Analiza vitkih razpokanih nosilcev na Winklerjevi zemljini z uporabo poenostavljenega računskega modela

This paper discusses the coupling of Winkler\u27s soil model with a simplified computational model that is widely used for the calculation of transverse displacements in transversely cracked slender beams. The bending problem of a cracked beam embedded in Winkler\u27s soil is addressed by means of an analytical approach. The solving of the corresponding differential equation solutions is studied in order to obtain exact analytical expressions for the transverse displacements of the simplified computational model. After the solutions for the displacements of the beam are obtained, the inner bending moment and the shear force distributions within the beam can be calculated, either by using known, established relationships from the Euler-Bernoulli beam theory or by implementing two mechanical equilibrium conditions. Numerical examples covering several load situations are briefly presented in order to support the discussed approach. The results obtained with the presented approach are then further compared with the values from huge 2D finite-element models, where a detailed description of the crack was achieved using the discrete approach. It is evident that any drastic difference in the computational effort is not reflected in the significant differences in the results between the models.Članek obravnava uporabo pogosto uporabljenega poenostavljenega računskega modela za analitični izračun prečnih premikov vitkih nosilcev, vgrajenih v Winklerjevi zemljini, ki so prečno razpokani. Prikazano je reševanje pripadajočih diferencialnih enačb in pridobitev natančnih analitičnih rešitev za izračun prečnih premikov poenostavljenega modela. Rešitve za pomike omogočajo izračun porazdelitve notranjih upogibnih momentov in strižnih sil z uporabo znanih zvez iz Euler-Bernoullijeve teorije upogiba ali z uporabo dveh mehanskih ravnotežnih pogojev. Numerična primera pokrivata obtežni situaciji, na kratko predstavljata možnosti uporabe modela in potrjujeta uporabnost predstavljenega pristopa. Rezultati, ki so pridobljeni s predstavljenim pristopom, so primerjani še z vrednostmi iz obsežnih diskretnih računskih modelov po metodi končnih elementov, tvorjenimi z 2D končnimi elementi. Očitno je, da se velike razlike obsega vloženega računskega dela modelov ne odražajo v pomembnih razlikah rezultatov med računskima modeloma