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Zbog svojih izuzetnih materijalnih karakteristika u pogledu čvrstoće i krutosti, male sopstvene težine, otpornosti na koroziju i niskih troškova održavanja, kompozitni laminati imaju potencijal za upotrebu u građevinarstvu. Sa porastom svesti o zaštiti životne sredine u 21. veku, sve je češća upotreba prirodnih materijala..., Laminar composites are extensively used in civil engendering due to their exceptional strength, stiffness, corrosion resistance, and cost-effectiveness...

Laminar composites are extensively used in civil engendering due to their exceptional strength, stiffness, corrosion resistance, and cost-effectiveness. They are ideal for high-reliability applications. The 21st century’s focus on environmental protection has led to increased use of natural-based materials like cross-laminated timber (CLT) in building construction. CLT panels have a high stiffness-to-weight ratio, making them well-suited as load-bearing elements, such as walls and floors. The optimal design of laminar composites is often hindered by uncertainties in failure prediction and the computational costs associated with progressive failure analysis (PFA), particularly for larger structures. This study introduces a novel prediction model that combines the smeared crack band (SCB) damage model with the full layerwise theory (FLWT). The aim is to enhance the computational efficiency of PFA in laminar composites while maintaining the accuracy of 3D finite element models. The SCB model accurately captures the response of damaged lamina in both fiber and matrix directions using distinct strain-softening curves, ensuring a precise representation of post-failure behaviour. The damage law is derived based on the assumption that the total energy required to cause failure in an element (released strain energy) is equivalent to the energy necessary to create a crack passing through it. To alleviate mesh dependency, the fracture energy is scaled by a characteristic element length. Failure initiation and modes are determined using the Hashin failure criterion. Furthermore, the model is extended to consider different failure behaviour of timber in tension and compression. This extension enhances the computational framework’s applicability to the field of computational mechanics for bio-based composites, such as CLT. The validity of the model is then confirmed through an extensive experimental program carried out at the Faculty of Civil Engineering, University of Belgrade., Zbog svojih izuzetnih materijalnih karakteristika u pogledu čvrstoće i krutosti, male sopstvene težine, otpornosti na koroziju i niskih troškova održavanja, kompozitni laminati imaju potencijal za upotrebu u građevinarstvu. Sa porastom svesti o zaštiti životne sredine u 21. veku, sve je češća upotreba prirodnih materijala. U skladu sa tim, u građevinarstvu sve veću popularnost stiče kompozitni laminat na bazi drveta - unakrsno-lamelirano drvo (CLT). Zbog visokog odnosa krutosti i sopstvene težine CLT-a, moguće je projektovati elemente male težine i velikog raspona. Nepouzdanost u predviđanju ponašanja oštećenih kompozitnih laminata, kao i kompleksnost proračuna progresivnog loma znatno otežavaju njihovo projektovanje. U okviru ove disertacije je razvijen numerički model za analizu progresivnog loma kompozitnih laminata, koristeći model razmazane pukotine (eng. "smeared crack band" - SCB) i slojevitu teoriju ploča. Model poseduje kapacitet trodimenzionalnih numeričkih modela uz smanjeno trajanje proračuna, čime se povećava efikasnost numeričke analize. Kod SCB modela, ponašanje oštećene lamine je opisano različitim krivama loma u naponsko-deformacijskom prostoru, kako bi se u makroskopskom pogledu opisala propagacija oštećenja koje nastaje usled kidanja vlakana i matrice, respektivno. Zakon omekšavanja materijala je određen na osnovu pretpostavke da je oslobođena energija deformacije jednaka energiji potrebnoj da dođe do loma vlakana, odnosno kidanja matrice. Inicijacija i oblici loma su određeni primenom Hashin-ovog kriterijuma loma. Nakon toga, izvršena je modifikacija modela kako bi se opisalo različito ponašanje drveta pri zatezanju i pritisku. Na taj način, mogućnosti razvijenog numeričkog modela su proširene i na analizu progresivnog loma prirodnih kompozitnih laminata, kao što je CLT. Validnost predloženog modela je potvrđena kroz detaljna eksperimentalna ispitivanja na Građevinskom fakultetu Univerziteta u Beogradu. Upotreba slojevitih konačnih elemenata u an

This paper considers the dynamic analysis of a spatially curved Bernoulli-Euler beam subjected to a moving load. The isogeometric approach is used for the spatial discretization of the weak form of the equation of motion. Both the reference geometry and the solution space are represented using the same NURBS basis functions that guarantee an accurate description of the beam centerline. The time integration is done by the explicit technique. The presented formulation is validated by the comparison with the existing results from the literature for the curved beam subjected to a constant load moving with a constant velocity. In addition, the influence of the moving load velocity on the dynamic response of a spatially curved beam has been investigated.

