Дисертації з теми "Carrera's Unified Formulation"

Cette thèse traite des problèmes des concentrations de contraintes locales, en particularité des effets des bords libres dans des structures stratifiés. À l'interface entre deux couches avec des propriétés élastiques différentes, les contraintes ont un comportement singulier dans le voisinage du bord libre en supposant un comportement de matériau élastique linéaire. Par conséquent, ils sont essentiels pour promouvoir le délaminage. Via Formulation unifiée de la Carrera (CUF) différents modèles cinématiques sont testés dans le but de capter les concentrations de contraintes. Dans la première partie de ce travail, les approches de modélisation dimensionnelle réduits sont comparées. Deux classe principale sont présentés: la couche équivalent (ESL) et l'approche par couche, LW. Par la suite leurs capacités à capter les singularités sont comparées. En utilisant une fonction a priori singulière, via une expression exponentielle, une mesure des contraintes singulières est introduite. Seulement deux paramètres décrivent pleinement les composantes des contraintes singulières au voisinage du bord libre. Sur la base des paramètres obtenus les modèles sont comparés et aussi les effets sous des charges d'extension et de flexion et pour différents stratifiés. Les résultats montrent une nécessité des modèles complexes dans le voisinage du bord libre. Cependant loin des bords libres, dans le centre de plaques composite, aucune différence significative ne peut être noté pour les modèles plutôt simples. La deuxième partie de ce travail est donc dédiée au couplage de modèles cinématique incompatibles. Modèles complexes et coûteux sont utilisés seulement dans des domaines locaux d'intérêt, tandis que les modèles économiques simples seront modéliser le domaine global. La eXtended Variational Formulation (XVF) est utilisé pour coupler les modèles de dimensionnalité homogènes mais de cinématique hétérogènes. Ici pas de recouvrement de domaine est présent. En outre, le XVF offre la possibilité d'adapter les conditions imposées à l'interface en utilisant un paramètre scalaire unique. On montre que, pour le problème de dimensionnalité homogène, que deux conditions différentes peuvent être imposées par ce paramètre. Un correspondant à des conditions fortes des Multi Point Constraints (MPC) et un second fournir des conditions faibles. La dernière offre la possibilité de réduire extrêmement le domaine qui utilise le modèle cinématique complexe, sans perte de précision locale. Comme il s'agit de la première application de la XVF vers les structures composites, le besoin d'un nouvel opérateur de couplage a été identifié. Un nouveau formulaire est proposé, testé et sa robustesse sera évaluée
This work considers local stress concentrations, especially the free-Edge effects of multilayered structures. At the interface of two adjacent layers with different elastic properties, the stresses can become singular in the intermediate vicinity of the free edge. This is valid while assuming a linear elastic material behaviour. As a consequence this zones are an essential delamination trigger. Via the Carrera Unified Formulation (CUF), different kinematical models are testes in order to obtain the correct local stress concentration. In the first part of this work, the reduced dimensional modelling approaches are compared. Two main class are presented: Equivalent Single Layer (ESL) models treating the layered structure like one homogenous plate of equal mechanical proper- ties, and the Layer Wise approach, treating each layer independently. Subsequently their capabilities to capture the appearing singularities are compared. In order to have a comparable measurement of those singularities, the obtained stress distributions will be expressed via a power law function, which has a priori a singular behaviour. Only two parameters fully describe therefore the singular stress components in the vicinity of the free edge. With the help of these two parameters not only the different models capabilities will be compared, but also the free edge effect itself will be measured and compared for different symmetrical laminates and the case of extensional and uniform bending load. The results for all laminates under both load cases confirm the before stated need for rather complex models in the vicinity of the free edge. However far from the free edges, in the composite plates centre, no significant difference can be noted for rather simple models. The second part of this work is therefore dedicated to the coupling of kinematically incompatible models. The use of costly expensive complex models is restricted to local domains of interest, while economic simple models will model the global do- main. The Extended Variational Formulation (XVF) is identified as the most suitable way to couple the kinematically heterogenous but dimensional homogenous models. As it uses a configuration with one common interface without domain overlap, the additional efforts for establishing the coupling are limited. Further the XVF offers the possibility to adapt the conditions imposed at the interface using a single scalar parameter. It will be shown that for the homogenous dimensional problem under consideration only two different conditions can be imposed by this parameter. One matching the strong conditions imposed by the classical Multi Point Constrains (MPC) and a second one providing a weak condition. The last one is shown to provide the possibility to reduce further the domain using the complex kinematical model, without the loss of local precision. As this is the first application of the XVF towards composite structures, the need for a new coupling operator was identified. A new form is proposed, tested and its robustness will be evaluated

