1,720,963 research outputs found
Static analysis of anisotropic doubly-curved shells with arbitrary geometry and variable thickness resting on a Winkler-Pasternak support and subjected to general loads
No full textLaminated doubly-curved shells constituted by innovative materials have become a standard application in several engineering fields. However, this requires a proper formulation of such structures, since several very complex issues affecting such applications must be kept in mind, among all, the curvature effect and the coupling issues between two adjacent layers. In the present work a generalized formulation based on Higher Order Theories is proposed for the linear static analysis of curved structures with completely anisotropic materials in each layer of the lamination scheme. The shell model is described according to the Equivalent Single Layer approach and a mapping procedure based on a Non-Uniform Rational Basis Spline (NURBS) description of the shell edges is applied for the geometric description. Different thickness variations have been considered in the analyses. The fundamental equations of the static problem are derived from the minimum potential energy principle directly in the strong form and the effect of the Winkler-Pasternak support has been accounted for. The external surface load has been applied in each principal direction and arbitrary actions have been enforced to the external edges of the structure. The proposed approach has been validated with respect to the outcomes of some 3D Finite Element models and very good agreement is found between such simulations. Shells characterized by very complex shapes have been accounted for and accurate results have been found with a reduced number of degrees of freedom
Higher-order modeling of anisogrid composite lattice structures with complex geometries
No full textThe work investigates the vibration behaviour of anisogrid composite lattice shell structures, typically formed by a system of geodesic unidirectional composite ribs. A homogenization approach is here embedded within an Equivalent Single Layer (ESL) formulation for doubly-curved shells, accounting for the geometric contribution of cell patterns. The lattice shells are modelled as anisotropic homogenized continuous structures characterized by effective stiffness parameters. The governing equations of motion are derived using the Higher-order Shear Deformation Theories (HSDTs) of shells, whereas the Generalized Differential Quadrature (GDQ) method is applied to determine the fundamental frequencies with a reduced computational effort. A piecewise field variable assumption is considered for a proper description of zigzag interfacial effects between the lattice core and the external skins. The reliability and efficiency of the proposed numerical strategy is verified by comparison with finite element-based predictions. A systematic analysis aims at studying the effect of different geometric and stiffness parameters, e.g. the number of ribs, their cross-sectional dimensions, orientation and spacing, on the magnitude of the fundamental frequencies for some lattice structural members that could be of great interest for design purposes in the aerospace or automotive engineering practice
Free vibration analysis of laminated doubly-curved shells with arbitrary material orientation distribution employing higher order theories and differential quadrature method
No full textIn the present work, the dynamic behaviour of laminated anisotropic doubly-curved shells characterized by a generalized distribution of the material orientation angle is investigated employing higher order theories. The structural problem is developed following the Equivalent Single Layer (ESL) methodology, setting up a unified approach for the assessment of the displacement field variable with higher order theories. Accordingly, a generalized three-dimensional distribution of the material orientation angle is associated to each layer of the stacking sequence, accounting for an in-plane bivariate power distribution and out-of-plane symmetric and unsymmetric profiles described with both polynomial and non-polynomial analytical expressions. The funda-mental equations are derived from the Hamiltonian Principle, and they are numerically tackled employing the Generalized Differential Quadrature (GDQ) method directly in the strong form. Moreover, a generalized three-dimensional set of linear elastic springs is implemented for the assessment of con-conventional boundary con-ditions. Furthermore, a generalized isogeometric mapping of the physical domain accounts for arbitrarily-shaped structures. The model is validated successfully with respect to refined three-dimensional classical models, and it is, then, applied systematically to check for the sensitivity of the mechanical response to the structural curvature, external constraints, and material orientation angle distributions
Structural Analysis of Doubly-Curved Shells with General Boundary Conditions
No full textThe paper focuses on a bi-dimensional (2D) formulation for the dynamic and static analysis of arbitrary shaped laminated doubly-curved shells enforced with general boundary conditions via the Generalized Differential Quadrature (GDQ). Following the Equivalent Single Layer approach, a 2D theory based on a miscel laneous assessment of the displacement field variable is provided, accounting for different higher order theories. The geometry of the structure is described with a set of principal coordinates. The fundamental equations are derived from the Hamil tonian principle, together with the natural boundary conditions. Unconventional constraints are assessed by means of in-plane and out-of-plane sets of linear elastic springs distributed along the shell edges. The accuracy of the formulation is out lined by means of a series of validating examples. Doubly-curved shells of variable thickness and different curvatures enforced with non-conventional boundary con ditions are investigated. In particular, mode frequencies and shapes, as well as the static three-dimensional deflection of the structure, have been calculated employ ing different kinematic assumptions. The results have been successfully compared to predictions by high-computationally demanding Finite Element simulations. The methodology outlined in this chapter well predicts with a reduced computational effort both the static and the dynamic response of generally anisotropic laminated structures embedding all the effects that are usually depicted by 3D formulations
Higher order formulations for doubly-curved shell structures with a honeycomb core
No full textAnisotropic doubly-curved shells reinforced with a honeycomb core are innovative structures for applications in civil, biomedical, and aerospace engineering. In this context, the homogenization technique represents one of the simplest way for analyzing such complex structures. A proper formulation must be capable to give accurate results for any cell configuration and/or curved shape. In the present work an innovative model is proposed, based on an Equivalent Single Layer (ESL) approach and higher order theories, for an accurate estimation of the vibrational response of plates, panels and shells, whose results are compared with predictions from a classical Finite Element Method (FEM). The work starts with a comparative study performed on aluminum sandwich plates with hexagonal, rectangular and re-entrant cells. Then, a sensitivity analysis evaluates the dynamic response of single- and doubly-curved panels with different cell typologies. The fundamental equations are tackled numerically by resorting to the 2D Generalized Differential Quadrature (GDQ) method. The influence of the kinematic assumptions throughout the thickness on the dynamic response of shells is investigated, accounting for different Representative Volume Element (RVE) deformation effects within the homogenized model. In all the analyses, cell units are analyzed by means of different geometric angles, thin and thick cores, as well as classic and double thickness vertical walls or commercial honeycomb cores
