Analogije modela stanja napona, stanja deformacija i stanja inercije masa napregnutih deformabilnih tela

摘要

The paper introduces the notions of the specific deformation vector δ_n for the line element drawn from the point N in the direction of the unit vector n and the mass inertia vector of the body for the axis oriented by the unit vector n. A comparative analogy is drawn between the total stress vector at the point N for the plane with the normal n and vector of the specific deformation for the line element in the direction of the unit vector n, and the mass inertia vector of the body for the axis oriented by the unit vector n. The paper points out analogies between the stress tensor matrices, the stressed deformable body, deformation tensor and the tensor matrices of mass inertia of a body. It also points out the identity of the mathematical models for the determination of the principal stress directions, principal dilations directions and principal inertia axes as well as an analogy between the plane of the shesring stresses extrime values, the line elements directions between which the extreme values of the specific deformation, i.e., sliding occur and the direction of the inertial asymmetry for the greatest values of the centrifugal moments body mass accur. Then an expression is deduced for the specific deformation work (elastic potencial) of the stressed body as the function of the specific deformation vector of the line elements in the three orthogonal directions and of the displacement vector.%U radu se uvode pojmovi: vektora totalne specifične deformacije za linijski element povučen iz tačke N u pravcu određenog jediničnog vektora i vektora inercije masa tela za osu povučenu iz iste tačke i pomoću njih i vektora totalnog napona za ravan određene normale analiziraju modeli stanja napona, stanja deformacije i stanja inercije masa u posmatranoj tački tela i ukazuje na identičnost matematičkih modela. Koristeći pojmove tenzora napona, tenzora inercije i tenzora specifične deformacije ističe se analogija pojmova, fizičkih i geometrijskih veličina modela stanja napona, stanja deformacija i stanja inercije masa tela. Na osnovu analogije izveden je niz zaključaka u teoriji deformacija i o momentima inercije masa te/a. U radu je izveden izraz za specifični deformacioni rad deformisanog tela, u funkciji vektora totalne specifične deformacije i vektora pomeranja.