At preliminary design stage, the global mechanical behavior of large marine vessels such as container ships has previously been analyzed idealizing them as a classical beam. These structures are complex and a classical beam idealization significantly compromises important structural behavior associated with cross section warping or in-plane displacements. On the other hand, 3D Finite Element (FE) models have been utilized which are accurate in capturing these details but pose high computational cost. In present work, structural analyses of marine vessels with realistic boundary conditions have been presented using well-known Carrera Unified Formulation (CUF). Using CUF, higher order theories can be implemented without the need of ad-hoc formulations. The finite element arrays are written in terms of fundamental nuclei for 1D beam elements that are independent of problem characteristics and the approximation order. Thus, refined models can be developed in an automatic manner. In the present work, the beam cross sections are discretized using elements with Lagrange polynomials and the FE model is regarded as Component-Wise (CW), allowing one to model complex 3D features, such as inclined hull walls, floors and girders in the form of components. The work is mainly divided in two parts: Hull in vacuo (in absence of water) and Hull with Hydrostatic Stiffness (in presence of water). The former involves static and dynamic structural analyses of hulls with realistic geometries without the effect of water. The later involves static and dynamic analyses of realistic hull geometries that are supported by buoyancy springs. The stiffness of buoyancy springs is made part of the fundamental nuclei and the corresponding FEM matrices for hydrostatic and hydrodynamic loads are obtained. The hydrodynamic loads have been considered in the form of Radiation Wave loads which include damping and added mass effects. Utilization of Component-Wise (CW) model under hydrodynamic loads has afforded an ease in modelling the complex geometrical configurations such as realistic boat shapes and the dynamic response analyses of aircraft carrier due to moving aircraft. All the analyses have been validated with published literature and their computational efficacy is established through their comparison with the results from commercial code.

The aerospace structure design is one of the most challenging field in the mechanical engineering. The advanced structural configurations, introduced to satisfy the weight and strength requirements, require advanced analysis techniques able to predict complex physical phenomena. Finite Element Method, FEM, is one of the most used approach to perform analyses of complex structures. The use of FEM method allows the classical structural models to be used to investigate complex structures where a close form solution is not available. The FEM formulation can be easily implemented in automatic calculation routines therefore this approach can take advantage of the improvements of computers. In the last fifty years many commercial codes, base on FEM, has been developed and commercialized, as examples it is possible to refer to Nastran R by MSC or Abaqus R by Dassault Systémes. All the commercial codes are based on classical structural models. The beam model are based on Euler-Bernoulli or Timoshenko theories while two-dimensional models deal with Kirchhoff or Mindlin theories. The limitations introduced by the kinematic assumptions of such theories make the FEM elements based oh these models inef- fective in the analysis of advanced structures. The physical phenomena introduced by composite and smart materials, multi-field application and unconventional loads configurations can not be investigated using the classical FEM models, where the only solution improvement can be reached by refining the mesh and increasing the number of degrees of freedom. This scenario makes the development of advanced structural models very attractive in the structural engineering. With the development of new materials and structural solutions, a number of new structural models have been introduced in order to perform an accurate design of advanced structures. Classical structural model have been im- proved introducing more refined kinematics formulation. One- and two- dimensional models are widely used in aerospace structure design, the limitations introduced by the classical models have been overcame by introducing refined kinematic formulations able to deal with the complexities of the problems. On the other hand, while in the classical models each point is characterized by 3 translations and 3 rotations, the use of advanced models with complex kinematic introduces a number of complication in the analysis of complex geometries, in fact is much more difficult to combine models with different kinematics. The aim of this thesis is to develop new approaches that allow different kinematic models to be used in the same structural analysis. The advanced models used in the present thesis have been derived using the Carrera Unified Formulations, CUF. The CUF allows any structural model do be derived by means of a general formulation independent from the kinematics assumed by the theory. One-, two- and three- dimensional models are derived using the same approach. These models are therefore combined together using different techniques in order to perform structural analysis of complex structures. The results show the capabilities of the present approach to deal with the analysis of typical complex aerospace structure. The performances of variable kinematics models have been investigated and many assessment have been proposed. This walled structure, reinforced structure and composite and sandwich material have been con- sidered. The advanced models introduced in this thesis have been used to perform static, dynamic and aeroelastic analysis in order to highlight the capabilities of the approach in different field. The results show that the present models are able to provide accurate results with a strong reduction in the computational cost with respect classical approaches.

