By A.M. Linkov
by the writer to the English version The publication goals to give a robust new device of computational mechanics, complicated variable boundary critical equations (CV-BIE). The e-book is conceived as a continuation of the classical monograph by means of N. I. Muskhelishvili into the pc period. years have handed because the Russian version of the current publication. we've seen transforming into curiosity in numerical simulation of media with inner constitution, and feature proof of the opportunity of the hot tools. The proof used to be specifically transparent in difficulties with regards to a number of grains, blocks, cracks, inclusions and voids. This caused me, while getting ready the English version, to put extra emphasis on such themes. the opposite switch used to be encouraged by way of Professor Graham Gladwell. It used to be he who prompt me to abridge the chain of formulae and to extend the variety of examples. Now the reader will locate extra examples displaying the aptitude and benefits of the research. the 1st bankruptcy of the publication incorporates a basic exposition of the idea of actual variable potentials, together with the hypersingular strength and the hypersingular equations. This makes up for the absence of such exposition in present textbooks, and divulges very important hyperlinks among the true variable BIE and the complicated variable opposite numbers. The bankruptcy can help readers who're studying or lecturing at the boundary point method.
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Extra info for Boundary Integral Equations in Elasticity Theory
It is also true in a more general case; its proof is given in § 26. For a single closed contour we have cp+(t) = cp(t), cp-(t) = 0 (see, e. g. Muskhelishvili [5, § 73]). 28) becomes
The initial complex fields U/(z"t) and U/(z,t) may be also easily obtained by substitution of the complex functions by Kolosov-Muskhelishvili (KM) for point forces (Muskhelishvili [5, § 57]) into Muskhelishvili's equations for displacements (Muskhelishvili [5, § 32]). This was illustrated by Linkov and Mogilevskaya . Here we have preferred to derive U/(z, t) and U/(z,t) directly from the real Kelvin's solution to follow the theory of real potentials without employing results based on other methods.
3) satisfy elasticity equations for displacements and have limits when a fIeld point x tends to a point Xo on the boundary L. 3) by applying the traction operator, give the corresponding fIelds of stresses, and also have limits. 19) satisfied. By taking the limit when a field point x tends to a point Xo on the contour, and using the boundary conditions, we arrive at boundary integral equations. 1) leads to a Fredholm equation of the first kind. This makes it inconvenient if displacements are prescribed on the boundary.