451 research outputs found
Special Issue "Mesh-Free and Finite Element-Based Methods for Structural Mechanics Applications"
Full text linkDear Colleagues,
The problem of solving complex engineering problems has been always a major topic in all industrial fields, such as aerospace, civil and mechanical engineering. The use of numerical methods increased exponentially in the last few years due to modern computers in the field of structural mechanics.
Moreover, a wide-range of numerical methods has been presented in the literature for solving such problems. Structural mechanics problems are dealt with using partial differential systems of equations that might be solved by following the two main classes of methods: Domain-decomposition methods or the so-called finite element methods and mesh-free methods where no decomposition is carried out. Both methodologies discretize a partial differential system into a set of algebraic equations that can be easily solved by computer implementation. The aim of the present Special Issue is to present a collection of recent works on these themes and a comparison of the novel advancements of both worlds in structural mechanics applications.
Assist. Prof. Dr. Nicholas Fantuzzi
Guest Edito
Strong and Weak Formulations for the Analysis of Arbitrarily Shaped Laminated Composite Structures
No full textA numerical approach is developed to deal with arbitrarily shaped structures. Two different methodologies are used to this aim, which are based on the Differential Quadrature and Integral Quadrature methods, respectively. These numerical methods are able to approximate both derivatives and integrals [1]. Therefore, the strong and weak formulations of the governing equations can be solved. As shown in the paper [2], these approaches are accurate, reliable and stable, when employed to obtain the mechanical response of various kinds of structures, such as plates, shells and membranes. In particular, their effectiveness is proven by means of the comparison with the analytical solutions available in the literature, both for isotropic and composite structures.
With respect to other approaches such as the Finite Element Method (FEM), the proposed methodologies are able to get the solution with few degrees of freedom. In addition, the convergence behavior is faster than the FEM.
A domain decomposition based on Isogeometric analysis is developed to analyze the mechanical behavior of arbitrarily shaped structures. The so-called blending functions are used to deal with discontinuities and distortions by means of a reduced number of elements [3, 4]. Thus, a nonlinear mapping is achieved by employing NURBS curves. According to the numerical method used in the computation, the strong and weak formulations are solved within each element. The effect of distorted meshes on the solution is investigated, as well. The numerical methods at issue are named Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM).
References
[1] Tornabene, F., Fantuzzi, N., Ubertini, F., Viola, E., "Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey", Applied Mechanics Reviews, 67, 02081-1-55 (2015).
[2] Tornabene, F., Fantuzzi, Bacciocchi, M., "Strong and weak formulations based on differential and integral quadrature methods for the free vibration analysis of composite plates and shells: Convergence and accuracy", Engineering Analysis with Boundary Elements. In press. DOI: 10.1016/j.enganabound.2017.08.020.
[3] Fantuzzi, N., Tornabene, F., "Strong Formulation Isogeometric Analysis (SFIGA) for Laminated Composite Arbitrarily Shaped Plates", Composites Part B - Engineering, 96, 173-203 (2016).
[4] Tornabene, F., Fantuzzi, Bacciocchi, M., "The GDQ Method for the Free Vibration Analysis of Arbitrarily Shaped Laminated Composite Shells Using a NURBS-Based Isogeometric Approach", Composite Structures, 154, 190-218 (2016)
Strong and Weak Formulations for the Analysis of Arbitrarily Shaped Laminated Composite Structures
No full textA numerical approach is developed to deal with arbitrarily shaped structures. Two different methodologies are used to this aim, which are based on the Differential Quadrature and Integral Quadrature methods, respectively. These numerical methods are able to approximate both derivatives and integrals [1]. Therefore, the strong and weak formulations of the governing equations can be solved. As shown in the paper [2], these approaches are accurate, reliable and stable, when employed to obtain the mechanical response of various kinds of structures, such as plates, shells and membranes. In particular, their effectiveness is proven by means of the comparison with the analytical solutions available in the literature, both for isotropic and composite structures.
With respect to other approaches such as the Finite Element Method (FEM), the proposed methodologies are able to get the solution with few degrees of freedom. In addition, the convergence behavior is faster than the FEM.
A domain decomposition based on Isogeometric analysis is developed to analyze the mechanical behavior of arbitrarily shaped structures. The so-called blending functions are used to deal with discontinuities and distortions by means of a reduced number of elements [3, 4]. Thus, a nonlinear mapping is achieved by employing NURBS curves. According to the numerical method used in the computation, the strong and weak formulations are solved within each element. The effect of distorted meshes on the solution is investigated, as well. The numerical methods at issue are named Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM).