Composites provide significant advantages in performance, efficiency and costs; thanks to these features, their application is increasing in many engineering fields, such as aerospace, naval and mechanical engineering. Although the adoption of composites is rising, there are still open issues to be investigated, in particular, understanding their failure mechanism has a prominent role in enhancing component designs. Numerous methodologies are available to compute accurate stress/strain fields for laminated structures, multi-scale approaches are required when micro- and macro-scales are accounted for. Despite the increasing development in computer hardware, the computational effort of these methods is still prohibitive for extensive applications, especially when a high number of layers is considered. Then, the reduction of the computational time and cost required to perform failure analysis is still a challenging task. This work proposes two multiscale approaches for the failure analysis of fiber-reinforced composites. A concurrent multiscale approach ("Component-Wise") and a hierarchical method are developed based on the 1D Carrera Unified Formulation (CUF). 1D higher order elements are very powerful tools for multiscale analysis since they provide accurate stress and strain fields with very low computational costs.

This thesis extends advanced one-dimensional models derived from the use of the Carrera Unified Formulation (CUF) to a High-Fidelity modeling approach, which has been used to perform analyses of multi-component aeronautical structures guaranteeing a proper description of each component regarding geometry and material. Static analyses and free vibration analyses have been performed to validate the current CUF model for the studies of structures, which present multi-component nature, sweep angle and non-prismatic shape; subsequently, its capabilities have been exploited to investigate different aeronautical topics. At first, the model has been used for the free vibration analysis of damaged structures and the possible use of the behavior alterations for the damage detection. Thanks to the capability of the model to control the stiffness arbitrarily, several scenarios have been analyzed where the damage has been introduced, for example, in the whole component or at the local level. The layer-wise capability of the model has allowed a wide tailoring analysis of thin-walled boxes to be performed. It has been used to evaluate the free-vibration behaviors according to the lamination used in the structure. Moreover, these analyses have been used to explore the possible influences on the geometrical coupling effects due to sweep angle or tapered shapes, in order to mitigate or emphasize them. The model has also been extended to the study of Variable Angle Tow (VAT) composites characterized by curvilinear fibers. After the validation with results from the open literature, the possible advantages in the aeronautic field of this technology have been explored through vibrational analyses of prismatic thin-walled boxes. The results confirm the capabilities of the current model to deal with very complex aeronautical structures providing accurate results with a sensible reduction of the computational cost compared to the classical used FEM models. Its performances are also tested with a displacement analyses in the second part of this thesis, which presents the work done during the apprenticeship related to the research project TIVANO with the company Leonardo Finmeccanica – Aircraft division.