Static and free vibration analysis of anisotropic doubly-curved shells with general boundary conditions
Full text linkIn the present work, a two-dimensional model based on a higher order Layer-Wise (LW) approach is presented for the static and dynamic analysis of doubly-curved anisotropic shell structures. The Equivalent Single Layer (ESL) methodology is also obtained as particular case of LW. Each lamina of the stacking sequence is modelled as an anisotropic continuum. The fundamental equations account for both surface and concentrated loads, as well as the effects of the Winkler-Pasternak foundation. Moreover, non-conventional boundary conditions are introduced, and the numerical solution is assessed from the Generalized Differential Quadrature (GDQ) method. The proposed formulation is validated with respect to refined three-dimensional simulations, pointing out its accuracy and computational efficiency
1D-Hierarchical Ritz and 2D-GDQ Formulations for the free vibration analysis of circular/elliptical cylindrical shells and beam structures
No full textThe present paper proposes a comparison between two different computational techniques to evaluate the natural frequencies of some selected structural components. More specifically, three case studies are investigated: i) Isotropic circular and elliptical cylindrical shells; ii) Non-homogeneous circular cylindrical shell sectors; iii) Homogeneous and non-homogeneous rectangular beams. The 1D-Hierarchical Ritz Formulation (HRF) with 3D capabilities and the 2D-Generalized Differential Quadrature (GDQ) formulation (both in a weak- and a strong-form) are assessed by using a Finite Element Method (FEM) software. For both computational methodologies the Method of Power Series Expansion of the Displacement Components (MPSEDCs) has been employed. A parametric investigation is performed to study the sensitivity of the natural frequencies to some significant parameters, namely, the boundary conditions, the length-to-thickness ratio, as well as some material and geometrical properties. The main advantages of the proposed solution techniques are discussed in terms of convergence and accuracy, for each selected case study
Dynamic analysis of anisotropic doubly-curved shells with general boundary conditions, variable thickness and arbitrary shape
No full textIn the present contribution a general formulation is proposed to account for general boundary conditions within the dynamic analysis of anisotropic laminated doubly-curved shell having arbitrary shape and variable thickness. Different analytical expressions are considered for the shell thickness variation along the geometrical principal directions, and the distortion of the physical domain is described by a mapping procedure based on Non-Uniform Rational Basis Spline (NURBS) curves. Mode frequencies and shapes are determined employing higher-order theories within an Equivalent Single Layer (ESL) framework. The related fundamental relations are tackled numerically by means of the Generalized Differential Quadrature (GDQ) method. The dynamic problem is derived from the Hamiltonian Principle, leading to a strong formulation of the governing equations. General external constraints are enforced along the edges of the shell employing a distribution of linear springs distributed on the faces of the three-dimensional solid and accounting for a spatial coordinate-dependent stiffness along both in-plane and out-of-plane directions. Moreover, a Winkler-type foundation with general distribution of linear springs is modelled on the top and bottom surfaces of the shell. A systematic set of numerical examples is carried out for the validation of the proposed theory by comparing mode frequencies with predictions from refined three-dimensional finite element analyses. Finally, we perform a sensitivity analysis of the dynamic response of mapped curved structures for different spring stiffnesses and general external constraints, according to various kinematic assumptions. © 2022 Elsevier Lt
Dynamic analysis of anisotropic doubly-curved shells with general boundary conditions, variable thickness and arbitrary shape
No full textIn the present contribution a general formulation is proposed to account for general boundary conditions within the dynamic analysis of anisotropic laminated doubly-curved shell having arbitrary shape and variable thickness. Different analytical expressions are considered for the shell thickness variation along the geometrical principal directions, and the distortion of the physical domain is described by a mapping procedure based on Non-Uniform Rational Basis Spline (NURBS) curves. Mode frequencies and shapes are determined employing higher-order theories within an Equivalent Single Layer (ESL) framework. The related fundamental relations are tackled numerically by means of the Generalized Differential Quadrature (GDQ) method. The dynamic problem is derived from the Hamiltonian Principle, leading to a strong formulation of the governing equations. General external constraints are enforced along the edges of the shell employing a distribution of linear springs distributed on the faces of the three-dimensional solid and accounting for a spatial coordinate-dependent stiffness along both in-plane and out-of-plane directions. Moreover, a Winkler-type foundation with general distribution of linear springs is modelled on the top and bottom surfaces of the shell. A systematic set of numerical examples is carried out for the validation of the proposed theory by comparing mode frequencies with predictions from refined three-dimensional finite element analyses. Finally, we perform a sensitivity analysis of the dynamic response of mapped curved structures for different spring stiffnesses and general external constraints, according to various kinematic assumptions
Higher-order theories for doubly curved laminated lattice and honeycomb structures
No full textA collocation model based on a Generalized Differential Quadrature Method (GDQM) is proposed for the dynamic analysis of anisotropic curved laminated structures with a central lattice core and different external constraints. The theory is based on the Equivalent Single Layer (ESL) approach, together with higher-order kinematic assumptions. The reliability of the proposed method is checked with respect to classical 3D FEM-based solutions, for different shell geometries, lamination schemes and unit cell configurations. Based on the numerical investigation, the proposed formulation reveals to be computationally performing even for complicated shapes and structural members, compared to more expensive commercial finite-element-based packages
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