Добірка наукової літератури з теми "Carrera Unified Formulation, Marine Structures, Component-wise Models"

The Component-Wise approach (CW) is a novel structural modeling strategy that stemmed from the Carrera Unified Formulation (CUF). This work presents an overview of the enhanced capabilities of the CW for the static and dynamic analysis of structures, such as aircraft wings, civil buildings, and composite plates. The CW makes use of the advanced 1D CUF models. Such models exploit Lagrange polynomial expansions (LE) to model the displacement field above the cross-section of the structure. The use of LE allows the improvement of the 1D model capabilities. LE models provide 3D-like accuracies with far fewer computational costs. The use of LE leads to the CW. Although LE are 1D elements, every component of an engineering structure can be modeled via LE elements independently of their geometry, e.g. 2D transverse stiffeners and panels, and of their scale, e.g. fiber/matrix cells. The use of the same type of finite elements facilitates the finite element modeling to a great extent. For instance, no interface techniques are necessary. Moreover, in a CW model, the displacement unknowns are placed along the physical surfaces of the structure with no need for artificial lines and surfaces. Such a feature is promising in a CAD/FEM coupling scenario. The CW approach can be considered as an accurate and computationally cheap analysis tool for many structural problems. Such as progressive failure analyses, multiscale, impact problems and health-monitoring.

In this paper, classical as well as various refined plate finite elements for the analysis of laminates and sandwich structures are discussed. The attention is particularly focussed on a new variable-kinematic plate element. According to the proposed modelling approach, the plate kinematics can vary through the thickness within the same finite element. Therefore, refined approximations and layer-wise descriptions of the primary mechanical variables can be adopted in selected portions of the structures that require a more accurate analysis. The variable-kinematic model is implemented in the framework of the Carrera unified formulation, which is a hierarchical approach allowing for the straightforward implementation of the theories of structures. In particular, Legendre-like polynomial expansions are adopted to approximate the through-the-thickness unknowns and develop equivalent single layer, layer-wise, as well as variable-kinematic theories. In this paper, the principle of virtual displacements is used to derive the governing equations of the generic plate theory and a mixed interpolation of tensorial components technique is employed to avoid locking phenomena. Various problems are addressed in order to validate and assess the proposed formulation, including multi-layer plates and sandwich structures subjected to different loadings and boundary conditions. The results are compared with those from the elasticity theory given in the literature and from layer-wise solutions. The discussion clearly underlines the enhanced capabilities of the proposed variable-kinematic mixed interpolation of tensorial component plate elements, which allows, if used properly, to obtain formally correct solutions in critical areas of the structure with a considerable reduction of the computational costs with respect to more complex, full layer-wise models. This aspect results particularly advantageous in problems where localized phenomena within complex structures play a major role.

The present work proposes a closed-form solution based on refined beam theories for the static analysis of fiber-reinforced composite and sandwich beams under simply supported boundary conditions. The higher-order beam models are developed by employing Carrera Unified Formulation, which uses Lagrange-polynomials expansions to approximate the kinematic field over the cross section. The proposed methodology allows to carry out analysis of composite structure analysis through a single formulation in global-local sense, i.e. homogenized laminates at a global scale and fiber-matrix constituents at a local scale, leading to component-wise analysis. Therefore, three-dimensional stress/displacement fields at different scales can be successfully detected by increasing the order of Lagrange polynomials opportunely. The governing equations are derived in a strong-form and solved in a Navier-type sense. Three benchmark numerical assessments are carried out on a single-layer transversely isotropic beam, a cross-ply laminate [Formula: see text] beam and a sandwich beam. The results show that accurate displacement and stress values can be obtained in different parts of the structure with lower computational cost in comparison with traditional, enhanced as well as three-dimensional finite element methods. Besides, this study may serve as benchmarks for future assessments in this field.

This paper deals with the evaluation of time response analyses of typical aerospace metallic structures. Attention is focussed on detailed stress state distributions over time by using the Carrera Unified Formulation (CUF) for modeling thin-walled reinforced shell structures. In detail, the already established component-wise (CW) approach is extended to dynamic time response by mode superposition and Newmark direct integration scheme. CW is a CUF-based modeling technique which allows to model multi-component structures by using the same refined finite element for each structural component, e.g. stringers, panels, ribs. Component coupling is realized by imposing displacement continuity without the need of mathematical artifices in the CW approach, so the stress state is consistent in the entire structural domain. The numerical results discussed include thin-walled open and closed section beams, wing boxes and a benchmark wing subjected to gust loading. They show that the proposed modeling technique is effective. In particular, as CW provides reach modal bases, mode superposition can be significantly efficient, even in the case of complex stress states.