In the framework of structural mechanics, the classical beam theories that are commonly adopted in many applications may be affected by inconsistencies, because they are not able to foresee higher-order phenomena, such as elastic bending/shear couplings, restrained torsional warping and 3D strain effects. Depending on the problem, those limitations can be overcome by using more complex and computationally expensive 2D and 3D models or, alternatively, by adopting refined beam models, to which many scientists have dedicated their research over the last century. % One of the latest contributions to the development of advanced models, including variable kinematic beam theories, is the Carrera Unified Formulation (CUF), which is the main subject of the research discussed in this thesis. According to CUF, the 3D displacement field can be expressed as an arbitrary expansion of the generalized displacements. Depending on the choice of the polynomials employed in the expansion, various classes of beam models can be implemented. In this work, for instance, Taylor-like and Lagrange polynomials are adopted. The former choice leads to the so-called TE (Taylor Expansion) beam models, whereas LE (Lagrange Expansion) beam models with only pure displacement variables are obtained by interpolating the problem unknowns by Lagrange polynomials. The strength of CUF lies in the fact that, independently of the choice of the polynomials, the governing equations are written in terms of fundamental nuclei, which are invariant with the theory class and order. In this thesis, both strong and weak form governing equations for arbitrarily refined CUF models are derived. Subsequently, exact closed-form and approximate solutions are sought. Exact solutions of any beam model with arbitrary boundary conditions are found by formulating a frequency-dependant Dynamic Stiffness (DS) matrix and by using the Wittrick-Williams algorithm to carry out the resulting transcendental eigenvalue problem for free vibration analysis. Conversely, a linear eigenvalue problem is also derived by approximating the strong form governing equations by Radial Basis Functions (RBFs). On the other hand, weak form solutions are discussed by Finite Element Method (FEM), which still deserves important attentions due to its versatility and numerical efficiency. The various problems of the mechanics are addressed, including static, free vibration and dynamic response problems. Based on CUF and the proposed numerical methods, advanced methodologies for the analysis of complex structures, such as aircraft structures and civil engineering constructions, are developed. Those advanced techniques make use of the Component-Wise (CW) and the Multi-Line approaches. The CW method exploits the natural capability of the LE CUF beam models to be assembled at the cross-section level. This characteristic allows the analyst to use only CUF beam elements to model each component (e.g., stringers, panels and ribs) of the structure and purely physical surfaces are employed to construct the mathematical models. In the ML framework, on the other hand, each component of the structure is modelled via TE beam elements of arbitrary order. Compatibility of displacements between two or more components is then enforced through the Lagrange multipliers method. The second part of this thesis deals with aeroelasticity. In particular, the Vortex (VLM) and the Doublet Lattice Methods (DLM) are employed and extended to CUF to develop aeroelastic models. VLM is used to model the steady contribution in the aerodynamic model, whereas DLM provides the unsteady contribution in the frequency domain. The infinite plate spline approach is adopted for the mesh-to-mesh transformation. Finally, the g-method is described as an effective means for the formulation of the flutter stability problem. Particular attention is given to the extension of this methodology to exact DS solutions of CUF beams. Simplified, discrete, dynamic gust response analysis by refined beam models is also discussed. In this work, vertical gusts and one-minus-cosine idealization is addressed. Accordingly, gust loads in terms of time-dependent load factors are formulated. Subsequently, the mode superposition method is briefly introduced in order to solve the linear dynamic response problem in the time domain by using both weak and strong form solutions of CUF models. In the final part of the work, extensions of 1D CUF models for Fluid-Dynamics problems are carried out. CUF approximation of laminar, incompressible, Stokes flows with constant viscosity was introduced in a recent thesis work and it is here extended to the hierarchical p-version of FEM, which makes use of Legendre-like polynomials to interpolate the generalized unknowns along the 1D computational domain. Finally, the structural, aeroelastic and fluid-dynamics formulations are validated by discussing some selected results. In particular, regarding structures, the efficiency of the various numerical approaches when applied to CUF is investigated and simple to complex problems are considered, including metallic and composite wings. The aeroelastic analyses show that classical beam models are not adequate for the flutter detection, and at least a third-order beam model is required. Contrarily, classical beam models can be quite accurate in dynamic gust response analysis if no coupling phenomena occur, i.e. when the response is dominated by only pure bending modes. Regarding fluid-dynamics, it is demonstrated that CUF models can reproduce the results by finite volume codes for both simple Poiseuille and complex non-axisymmetric fluids in cylinders. In general, the capability of the proposed CUF models to provide accurate results with very low computational efforts is firmly highlighted. Similar analyses are possible only by using 3D models, which usually require a number of degrees of freedom that is some two order of magnitude higher.