References
[1] Tornabene, F., Fantuzzi, N., Ubertini, F., Viola, E., "Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey", Applied Mechanics Reviews, 67, 02081-1-55 (2015).
[2] Tornabene, F., Fantuzzi, Bacciocchi, M., "Strong and weak formulations based on differential and integral quadrature methods for the free vibration analysis of composite plates and shells: Convergence and accuracy", Engineering Analysis with Boundary Elements. In press. DOI: 10.1016/j.enganabound.2017.08.020.
[3] Fantuzzi, N., Tornabene, F., "Strong Formulation Isogeometric Analysis (SFIGA) for Laminated Composite Arbitrarily Shaped Plates", Composites Part B - Engineering, 96, 173-203 (2016).
[4] Tornabene, F., Fantuzzi, Bacciocchi, M., "The GDQ Method for the Free Vibration Analysis of Arbitrarily Shaped Laminated Composite Shells Using a NURBS-Based Isogeometric Approach", Composite Structures, 154, 190-218 (2016)
Erratum to: Inter-laminar stress recovery procedure for doubly-curved, singly-curved, revolution shells with variable radii of curvature and plates using generalized higher-order theories and the local GDQ method (Mechanics of Advanced Materials and Structures, (2016), 23, 9, (1019-1045), 10.1080/15376494.2015.1121521)
No full textIn the above article, published in issue 23(9) of Mechanics of Advanced Materials and Structures, the second author’s name was spelled incorrectly. The correct spelling is Nicholas Fantuzzi. The publisher apologizes for the error
Modelling of Damaged Laminated and Sandwich Shell Structures by means of Higher-order Shear Deformation Theories
No full textThe main aim of the current research is the development of a mathematical formulation for the modelling of damage in laminated and sandwich composite shells. For this purpose, the damage of some areas of the structures can be seen as concentrated decays of the mechanical properties of the elastic constituents. In general, several kinds of damage can affect the mechanical behavior of a generic laminated structure, such as microcracking, debonding, fiber ruptures, and transverse matrix cracking, as specified in [1].
Without investigating the causes of the damage, the current approach suggests to introduce peculiar functions that multiply directly the mechanical properties of the elastic media, expressed in terms of engineering constants. To this aim, the Gaussian function and an ellipse shaped law are used to model a quick variation of the mechanical properties within the whole structural domain. By setting properly the parameters that characterize these distributions, it is possible to control the intensity of the deterioration and the width of the damaged areas, as well as the point of applications.
The present approach is employed to characterize the damage in some doubly-curved shells characterized by different radii of curvature. The difficulties related to the description of these curved surfaces are overcome by means of an analytical formulation based on differential geometry [2]. As far as the mechanical properties are concerned, several constituents are considered and combined.
The theoretical framework is based on a formulation that allows to develop easily different kinematic models and expansions in a unified manner. Thus, several Higher-order Shear Deformation Theories, which can include also the zig-zag effect, are employed. In fact, it has been proven that peculiar mechanical configurations require an enriched structural model, since lower-order theories could be inadequate to capture the effective mechanical behavior.
Finally, a numerical technique able to solve the strong form of the governing equations is used. For this purpose, the partial derivatives that appear in the fundamental system are directly approximated through the Generalized Differential Quadrature method due to its accuracy [3].
References
[1] Tornabene, F., Fantuzzi, N., Bacciocchi, M., “Linear Static Behavior of Damaged Laminated Composite Plates and Shells”, Materials, 10, 811, 1-52 (2017).
[2] Tornabene, F., Fantuzzi, N., Bacciocchi, M., and E. Viola, Laminated Composite Doubly-Curved Shell Structures. Differential Geometry. Higher-order Structural Theories, Esculapio, Bologna (2016).
[3] Tornabene, F., Fantuzzi, N., Ubertini, F., Viola, E., “Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey”, Applied Mechanics Reviews, 67, 020801-1-55
New insights into the strong formulation finite element method for solving elastostatic and elastodynamic problems
No full textThis present paper has a complete and homogeneous
presentation of plane stress and plane strain problems
using the Strong Formulation Finite Element Method
(SFEM). In particular, a greater emphasis is given to the
numerical implementation of the governing and boundary
conditions of the partial differential system of equations.
