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Advances in Structural Mechanics Modeled with FEM

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A special issue of Materials (ISSN 1996-1944). This special issue belongs to the section "Materials Simulation and Design".

Deadline for manuscript submissions: closed (2 February 2021) | Viewed by 37684

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Prof. Dr. Angelo Marcello Tarantino

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University of Modena and Reggio Emilia, via P. Vivarelli 10, 41125 Modena, Italy
Interests: viscoelasticity; fracture mechanics and dynamic propagation of cracks; bifurcation theory, nonlinear dynamics, and chaos; piezoelasticity and magnetoelasticity; contact problems; equilibrium, bifurcation, and stability in finite elasticity; fiber-reinforced concretes and earthquake engineering
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Prof. Dr. Carmelo Majorana

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Department of Civil, Environmental and Architectural Engineering (DICEA), University of Padova, Via F. Marzolo, 35131 Padova, Italy
Interests: dynamic stability of structural systems; thermo-hydro-mechanical constitutive behavior of cementitious materials at high temperatures; coupled multi-physics formulations for multi-phase, porous media in unsaturated regime; high-performance concrete characterization and modeling; large strain formulation; plasticity of building materials
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Prof. Dr. Raimondo Luciano

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Engineering Department, University of Napoli Parthenope, Via Ammiraglio Ferdinando Acton, 80133 Napoli, Italy
Interests: computational mechanics of structures and of materials and specifically unilateral problems; computational analysis of masonry structures; computational mechanics of composite materials; finite element method; computational micromechanics; nonlinear and non-local theories
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Dr. Michele Bacciocchi

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Dipartimento di Economia, Scienze e Diritto (DESD), University of San Marino, Via Consiglio dei Sessanta, 47891 Dogana, San Marino
Interests: finite element methods; structural mechanics; plates and beams; numerical analysis; laminated composites; multiphase composites; innovative composite materials; functionally graded materials; carbon nanotubes; non-local theories
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Special Issue Information

Dear Colleagues,

It is well-known that many structural and physical problems cannot be solved by analytical approaches. Such problems require the development of numerical methods to get approximate but accurate solutions. The Finite Element Method (FEM) represents one of the most typical methodologies that can be used to achieve this aim, due to its simple implementation, easy adaptability, and very good accuracy. For these reasons, the FEM is a widespread technique which is employed in many engineering fields, such as civil, mechanical, and aerospace engineering.

The large-scale deployment of powerful computers and the consequent recent improvement of the computational resources have provided the tools to develop numerical approaches that are able to solve more complex structural systems characterized by peculiar mechanical configurations. Laminated or multi-phase composites, structures made of innovative materials, and nanostructures are just some examples of applications that are commonly and accurately solved by FEM. Analogously, the same numerical approaches can be employed to validate the results of experimental tests.

The main aim of this Special Issue is to collect numerical investigations focused on the use of the Finite Element Method. Authors are encouraged to submit innovative applications solved by means of the FEM. The structural systems analyzed in the researches should be also well-described from the mechanical point of view, and particular emphasis may be given to advanced materials.

The topics of interest include, but are not limited to

Numerical analyses of structural systems by FEM;
Investigations of the mechanical behaviors of beams, plates, and shells;
Numerical studies of laminated composite systems;
Advanced and innovative composites;
Accuracy and convergence analyses of FEM or Finite Element-based methods;
Numerical approaches for the mechanical analysis of nanostructures;
FEM applications for elasticity problems;
Linear and nonlinear behaviors of structures;
Mechanical characterization of innovative constituents;
Validation of experimental procedures.