The aim of this work is the development of a refined reduced order model suitable for numerical applications in solid and fluid mechanics with a remarkable reduction in computational cost. Nowadays, numerical reduced order models are widely exploited in many areas, such as aerospace, mechanical and biomechanical engineering for structural analysis, fluid dynamic analysis and coupled (aeroelastic) fluid-structure interaction analysis. One-dimensional (1D) structural models, commonly known as beams, are for instance used in many applications to analyze the structural behavior of slender bodies, such as columns, arches, blades, aircraft wings, bridges, skyscrapers, rotor and wind turbine blades. One-dimensional structural elements are simpler and computationally more efficient than 2D (plate/shell) and 3D (solid) elements. This feature makes beam theories still very attractive for the static, dynamic response, free vibration and aeroelastic analyses, despite the approximations which they introduce in the simulation. Recently, 1D models are intensively exploited for the simulation of the human cardiovascular system under either physiological or pathological conditions. As it is easily comprehensible, fluid flows in pipes, channel, capillaries or even arteries are particularly suitable for the application of one-dimensional models also to fluid dynamics. Typically, one-dimensional models for fluid dynamics and fluid-structure interaction (FSI) problems are again remarkably more efficient than three-dimensional methods in terms of computational cost. A key point for reduced order models is the capability in simulating in an accurate way the investigated physical problem. For instance, in last decades the growing use of advanced composite and sandwich materials in thin-walled beam-like structures has revealed that 1D theories have to be refined in order to predict the behavior of such complex structures with high fidelity. For this purpose, a higher-order one-dimensional method is introduced in this work and its capabilities are highlighted and discussed. The present work is subdivided into three fundamental parts corresponding to the physical fields the proposed refined model is applied to. Firstly, a structural part presents the formulation of a displacement-based higher-order one-dimensional model for the analysis of beam-like structures. Classical beam theories (Euler-Bernoulli and Timoshenko) have intrinsic limitations which preclude their applications for the analysis of a wide class of engineering problems. The Carrera Unified Formulation (CUF) is employed to introduce a hierarchical modeling with a variable order of expansion for the displacement unknowns over the beam cross-section. The finite element method (FEM) is used to handle arbitrary geometries and loading conditions. The influence of higher-order effects over the cross-section deformation, not detectable by classical and low-order beam theories, on the static, free vibration and time-dependent response of several structures with arbitrary cross-section geometries and made of arbitrary materials is remarked through the numerical results presented. Secondly, an aeroelastic part describes the extension of the refined structural model to the static aeroelastic analysis of lifting surfaces made of metallic and composite materials. A coupled aeroelastic computational model based on the Vortex Lattice aerodynamic Method and the finite element method (FEM) is formulated. A refined aeroelastic approach is also presented by replacing the Vortex Lattice aerodynamic Method with the more powerful 3D Panel Method. Comparison with results obtained by existing plate/shell aeroelastic models shows that the present 1D model could result less expensive from the computational point of view with respect to shell cases with same accuracy. The effect of the cross-section deformation on the aeroelastic static response and on the critical wing divergence velocity is evaluated for different wing configurations. The beneficial effects of aeroelastic tailoring in the case of wings made of composite anisotropic materials are also confirmed by using the present model. Finally, a third part concerning the use of the refined one-dimensional CUF model for fluid dynamic problems is presented. The basic partial differential equations (PDEs) of fluid mechanics (Navier-Stokes and Stokes equations) are faced and 1D refined models with variable velocity-pressure accuracy are presented on the basis of the one-dimensional Carrera Unified Formulation and the finite element method. The application of these higher-order models to describe the three-dimensional fluid flow evolution on a computational domain is formulated for the Stokes problem. The present approach reveals its capabilities in predicting accurately, with a reduced computational cost with respect to more consuming two-dimensional or three-dimensional methods, nonclassical and complex fluid flows. Moreover, the numerical results show the promising potentiality of such an approach to the future extension of fluid-structure CUF-CUF models, i.e. the coupling of CUF models used for both structural and fluid dynamic analyses.