The paper’s focus is on numerical stability and accuracy
related to elastostatic and elastodynamic problems.
In the engineering literature, results are mainly reported
for isotropic and homogeneous structures. In this paper, a
composite structure is investigated. The SFEM solution is
compared to the ones obtained using commercial finite element
codes. Generally, the SFEM observes fast accuracy
and all the results are in very good agreement with the
ones presented in literature
Dynamics for anisotropic homogenized materials
No full textMaterials such as ceramic and metal composites, poly-crystals, masonry, porous rocks are examples of particle composites: their macroscopic behavior is strongly dependent on the internal microstructure, moreover discontinuities and heterogeneities cannot be neglected. For these reasons, a non-local description is necessary to take into account the microscopic influence on the mechanical response. In this work the goal is to highlight the advantages of a description of these materials as micropolar continua compared to the classical continua. A homogenization technique, based on an energy equivalence criterion, between the discrete model, assumed as the benchmark, and the continuum model, is adopted to detect the anisotropic constitutive characteristics [1]. A possible numerical approach is presented in order to have a right identification of the representative volume element, needful for a correct homogenization [2].
Starting from other works of the same authors where the statics of two-dimensional bodies has been analysed [3-5], this study goes to further enrich the discussion and shows the influences of the material internal length on the dynamic response and consequently the necessity of a micropolar description. Particle composites with an internal microstructure made of three different hexagonal rigid blocks and thin elastic interfaces are considered at three different scale level, the numerical tests bring out how an increasing in the level of material anisotropy affect both frequencies and mode-shapes.
[1] P. Trovalusci and R. Masiani, “Material symmetries of micropolar continua equivalent to lattices,” Int. J. Solids Struct., vol. 36, no. 14, pp. 2091–2108, 1999, doi: 10.1016/S0020-7683(98)00073-0.
[2] M. Colatosti, N. Fantuzzi, P. Trovalusci, and R. Masiani, “New insights on homogenization for hexagonal-shaped composites as Cosserat continua”. Meccanica, 2021. https://doi.org/10.1007/s11012-021-01355-x
[3] N. Fantuzzi, P. Trovalusci, and R. Luciano, “Multiscale analysis of anisotropic materials with hexagonal microstructure as micropolar continua,” Int. J. Multiscale Comput. Eng., vol. 18, no. 2, pp. 265–284, 2020, doi: 10.1615/IntJMultCompEng.2020032920.
[4] N. Fantuzzi, P. Trovalusci, and R. Luciano, “Material symmetries in homogenized hexagonal-shaped composites as cosserat continua,” Symmetry, vol. 12, no. 3, pp. 1–21, 2020, doi: 10.3390/sym12030441.
[5] L. Leonetti, N. Fantuzzi, P. Trovalusci, and F. Tornabene, “Scale effects in orthotropic composite assemblies as micropolar continua: A comparison between weak and strong-form finite element solutions,” Materials, vol. 12, no. 5, 2019, doi: 10.3390/ma12050758
21th International Conference on Composite Structures (ICCS21)
No full textIt is well-known that the topic of composite materials affects many engineering fields, such as civil, mechanical, aerospace, automotive and chemical. In the last decades, in fact, a huge number of scientific papers concerning these peculiar constituents has been published. Analogously, the industrial progress has been extremely noticeable.
The study of composite materials, in general, is a challenging activity since the advancements both in the academia and in the industry provide continually new sparks to develop innovative ideas and applications. The communication, the sharing and the exchange of views can surely help the works of many researchers. This aspect represents the main purpose of this Conference, which aims to collect high-level contributions on the development and the application of composite materials.
The establishment of this 21st edition of International Conference on Composite Structures has appeared appropriate to continue what has been begun during the previous editions. ICCS wants to be an occasion for many researchers from each part of the globe to meet and discuss about the recent advancements regarding the use of composite structures, sandwich panels, nanotechnology, bio-composites, delamination and fracture, experimental methods, manufacturing and other countless topics that have filled many sessions during this conference. As a proof of this event, which has taken place in Bologna (Italy), selected plenary and key-note lectures have been collected in the present book.
The conference attracted 350+ delegates from around the world of composites. The plenary lectures were given by, Johannes Michael Sinapius (Technische Universität Braunschweig, Germany), Aurelio Araujo (University of Lisbon, Portugal), Francesco Tornabene (University of Bologna, Italy), Andreas Echtermeyer (NTNU-Norwegian University of Science and Technology, Norway), Raimondo Luciano (University of Cassino and Southern Lazio, Italy).
