Special Issue "Mesh-Free and Finite Element-Based Methods for Structural Mechanics Applications"

A special issue of Mathematical and Computational Applications (ISSN 2297-8747). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: 15 February 2020.

Special Issue Editor

Assist. Prof. Dr. Nicholas Fantuzzi
E-Mail Website
Guest Editor
Department of Civil, Chemical, Environmental and Materials Engineering, University of Bologna, 40136 Bologna, Italy
Tel. +390512093494
Interests: modeling of offshore structures and offshore structural components; structural theories of plates and shells and applied mathematical modelling; mechanics of solids and structures; study of composite laminated structures and advanced composite materials; fracture mechanics and crack propagation and initiation; applied numerical methods such as finite element method, differential quadrature technique and mesh free element method
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Special Issue Information

Dear 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 Editor

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Published Papers (9 papers)

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Research

Open AccessFeature PaperArticle
A Continuation Procedure for the Quasi-Static Analysis of Materially and Geometrically Nonlinear Structural Problems
Math. Comput. Appl. 2019, 24(4), 94; https://doi.org/10.3390/mca24040094 - 02 Nov 2019
Abstract
Discussed is the implementation of a continuation technique for the analysis of nonlinear structural problems, which is capable of accounting for geometric and dissipative requirements. The strategy can be applied for solving quasi-static problems, where nonlinearities can be due to geometric or material [...] Read more.
Discussed is the implementation of a continuation technique for the analysis of nonlinear structural problems, which is capable of accounting for geometric and dissipative requirements. The strategy can be applied for solving quasi-static problems, where nonlinearities can be due to geometric or material response. The main advantage of the proposed approach relies in its robustness, which can be exploited for tracing the equilibrium paths for problems characterized by complex responses involving the onset and propagation of cracks. A set of examples is presented and discussed. For problems involving combined material and geometric nonlinearties, the results illustrate the advantages of the proposed hybrid continuation technique in terms of efficiency and robustness. Specifically, less iterations are usually required with respect to similar procedures based on purely geometric constraints. Furthermore, bifurcation plots can be easily traced, furnishing the analyst a powerful tool for investigating the nonlinear response of the structure at hand. Full article
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Open AccessArticle
Hydrodynamic and Acoustic Performance Analysis of Marine Propellers by Combination of Panel Method and FW-H Equations
Math. Comput. Appl. 2019, 24(3), 81; https://doi.org/10.3390/mca24030081 - 09 Sep 2019
Abstract
The noise emitted by ships is one of the most important noises in the ocean, and the propeller noise is one of the major components of the ship noise. Measuring the propeller noise in a laboratory, despite the high accuracy and good reliability, [...] Read more.
The noise emitted by ships is one of the most important noises in the ocean, and the propeller noise is one of the major components of the ship noise. Measuring the propeller noise in a laboratory, despite the high accuracy and good reliability, has high costs and is very time-consuming. For this reason, the calculation of propeller noise using numerical methods has been considered in recent years. In this study, the noise of a propeller in non-cavitating conditions is calculated by the combination of the panel method (boundary element method) and solving the Ffowcs Williams-Hawkings (FW-H) equations. In this study, a panel method code is developed, and the results are validated by the experimental results of the model tests carried out in the cavitation tunnel of the Sharif University of Technology. Software for numerical calculation of propeller noise, based on FW-H equations, is also developed and the results are validated by experimental results. This study shows that the results of the panel method code have good agreement with experimental results, and that the maximum error of this code for the thrust and torque coefficients is 4% and 7%, respectively. The results of the FW-H noise code are also in good agreement with the experimental data. Full article
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Open AccessFeature PaperArticle
Natural Frequency Analysis of Functionally Graded Orthotropic Cross-Ply Plates Based on the Finite Element Method
Math. Comput. Appl. 2019, 24(2), 52; https://doi.org/10.3390/mca24020052 - 19 May 2019
Cited by 1
Abstract
This paper aims to present a finite element (FE) formulation for the study of the natural frequencies of functionally graded orthotropic laminated plates characterized by cross-ply layups. A nine-node Lagrange element is considered for this purpose. The main novelty of the research is [...] Read more.
