlV grad iP = iP Iii = {i (r;; Yg gjk iP ,k ) ,j . 41} 16 2 Tensor algebra and analysis Example: Application of the previous formulas to cylindrical coordinates Single-valued relations between Cartesian coordinates xi and cylindrical coordinates i read as follows (see Fig. 4a) For example: g22 = g2 . 22 ) sm e + (e12) cos 22e = (12 e) . 5c), because of ---+ for i =f. 5c) g (ii) g(ii) = 1 -+ ( ii) g 1 =-g( ii) Fig. 45) Determinant g of the covariant metric tensor Ig I = I I = gij 1 0 0 0 U1)2 0 o o 1 = (,1)2 .

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Applied Structural Mechanics: Fundamentals of Elasticity, Load-Bearing Structures, Structural Optimization by Prof. Dr.-Ing. H. Eschenauer, Prof. Dr. techn. N. Olhoff, Prof. Dr. Dr.-Ing.E.h W. Schnell (auth.)


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