Dynamic analysis of a spatially curved Bernoulli-Euler beam subjected to the moving load is considered in this paper. The isogeometric approach is used for the spatial discretization of the weak form of the equation of motion. Both the reference geometry and the solution space are represented using the same NURBS basis functions that guarantee an accurate description of beam’s centerline. The time integration is done by the explicit technique. The presented formulation is validated by the comparison with the existing results from the literature for the curved beam subjected to the constant load moving with the constant velocity.

Accurate numerical modeling of curved beams is of significant importance in different engineering fields. Several challenges can be present during the curved beam formulation, primarily due to the issues regarding the beam geometry, discretization and beam theory assumptions. In this dissertation, the isogeometric approach is applied in the dynamic analysis of spatial curved beams. A novel beam element was formulated using the Bernoulli - Euler hypothesis and the fundamental relations of the differential geometry, as well as the Cauchy continuum beam model. The geometry of the beam, as well as the displacement, velocity and acceleration fields, were defined using the Non-Uniform Rational B-Spline (NURBS) basis functions, which present the basis concept of the isogeometric approach. Complex geometry of the curved beams can be modeled accurately using NURBS - based isogeometric approach. Formulation of the spatial beam is conducted for the linear case, while the geometrically nonlinear formulation is conducted only for the plane curved beam using an explicit integration procedure. Free and forced vibration analyses of the curved beams are studied. In the latter, the influence of the moving mass on the curved beams is analyzed. The presented approach had shown that, in comparison to the classical finite element method (FEM), a less number of degrees of freedom are required in order to obtain accurate results. Consequently, fewer computational resources are needed to reach the appropriate level of accuracy for the curved beams. This makes the presented approach competitive with the conventional FEM, especially in the analysis of the flexible spatial engineering structures with complex geometry., Tacno numericko modelitanje krivolinijskih gredna nosac je od izuzetnog znacaja u mnogim inženjerskim oblastima. Geometrija krivolinijskog grednog nosaca, diskretizacija grede kao i potrebne pretpostavke grede, predstavljaju poteškoce prilikom formulacije krivolinijskog grednog elementa. U ovom radu je primenjen izogeometrijski pristup u dinamickoj analizi prostornih krivolinijskih grednih nosaca. Novi gredni element je definisan primenom Bernuli - Ojelerove pretpostavke, kao i osnovnih relacija diferencijalne geometrije i mehanike kontinuuma Košijeve grede. Geometrija grede, kao i polje pomeranja, brzine i ubrzanja su definisani primenom NURBS baznih funkcija, što predstavlja fundamentalnu osobinu isogeometrijskog pristupa. Složena geometrija krivolinijskog grednog nosaca može se tacno modelirati primenom izogeometrijskog pristupa zasnovanog na NURBS baznim funkcijama. Formulacija prostornog krivolinijskog grednog nosaca je izvedena u uslovina linearne teorije, dok je geometrijski nelinearna teorija primenjena samo na ravanskom krivolinijskom grednom nosacu, primenom eksplicitne metode integracije. Izvšena je analiza slobodnih i prinudnih vibracija. Analiza prinudnih vibracija je fokusirana na uticaj pokretnog opterecenja na krivolinijski gredni nosac. Primenom date formulacije dobijeni su rezultati zadovoljavajuce tacnosti sa manje stepeni slobode u poredjenju sa klasicnom metodom konacnih elemenata. U sladu sa tim, u cilju dobijanja rezultata zadovoljavajuce tacnosti krivolinijskog grednog nosaca nepohodna je primena manje resursa. Ovo cini prikazani pristup konkurentnijim klasicnoj metodi konacnih elemenata u analizi fleksibilnih inženjerskih konstrukcija sa složenom geometrijom.