Questa dissertazione propone un nuovo paradigma per l'analisi multi-scala delle strutture di tipo trave, utilizzando la formulazione unificata di Carrera ("Carrera's Unified Formulation", CUF). La modellizzazione multi-scala collega la micromeccanica e la teoria strutturale macroscopica. I risultati del processo di esplorazione possono essere riassunti nei due aspetti seguenti: un modello macroscopico di trave, contenente non-linearità geometriche, ed un modello di trave multi-scala, anch'esso non-lineare da un punto di vista geometrico. L'indagine qui presentata inizia con uno studio della modellazione macroscopica non lineare. Il modello strutturale viene stabilito accoppiando la CUF non-lineare con il Metodo Numerico Asintotico ("Asymptotic Numerical Method", ANM). Questo modello di trave, basato sulla CUF contenente non-linearità geometriche, è realizzato in collaborazione con G. De Pietro: si tratta di uno dei primi studi che estende i modelli CUF unidimensionali accoppiati con il metodo ANM. Si presentano analisi non lineari statiche, post-buckling e snap-through delle strutture traviformi e se ne valutano le corrispondenti curve carico-spostamento e carico-sforzo. I risultati sono confrontati con soluzioni agli elementi finiti bidimensionali. Si dimostra che, per i casi considerati, una descrizione quadratica attraverso lo spessore garantisce accurati spostamenti a componente di tensione assiale. Inoltre, si necessita di un ordine di espansione più elevato al fine di prevedere con precisione la componente di sollecitazione di taglio. Nell'analisi post-buckling considerata, i modelli CUF di ordine basso rilevano il punto di biforcazione in modo accurato. Tuttavia, al fine di ottenere risultati accurati riguardanti la sollecitazione di taglio, si richiede un modello di ordine superiore. Nell'analisi di snap-through, è necessaria una teoria raffinata per tracciare accuratamente il percorso di equilibrio. Per affrontare problemi contenenti non-linearità geometriche provenienti da scale diverse, un modello di trave multi-scala, basato sulla CUF contenente non-linearità geometriche, viene derivato accoppiando il modello macroscopico proposto ed il framework agli Elementi Finiti Multilivello (noto anche come FE$^2$). La soluzione consiste in un'analisi macroscopico/strutturale e un'analisi microscopica/materiale. Alla scala macroscopica, la legge costitutiva incognita è calcolata attraverso un'omogeneizzazione numerica di un Elemento di Volume Rappresentativo ("Representative Volume Element", RVE). Viceversa, il gradiente di deformazione microscopico è calcolato tramite modello macroscopico. Il sistema matematico non-lineare risultante è risolto attraverso il metodo ANM, il quale risulta essere più affidabile e meno dispendioso dal punto di vista dei tempi di calcolo, rispetto ai metodi iterativi classici. La metodologia proposta viene utilizzata per studiare l'effetto delle imperfezioni alla scala microscopica (fibre di carbonio non perfettamente diritte) sulla risposta macroscopica (instabilità). I risultati vengono analizzati in termini di accuratezza e costi computazionali, rispetto alle soluzioni FEM. Tre fattori sono identificati per un'analisi parametrica di sensibilità alle imperfezioni: lunghezza d'onda ed, ampiezza della imperfezione e dimensione dell'RVE.

The use of composite laminated structures helped in the last two decades to reduce overall weight of transportation structures. As a consequence the energy needed to power those transportation means is reduced and hence fuel and monetary resources are economized and emissions are reduced. Especially the aerospace sector has a high need of a favourable weight to power ratio. Orthotropic laminated structures are able to provide a higher stiffness combined with a lower density compared to monolithic isotropic materials used in the past. It seems hence, that they are perfect for the use in even a wider spectrum of applications. However through the assembly of differently layers, it is more difficult to model and predict the structures mechanical response to outer loadings. In the recent past different computational methods were developed. Most of them under the scope of being capable to deliver very detailed results of the global behaviour of the structure but also of the interaction between the different layers of the laminate. As a major drawback, a detailed result comes with high computational costs. Hence a need for a good compromise between costs and accuracy has to be found. This benefits especially from the fact that stress concentrations in composites occur mainly in local domains of the structure. The use of detailed models only in those local domains of interest seems therefore straightforward. Examples for such local domains with stress concentrations are laminates with free edges. At the interface between two layers with different elastic properties the stresses have singular behaviour in the immediate vicinity of the free edge, assuming linear elastic material behaviour. This is due to the material discontinuity and the resulting mismatch of the elastic properties at the interface of the layers, the condition of traction-free edges and the equilibrium between the layers. Therefore they are critical to promote delamination. An adequate analysis method for this would be the use of a full three-dimensional analysis model. However it’s computational cost is significant. Composites are often rather thin planar structures, allowing the use of reduced dimensional models, which are also more attractive through their reduced computational cost. Therefore different reduced models with their appropriate hypotheses in the thickness direction are under consideration in this work. Via different thickness expansion functions suitable kinematical theories, are expressed. The Carrera’s Unified Formulation (CUF) is used to have a common base to build the models with the different kinematical theories. The CUF allowing not only purely displacement based models using the Principle