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Plane Insteady Problem of Punch

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image of Multidiscipline Modeling in Materials and Structures

The mixed unsteady problem of stress intensity coefficients calculations near edge of rigid punch acted on elastic halfplane is solved analytically and numerically. The obtained tables are important to clarify possibility of fracture of material of halfplane for any given boundary displacement of punch, which is realized by placing of calculated stress intensity coefficients in known yielding conditions. The solution of this boundary value problem, when on left part of boundary of halfplane stresses are equal to zero, and on right one are given displacements, is solved by method of integral transformations and solution of second order Wienner-Hopf system. The transformed Hilbert problem has discontinuous on infinity matrix, which is improved and for new continuous coefficient solution is brought to Fredholm system, the last one is solved numerically. Furthermore are carried out inverse integral transformations, solutions for stresses under punch are brought to effective Smirnov-Sobolev form in one quadrature, which is calculated numerically.

Affiliations: 1: Institute of Mechanics, Armenian National Academy of Sciences, Marshal Baghramyan 24b, Yerevan, 375019, Armenia; 2: Doctor of Phis.-Math sciences, Goris State University, Goris, str. Avangard, 2, Armenia


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