The Conference Chair: Antonio J.M. Ferreira (University of Porto, Portugal), Francesco Tornabene (University of Bologna, Italy), Nicholas Fantuzzi (University of Bologna, Italy), Erasmo Viola (University of Bologna, Italy).
The Local Organizing Committee: Michele Bacciocchi (University of Bologna, Italy)
Mathematical and Computational Applications
No full textMathematical and Computational Applications (MCA) is devoted to original research in the field of engineering, natural sciences or social sciences where mathematical and/or computational techniques are necessary for solving specific problems. The aim of the journal is to provide a medium by which a wide range of experience can be exchanged among researchers from diverse fields such as engineering (electrical, mechanical, civil, industrial, aeronautical, nuclear etc.), natural sciences (physics, mathematics, chemistry, biology etc.) or social sciences (administrative sciences, economics, political sciences etc.). The papers may be theoretical where mathematics is used in a nontrivial way or computational or combination of both. Each paper submitted will be reviewed and only papers of highest quality that contain original ideas and research will be published. Papers containing only experimental techniques and abstract mathematics without any sign of application are discouraged
Di.Qu.M.A.S.P.A.B. - Differential Quadrature for Mechanics of Anisotropic Shells, Plates, Arches and Beams
No full textDiQuMASPAB is an acronym for Differential Quadrature for Mechanics of Anisotropic Shells, Plates, Arches and Beams. The purpose of this software is to provide a general framework for modelling complex structures such as moderately thick doubly-curved shells and plates, using the Generalized Differential Quadrature (GDQ) method. DiQuMASPAB project is one of the activities of CIMEST Research Centre promoted by Prof. Erasmo Viola, Ass. Prof. Francesco Tornabene and Ph.D. Nicholas Fantuzzi. This code allows the user to investigate the static and dynamic analyses of doubly-curved, singly-curved laminated composite and functionally graded (FGM) shells, panels and degenerate plates.
To the best knowledge of the authors, there are three different ways to study anisotropic shell structures: the 3D Elasticity, Equivalent-Single-Layer (ESL) and Layer-Wise (LW) theories. A 2D generalized displacement field suitable to represent in a unified form most of the kinematical hypothesis presented in literature is implemented in DiQuMASPAB software. The mechanical model used is based on the Carrera’s Unified Formulation (CUF) with curvature effect included for the ESL and LW approaches. The zig-zag effect is also considered in the ESL theory using the Murakami function. Various shear functions through the thickness of the shell structure can be chosen, combined and compared with each other by the user in order to study different types of higher-order theories.
The theoretical implementation of these theories leads to an explicit form of the Fundamental Nuclei (FN) for laminated completely doubly-curved shells. The FN can be used not only for the ESL approach, but also for the LW theory. Concerning a laminated composite doubly-curved shell in orthogonal curvilinear coordinate system, the fundamental operators are explicitly obtained for the first time by the authors. Thanks to the generality of the developed CUF approach, the general theoretical formulation of 2D Higher-order Shear Deformation Theory (HSDT) for doubly-curved shells can also be computed, as well as the classical First-order and Third-order Shear Deformation Theories. DiQuMASPAB software allows to consider up to 24 degrees of freedom for the ESL theory and up to 18 degrees of freedom for each layer when the LW theory is selected.
To define the arbitrary shape of the middle surface of shells and panels with different curvatures, the Differential Geometry theory is used coupled with GDQ technique. The GDQ rule permits to numerically evaluate all the derivatives required for describing the geometry of doubly-curved shell structures.
The shell governing equations are expressed as functions of various kinematic parameters, when the constitutive and the kinematic relationships are known. The system of second-order linear partial differential equations is solved using the GDQ approach.
A three-dimensional stress recovery procedure based on the 3D Elasticity equations in orthogonal curvilinear coordinate system for doubly-curved shells and panels is also used to reconstruct all the stresses and strains through the thickness of the shell structure.and to satisfy the top and bottom boundary conditions of the laminated composite shell or panel. The numerical procedure related to the stress and strain recovery is solved using the GDQ technique. All displacements, strains and stresses can be plotted through the thickness of the selected shell structure. Several lamination schemes, FGM distributions through the thickness, loadings and boundary conditions can be considered. Moreover, DiQuMASPAB software has an embedded tool for the comparison with throught-the-thickness plots obtained with numerical solutions of different codes
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