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.

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.

In the present work, a higher-order beam model able to characterize correctly the three-dimensional strain and stress fields with minimum computational efforts is proposed. One-dimensional models are formulated by employing the Carrera Unified Formulation (CUF), according to which the generic 3D displacement field is expressed as the expansion of the primary mechanical variables. In such a way, by employing a recursive index notation, the governing equations and the related finite element arrays of arbitrarily refined beam models can be written in a very compact and unified manner. A Component-Wise (CW) approach is developed in this work by using Lagrange polynomials as expanding cross-sectional functions. By using the principle of virtual work and CUF, free vibration and linearized buckling analyses of composite aerospace structures are investigated. The capabilities of the proposed methodology and the advantages over the classical methods and state-of-the-art tools are widely demonstrated by numerical results.

Using advanced beam models based on the Carrera Unified Formulation, this paper presents an analysis of a damaged tapered aircraft structure. Results obtained from static and free vibration analyses are presented to evaluate the evolution of the stress and the modal behaviour in a multi-component damaged structure. This 1-D model is able to modify the material proprieties, then the stiffness, at the local level. In this way, many types of local and global damage can be introduced into the structure. The results show the capability of the present model to obtain with a low computational cost, displacements, stresses and vibration characteristics of damaged structures making him a good candidate for design and maintenance tools.

This paper proposes an advanced approach to the analysis of reinforced-shell aircraft structures. This approach, denoted as Component-Wise (CW), is developed by using the Carrera Unified Formulation (CUF). CUF is a hierarchical formulation allowing for the straightforward implementation of any-order one-dimensional (1D) beam theories. Lagrange-like polynomials are used to discretize the displacement field on the cross-section of each component of the structure. Depending on the geometrical and material characteristics of the component, the capabilities of the model can be enhanced and the computational costs can be kept low through smart discretization strategies. The global mathematical model of complex structures (e.g. wings or fuselages) is obtained by assembling each component model at the cross-section level. Next, a classical 1D finite element (FE) formulation is used to develop numerical applications. It is shown that MSC/PATRAN can be used as pre- and post-processor for the CW models, whereas MSC/NASTRAN DMAP alters can be used to solve both static and dynamic problems. A number of typical aeronautical structures are analyzed and CW results are compared to classical beam theories (Euler-Bernoulli and Timoshenko), refined models and classical solid/shell FE solutions from the commercial code MSC/NASTRAN. The results highlight the enhanced capabilities of the proposed formulation. In fact, the CW approach is clearly the natural tool to analyze wing structures, since it leads to results that can be only obtained through three-dimensional elasticity (solid) elements whose computational costs are at least one-order of magnitude higher than CW models.

This paper presents the static analysis of tapered structures made of composite material using 1D models. These models are based on a one-dimensional formulation derived using the Carrera Unified Formulation (CUF). This formulation allows us to obtain 3D-like results thanks to the use of polynomial expansions to describe the displacement field over the cross-section. According to the types of expansion used, different classes of refined one-dimensional elements are obtained. In this work the Lagrange expansions were used. The use of LE models allows each structural component to bo considered separately; this approach is called component wise (CW). The thin-walled structures are usually made of composite materials, in particular, the aeronautical structures. For this reason, these kinds of structures are taken into account. The stress and displacement fields due to simple load cases have been obtained. The results have been compared with those obtained using commercial tools. The results show the capability of the present refined one-dimensional models to achieve results usually obtained by the use of solid models and therefore, with higher computational cost.

The space structures are realized by combining skin and reinforced components, such as longitudinal reinforcements called stringers and transversal reinforcements called ribs. These reinforced structures allow two main design requirements to be satisfied, the former is the light weight and the latter is a high strength. Solid models (3D) are widely used in the Finite Element Method (FEM) to analyse space structures because they have a high accuracy, in contrast they also have a high number of degrees of freedoms (DOFs) and huge computational costs. For these reasons the one-dimensional models (1D) are gaining success as alternative to 3D models. Classical models, such as Euler-Bernoulli or Timoshenko beam theories, allow the computational cost to be reduced but they are limited by their assumptions. Different refined models have been proposed to overcome these limitations and to extend the use of 1D models to the analysis of complex geometries or advanced materials. In this work very complex space structures are analyzed using 1D model based on the Carrera Unified Formulation (CUF). The free-vibration analysis of isotropic and composite structures are shown. The effects of the loading factor on the natural frequencies of an outline of launcher similar to the Arian V have been investigated. The results highlight the capability of the present refined one-dimensional model to reduce the computational costs without reducing the accuracy of the analysis.