This paper aims to present a finite element (FE) formulation for the study of the natural frequencies of functionally graded orthotropic laminated plates characterized by cross-ply layups. A nine-node Lagrange element is considered for this purpose. The main novelty of the research is the modelling of the reinforcing fibers of the orthotropic layers assuming a non-uniform distribution in the thickness direction. The Halpin–Tsai approach is employed to define the overall mechanical properties of the composite layers starting from the features of the two constituents (fiber and epoxy resin). Several functions are introduced to describe the dependency on the thickness coordinate of their volume fraction. The analyses are carried out in the theoretical framework provided by the first-order shear deformation theory (FSDT) for laminated thick plates. Nevertheless, the same approach is used to deal with the vibration analysis of thin plates, neglecting the shear stiffness of the structure. This objective is achieved by properly choosing the value of the shear correction factor, without any modification in the formulation. The results prove that the dynamic response of thin and thick plates, in terms of natural frequencies and mode shapes, is affected by the non-uniform placement of the fibers along the thickness direction. Full article
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Open AccessArticle
A Transdisciplinary Approach for Analyzing Stress Flow Patterns in Biostructures
Math. Comput. Appl. 2019, 24(2), 47; https://doi.org/10.3390/mca24020047 - 26 Apr 2019
Abstract
This work presents a transdisciplinary, integrated approach that uses computational mechanics experiments with a flow network strategy to gain fundamental insights into the stress flow of high-performance, lightweight, structured composites by investigating the rostrum of paddlefish. Although computational mechanics experiments give an overall [...] Read more.
This work presents a transdisciplinary, integrated approach that uses computational mechanics experiments with a flow network strategy to gain fundamental insights into the stress flow of high-performance, lightweight, structured composites by investigating the rostrum of paddlefish. Although computational mechanics experiments give an overall distribution of stress in the structural systems, stress flow patterns formed at nascent stages of loading a biostructure are hard to determine. Computational mechanics experiments on a complex model will involve a high degree of freedom thereby making the extraction of finer details computationally expensive. To address this challenge, the evolution of the stress in the rostrum is formulated as a network flow problem generated by extracting the node and connectivity information from the numerical model of the rostrum. The flow network is weighted based on the parameter of interest, which is stress in the current research. The changing kinematics of the system is provided as input to the mathematical algorithm that computes the minimum cut of the flow network. The flow network approach is verified using two simple classical problems. When applied to the model of the rostrum, the flow network approach identifies strain localization in tensile regions, and buckling/crushing in compressive regions. Full article
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Open AccessArticle
Nonlocal FEM Formulation for Vibration Analysis of Nanowires on Elastic Matrix with Different Materials
Math. Comput. Appl. 2019, 24(2), 38; https://doi.org/10.3390/mca24020038 - 06 Apr 2019
Cited by 1
Abstract
In this study, free vibration behaviors of various embedded nanowires made of different materials are investigated by using Eringen’s nonlocal elasticity theory. Silicon carbide nanowire (SiCNW), silver nanowire (AgNW), and gold nanowire (AuNW) are modeled as Euler–Bernoulli nanobeams with various boundary conditions such [...] Read more.
In this study, free vibration behaviors of various embedded nanowires made of different materials are investigated by using Eringen’s nonlocal elasticity theory. Silicon carbide nanowire (SiCNW), silver nanowire (AgNW), and gold nanowire (AuNW) are modeled as Euler–Bernoulli nanobeams with various boundary conditions such as simply supported (S-S), clamped simply supported (C-S), clamped–clamped (C-C), and clamped-free (C-F). The interactions between nanowires and medium are simulated by the Winkler elastic foundation model. The Galerkin weighted residual method is applied to the governing equations to gain stiffness and mass matrices. The results are given by tables and graphs. The effects of small-scale parameters, boundary conditions, and foundation parameters on frequencies are examined in detail. In addition, the influence of temperature change on the vibrational responses of the nanowires are also pursued as a case study. Full article
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Open AccessArticle
Trustworthiness in Modeling Unreinforced and Reinforced T-Joints with Finite Elements
Math. Comput. Appl. 2019, 24(1), 27; https://doi.org/10.3390/mca24010027 - 20 Feb 2019
Cited by 1
Abstract
As required by regulations, Finite Element Analyses (FEA) can be used to investigate the behavior of joints which might be complex to design due to the presence of geometrical and material discontinuities. The static behavior of such problems is mesh dependent, thus these [...] Read more.
As required by regulations, Finite Element Analyses (FEA) can be used to investigate the behavior of joints which might be complex to design due to the presence of geometrical and material discontinuities. The static behavior of such problems is mesh dependent, thus these results must be calibrated by using laboratory tests or reference data. Once the Finite Element (FE) model is correctly setup, the same settings can be used to study joints for which no reference is available. The present work analyzes the static strength of reinforced T-joints and sheds light on the following aspects: shell elements are a valid alternative to solid modeling; the best combination of element type and mesh density for several configurations is shown; the ultimate static strength of joints can be predicted, as well as when mechanical properties are roughly introduced for some FE topologies. The increase in strength of 12 unreinforced and reinforced (with collar or doubler plate) T-joints subjected to axial brace loading is studied. The present studies are compared with the literature and practical remarks are given in the conclusion section. Full article
