Analiza Kirschovog problema klasičnom i mikropolarnom teorijom elastičnosti

Abstract

U radu se provodi analitička analiza jednoosno vlačno opterećene beskonačnehomogene ploče s kružnim otvorom (tzv. Kirschov problem). Eksperimentalnirezultati iz literature daju vrijednosti koncentracije naprezanja na rubu otvora, kojesu uvijek manje od teorijske pretpostavke temeljene na klasičnoj teoriji elastičnosti tese za bolje opisivanje razmatranog problema predlaže primjena mikropolarne teorijekontinuuma. U radu je stoga prikazana detaljna analiza temeljena na mikropolarnojteoriji, a dobiveni rezultati tvore bitnu teorijsku podlogu za budući rad.

Hexahedral finite elements with enhanced fixed‐pole interpolation for linear static and vibration analysis of 3D micropolar continuum

“…To the best of our knowledge, an analytical solution for the discussed problem according to the micropolar theory only exists in the case of an infinite plate 76,77 . The stress concentration factor in those solutions decreases compared to Kirsch's analytical solution when the values of the coupling number and the characteristic length for bending are increased 78 …”

“…76,77 The stress concentration factor in those solutions decreases compared to Kirsch's analytical solution when the values of the coupling number and the characteristic length for bending are increased. 78 A plate with the dimensions much larger than the circular hole in the middle is numerically analysed to test the proposed micropolar finite element and compare it to some existing finite elements. Only a quarter of the plate has been analysed with the appropriate boundary conditions along the symmetry lines constraining the microrotations and displacements perpendicular to these lines (as shown in Figure 7).…”