1,721,152 research outputs found
Component-wise models for static, dynamic and aeroelastic analyses of metallic and composite aerospace structures
Get PDFIn 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
Gasdynamics of rapid and explosive decompressions of pressurized aircraft including active venting
Get PDFIn this paper, a zero-dimensional mathematical formulation for rapid and explosive decompression analyses of pressurized aircraft is developed. Air flows between two compartments and between the damaged compartment and external ambient are modeled by assuming an adiabatic, reversible transformation. Both supercritical and subcritical decompressions are considered, and the attention focuses on intercompartment venting systems. In particular, passive and active vents are addressed, and mathematical models of both swinging and translational blowout panels are provided. A numerical procedure based on an explicit Euler integration scheme is also discussed for multi-compartment aircraft analysis. Various numerical solutions are presented, which highlight the importance of considering the opening dynamics of blowout panels. The comparisons with the results from the literature demonstrate the validity of the proposed methodology, which can be also applied, with no lack of accuracy, to the decompression analysis of spacecraf
On the effectiveness of Component-Wise models in analysing civil engineering framed structures
No full textAccurate response of wing structures to free-vibration, load factors and non-structural masses
Get PDFBased on the Carrera Unified Formulation (CUF), this work extends variable kinematic finite beam elements to include load factors and non-structural masses for the static and vibration analyses of complex, metallic wing structures. According to CUF, variable kinematic beam theories are formulated in an automatic and hierarchical manner by expressing the displacement field as an arbitrary expansion through generic cross-sectional functions. Both Taylor-like and Lagrange polynomials are used in this paper to develop refined beam kinematics, and the related theories are referred to as TE and LE, respectively. The generalized unknowns of TE models are the beam axis displacements and the N-order displacement derivatives, N being a free parameter of the analysis. Classical beam theories are clearly particular cases of the linear (N=1) TE model. On the other hand, LE models have only pure translational displacements as unknowns. By exploiting this characteristic of LE, a Component-Wise (CW) approach is implemented and used for the analysis of multi-component reinforced-shell structures. Numerical applications are developed by classical finite element procedures, and both static response and free vibration analyses are addressed. Various configurations of a benchmark wing are considered, and the capabilities of the present methodologies when dealing with higher-order effects due to deformable cross-sections and geometrical discontinuities (e.g. underside windows) are evaluated. The attention is focused on the applicability of the present refined beam models to problems involving complex, external inertial loadings. The results are compared to finite element solutions from commercial tools, including full 3D models and models obtained by assembling 2D shell and 1D finite element
Component-Wise Method Applied to Static and Dynamic Analysis of Reinforced Structures with Applications to Aerospace, Civil Engineering and Marine Constructions
Get PDFIn this work, an advanced formulation for the analysis of multi-component structures is presented. By employing the Carrera Unified Formulation (CUF), one-dimensional theories of structures are unified and written in a compact form by using fundamental nuclei. The principle of virtual displacement is then used to write the governing equations and the related finite element arrays. Classical one-dimensional shape functions are utilized to discretize the problem along the beam axis and to deal with complex geometries and loadings. Thanks to CUF, various one-dimensional beam theories are included within the same hierarchical finite element. Particular attention is paid to the Component-Wise (CW) approach. CW models are generated by developing beam theories based on Lagrange polynomial expansions of the generalized displacements. The enhanced capabilities of the present CW models when applied to the analysis of short beams, thin-walled structures and multi-component constructions are widely discusse
Evaluation of the accuracy of classical beam FE models via locking-free hierarchically refined elements
Get PDFIt is well known that the classical 6-DOF (Degrees of Freedom) beam theories that are incorporated in commercial finite element (FE) tools are not able to foresee higher-order phenomena, such as elastic bending/shear coupling, restrained torsional warping and three-dimensional strain effects. In this work, the accuracy of one-dimensional (1D) finite elements based on the classical theories (Euler-Bernoulli and Timoshenko theories as well as a 6-DOF model including torsion) is evaluated for a number of problems of practical interest and modelling guidelines are given. The investigation is carried out by exploiting a novel hierarchical, locking-free, finite beam element based on the well-known Carrera Unified Formulation (CUF). Thanks to CUF, the FE arrays of the novel beam element are written in terms of fundamental nuclei, which are invariant with respect to the theory approximation order. Thus, results from classical as well as arbitrarily refined beam models can be formally obtained by the same CUF beam element. Linear Lagrange shape functions are used in this paper to interpolate the generalized unknowns and shear locking phenomena are avoided by adopting an MITC (Mixed Interpolation of Tensorial Components) scheme. Different sample problems are addressed, including rectangular and warping-free circular cross-sections as well as thin-walled beams. The results from classical theories and the 6-DOF model are compared to those from higher-order refined beam models, both in terms of displacement and stress fields for various loading conditions. The discussion focuses on the limitations of the commonly used 1D FEs and the need for refined kinematics beams for most of the problems of common interest. The research clearly depicts CUF as a valuable framework to assess FE formulations such as the 6-DOF model herein considered, which is one of the most known and used finite element for the analysis of structures
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