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Open AccessArticle
A Complex Variable Solution for Lining Stress and Deformation in a Non-Circular Deep Tunnel II Practical Application and Verification
Math. Comput. Appl. 2018, 23(3), 43; https://doi.org/10.3390/mca23030043 - 30 Aug 2018
Abstract
A new complex variable method is presented for stress and displacement problems in a non-circular deep tunnel with certain given boundary conditions at infinity. In order to overcome the complex problems caused by non-circular geometric configurations and the multiply-connected region, a complex variable [...] Read more.
A new complex variable method is presented for stress and displacement problems in a non-circular deep tunnel with certain given boundary conditions at infinity. In order to overcome the complex problems caused by non-circular geometric configurations and the multiply-connected region, a complex variable method and continuity boundary conditions are used to determine stress and displacement within the tunnel lining and within the surrounding rock. The coefficients in the conformal mapping function and stress functions are determined by the optimal design and complex variable method, respectively. The new method is validated by FLAC3D finite difference software through an example. Both the new method and the numerical simulation obtained similar results for the stress concentration and the minimum radial displacement occurred at a similar place in the tunnel. It is demonstrated that the new complex variable method is reliable and reasonable. The new method also provides another way to solve non-circular tunnel excavation problems in a faster and more accurate way. Full article
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Open AccessFeature PaperArticle
4D Remeshing Using a Space-Time Finite Element Method for Elastodynamics Problems
Math. Comput. Appl. 2018, 23(2), 29; https://doi.org/10.3390/mca23020029 - 25 May 2018
Cited by 1
Abstract
In this article, a Space-Time Finite Element Method (STFEM) is proposed for the resolution of mechanical problems involving three dimensions in space and one in time. Special attention will be paid to the non-separation of the space and time variables because this kind [...] Read more.
In this article, a Space-Time Finite Element Method (STFEM) is proposed for the resolution of mechanical problems involving three dimensions in space and one in time. Special attention will be paid to the non-separation of the space and time variables because this kind of interpolation is well suited to mesh adaptation. For that purpose, we have developed a technique of 4D mesh generation adapted to space-time remeshing. A difficulty arose in the representation of 4D finite elements and meshes. This original technique does not require coarse-to-fine and fine-to-coarse mesh-to-mesh transfer operators and does not increase the size of the linear systems to be solved, compared to traditional finite element methods. Space-time meshes are composed of simplex finite elements. Computations are carried out in the context of the continuous Galerkin method. We have tested the method on a linearized elastodynamics problem. Our technique of mesh adaptation was validated on elementary examples and applied to a problem of mobile loading. The convergence and stability of the method are studied and compared with existing methods. This work is a first implementation of 4D space-time remeshing. A stability criterion for the method is established, as well as a convergence rate of about two. Using simplex elements, it is possible to develop a technique of mesh adaptation able to follow a mobile loading zone. Full article
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Open AccessFeature PaperArticle
Integration of Direction Fields with Standard Options in Finite Element Programs
Math. Comput. Appl. 2018, 23(2), 24; https://doi.org/10.3390/mca23020024 - 07 May 2018
Cited by 1
Abstract
The two-dimensional differential equation y’ = f(x,y) can be interpreted as a direction field. Commercial Finite Element (FE) programs can be used for this integration task without additional programming, provided that these programs have options for the calculation of orthotropic heat conduction problems. [...] Read more.
The two-dimensional differential equation y’ = f(x,y) can be interpreted as a direction field. Commercial Finite Element (FE) programs can be used for this integration task without additional programming, provided that these programs have options for the calculation of orthotropic heat conduction problems. The differential equation to be integrated with arbitrary boundaries is idealized as an FE model with thermal 2D elements. Its orthotropic thermal conductivities are specified as k1 = 1 and k2 = 0. In doing so, k1 is parallel to y´, and k2 is oriented perpendicular to this. For this extreme case, it is shown that the isotherms are identical to the solution of y’ = f(x,y). The direction fields, for example, can be velocity vectors in fluid mechanics or principal stress directions in structural mechanics. In the case of the latter, possibilities for application in the construction of fiber-reinforced plastics (FRP) arise, since fiber courses, which follow the local principal stress directions, make use of the superior stiffness and strength of the fibers. Full article
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