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Abstract
A new finite element for modelling laminated bending plates was defined based on the effective triangular finite element of the discrete Kirchhoff's theory. The plates can be made of layers arranged in any order and consisting of different but orthotropic materials. The suggested finite element has 6 degrees of freedom in every node, i e 3 linear displacements and 3 rotations about the axis of coordinates. A mathematical model of the element describes stress and strain effects both in the plane of the element or perpendicular to it, except for shear. The suggested element can be used for calculating laminated plates or beams, not subjected to heavy shear stresses. Some numerical case studies are provided, while the results obtained are compared with the well‐known analytical and numerical solutions.
Santrauka
Efektyvaus diskretines Kirchhofo teorijos trikampio baigtinio elemento DKT pagrindu suformuluotas naujas baigtinis elementas lenkiamoms daugiasluoksnems plokštelems modeliuoti. Plokšteles gali būti sudarytos iš keliu bet kokia tvarka išdestytu sluoksniu, kuriu medžiaga gali būti skirtinga bei ortotropine. Naujas trikampis baigtinis elementas turi 6 laisvumo laipsnius kiekviename mazge: 3 linijinius poslinkius ir 3 posūkius apie koordinačiu ašis. Elemento matematinis modelis apima visus deformaciju ir itempiu efektus tiek elemento plokštumoje, tiek statmena šiai plokštumai kryptimi, išskyrus šlyti. Elementas gali būti naudojamas sluoksniuotoms lenkiamoms plokštelems arba sijoms, kurioms šlyties itaka nežymi, skaičiuoti. Darbe pateikti skaitiniai pavyzdžiai, gauti rezultatai palyginti su žinomais analitiniais ir skaitiniais sprendiniais.