By Mark L. Kachanov, B. Shafiro, I. Tsukrov

This guide is a suite of elasticity suggestions. a few of the effects offered the following can't be present in textbooks and come in clinical articles simply. a few of them have been received within the closed shape particularly lately. The recommendations were completely checked and diminished to a "user pleasant" shape. each attempt has been made to maintain the e-book freed from misprints. the speculation of elasticity is a mature box and a number of strategies are ava- capable. We needed to make offerings in deciding on fabric for this ebook. The emphasis is made on effects suitable to common good mechanics and fabrics technology appli- tions. options relating to structural mechanics (beams, plates, shells, etc.) are ignored. The content material is proscribed to the linear elasticity. we're thankful to B. Nuller for numerous clarifications in regards to the touch pr- lem and to V. Levin for feedback on Eshelby's challenge. We additionally take pleasure in a n- ber of comments and reviews made via L. Germanovich, I. Sevostianov, O. Zharii and R. Zimmerman. we're relatively indebted to E. Karapetian for a considerable assist in placing the fabric together.

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However, the latter appears to have a number of misprints and undefined constants, and the attempts to obtain corrected version of the solution directly from the authors were unsuccessful. 1. Force normal to the boundary Point force F are: = F3e3 is normal to the boundary of the half-space. The displacements where gi aOl = C11 - C13 h i (i = 1,2) g2 = -F3-----21r(blg2 - b2g1) The stress field in this problem is given by {g' z. I 2 0"12 =2C66 LaOiVi[ . I ~)] D. D. 1 1 I)]} +----z-;;z 49 Point forces and systems of point forces where aR3 denotes shear stress component associated with the directions of R and e3.

2. Plane of elastic symmetry If XIX2 is a plane of elastic symmetry, there are 13 independent elastic constants: components 1113,1123,1213,1223,1322,1333,2223 and 2333 of Sijkl and Cijkl are equal to zero. In two index Voight's notation, the matrix of elastic compliances has the form Sll S12 S13 SI2 S22 S23 S13 S23 S33 0 0 SI6 0 0 S26 0 0 S36 0 0 0 0 0 0 S44 S45 S45 S55 0 0 SI6 S26 S36 0 0 S66 Note that the plane problem of elasticity for an anisotropic solid can be formulated only in the plane of elastic symmetry (imposition of a 2-D stress (or strain) in other planes may result in 3-D strain (or stress) state).

A major simplification is possible in the case when this system of forces is distributed in a small volume (the distance from ~ to the point of observation x is much larger than the size of this volume). In this case, the fields at the point x can be represented, to within small values of higher order, as a sum of the fields generated by the following force system resultants applied at the point ~ (see Lur'e, 1964, 1970, for discussion): (a) Principal vector N F= LF(i) i=1 (b) Moment about point ~ N M~ N = LM~(F(i») = Lr(i) i=1 x F(i) i=1 (c) Three mutually orthogonal dipoles.