of Virtual Displacements (PVD), but also mixed stress and displacement based models with the Reissner’s Mixed Variational Theorem (RMVT). In the first part of this work, the reduced dimensional modelling approaches are compared. Two main class are presented: Equivalent Single Layer (ESL) models treating the layered structure like one homogenous plate of equal mechanical properties, and the Layer Wise approach, treating each layer independently. Subsequently their capabilities to capture the appearing singularities are compared. In order to have a comparable measurement of those singularities, the obtained stress distributions will be expressed via a power law function, which has a priori a singular behaviour. Only two parameters fully describe therefore the singular stress components in the vicinity of the free edge. With the help of these two parameters not only the different models capabilities will be compared, but also the free edge effect itself will be measured and compared for different symmetrical laminates and the case of extensional and uniform bending load. The results for all laminates under both load cases confirm the before stated need for rather complex models in the vicinity of the free edge. However far from the free edges, in the composite plates centre, no significant difference can be noted for rather simple models. The second part of this work is therefore dedicated to the coupling of kinematically incompatible models. The use of costly expensive complex models is restricted to local domains of interest, while economic simple models will model the global domain. The Extended Variational Formulation (XVF) is identified as the most suitable way to couple the kinematically heterogenous but dimensional homogenous models. As it uses a configuration with one common interface without domain overlap, the additional efforts for establishing the coupling are limited. Further the XVF offers the possibility to adapt the conditions imposed at the interface using a single scalar parameter. It will be shown that for the homogenous dimensional problem under consideration only two different conditions can be imposed by this parameter. One matching the strong conditions imposed by the classical Multi Point Constrains (MPC) and a second one providing a weak condition. The last one is shown to provide the possibility to reduce further the domain using the complex kinematical model, without the loss of local precision. As this is the first application of the XVF towards composite structures, the need for a new coupling operator was identified. A new form is proposed, tested and its robustness will be evaluated.

A class of computationally-efficient tools to undertake progressive failure and damage analysis of composites across scales is presented. The framework is based on a class of refined one-dimensional (1D) theories referred to as the Carrera Unified Formulation (CUF), a generalized hierarchical formulation that generates a class of refined structural theories through variable kinematic description. 1D CUF models can provide accurate 3D-like stress fields at a reduced computational cost, e.g., approximately one to two orders of magnitude of degrees of freedom less as compared to standard 3D brick elements. The effectiveness of 1D CUF models to undertake physically nonlinear simulation is demonstrated through a class of problems with varying constitutive models. The virtual testing platform consists of a variety of computational tools such as failure index evaluations using component-wise modeling approaches (CUF-CW), CUF-CW micromechanics, concurrent multiscale framework, interface, and impact modeling. Failure index evaluation of a class of composite structures underlines the paramount importance of the accurate stress resolutions. Within the micromechanical framework, the Component-Wise approach (CW) is utilized to represent various components of the RVE. The crack band theory is implemented to capture the damage propagation within the constituents of composite materials and the pre-peak nonlinearity within the matrix constituents is modeled using the $J_2$ von-Mises theory. A novel concurrent multiscale framework is developed for nonlinear analysis of fiber-reinforced composites. The two-scale framework consists of a macro-scale model to describe the structural level components, e.g, open-hole specimens, coupons, using CUF-LW models and a sub-scale micro-structural model encompassed with a representative volume element (RVE). The two scales are interfaced through the exchange of strain, stress and stiffness tensors at every integration point in the macro-scale model. Explicit finite element computations at the lower scale are efficiently handled by the CUF-CW micromechanics tool. The macro tangent computation based on perturbation method which leads to meliorated performances. A novel numerical framework to simulate progressive delamination in laminated structures based on component-wise models is presented. A class of higher-order cohesive elements along with a mixed-mode cohesive constitutive law are integrated within the CUF-CW framework to simulate interfacial cohesive mechanics between various components of the structure. A global dissipation energy-based arc -length method to trace the complex equilibrium path exhibited by delamination problem. The capabilities of the framework are further extended through the introduction of contact kinematics to handle impact problems. A combination of the above tools is used to obtain an accurate material response of the structure in the non-linear regime, from the structural level i.e. macro-scale to the material constituent level i.e. the micro-scale, in a computationally efficient manner, providing a suitable virtual testing environment for the progressive damage analysis of composite structures. The accuracy and efficiency of the proposed computational platform are assessed via comparison against the traditional approaches as well as experimental results found in the literature.