Prof. Dr. Angelo Marcello Tarantino
Prof. Dr. Carmelo Majorana
Prof. Dr. Raimondo Luciano
Dr. Michele Bacciocchi
Collection Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Materials is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (14 papers)

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Editorial

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3 pages, 162 KiB

Open AccessEditorial

Special Issue: “Advances in Structural Mechanics Modeled with FEM”

by Angelo Marcello Tarantino, Carmelo Majorana, Raimondo Luciano and Michele Bacciocchi

Materials 2021, 14(4), 780; https://0-doi-org.brum.beds.ac.uk/10.3390/ma14040780 - 07 Feb 2021

Viewed by 1327

Abstract

The current Special Issue entitled “Advances in Structural Mechanics Modeled with FEM” aims to collect several numerical investigations and analyses focused on the use of the Finite Element Method (FEM) [...] Full article

(This article belongs to the Special Issue Advances in Structural Mechanics Modeled with FEM)

Research

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12 pages, 3245 KiB

Open AccessArticle

Fire Analysis of Timber-Framed Walls Lined with Gypsum

by Paulo A. G. Piloto, Sergio Rodríguez-del-Río and Diego Vergara

Materials 2022, 15(3), 741; https://0-doi-org.brum.beds.ac.uk/10.3390/ma15030741 - 19 Jan 2022

Cited by 4 | Viewed by 1680

Abstract

This investigation analyses the influence of the depth and the distance between studs on the fire resistance of lightweight timber-framed (LTF) walls lined with gypsum plasterboards. The simplified model used to determine the fire resistance in Eurocode EN 1995-1-2 provides very conservative values, as few parameters are considered. The new generation of Eurocode EN 1995-1-2 includes an upgrade of the simplified model, allowing us to predict the fire resistance of LTF wall assemblies more accurately. This separating function method considers the number, the thickness and the material of the protection layers, but does not explicitly consider the variation of the depth and the distance between the studs for the calculation of the insulation time of the assembly, besides including some limitations for both parameters. To demonstrate the influence of these parameters, 36 numerical simulations were carried out using the finite element method previously validated with experimental tests. The results obtained from the parametric analyses confirmed that such parameters affect the fire resistance of the LTF wall assemblies in a significant way. In addition, the results revealed an important contribution in the study of LTF wall assemblies against fire resistance, demonstrating the need for including extra geometric parameters in the simplified model in order to increase the accuracy of current models. Full article

(This article belongs to the Special Issue Advances in Structural Mechanics Modeled with FEM)

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24 pages, 10225 KiB

Open AccessArticle

A Practical Finite Element Modeling Strategy to Capture Cracking and Crushing Behavior of Reinforced Concrete Structures

by Alexandre Mathern and Jincheng Yang

Materials 2021, 14(3), 506; https://0-doi-org.brum.beds.ac.uk/10.3390/ma14030506 - 21 Jan 2021

Cited by 17 | Viewed by 4373

Abstract

Nonlinear finite element (FE) analysis of reinforced concrete (RC) structures is characterized by numerous modeling options and input parameters. To accurately model the nonlinear RC behavior involving concrete cracking in tension and crushing in compression, practitioners make different choices regarding the critical modeling issues, e.g., defining the concrete constitutive relations, assigning the bond between the concrete and the steel reinforcement, and solving problems related to convergence difficulties and mesh sensitivities. Thus, it is imperative to review the common modeling choices critically and develop a robust modeling strategy with consistency, reliability, and comparability. This paper proposes a modeling strategy and practical recommendations for the nonlinear FE analysis of RC structures based on parametric studies of critical modeling choices. The proposed modeling strategy aims at providing reliable predictions of flexural responses of RC members with a focus on concrete cracking behavior and crushing failure, which serve as the foundation for more complex modeling cases, e.g., RC beams bonded with fiber reinforced polymer (FRP) laminates. Additionally, herein, the implementation procedure for the proposed modeling strategy is comprehensively described with a focus on the critical modeling issues for RC structures. The proposed strategy is demonstrated through FE analyses of RC beams tested in four-point bending—one RC beam as reference and one beam externally bonded with a carbon-FRP (CFRP) laminate in its soffit. The simulated results agree well with experimental measurements regarding load-deformation relationship, cracking, flexural failure due to concrete crushing, and CFRP debonding initiated by intermediate cracks. The modeling strategy and recommendations presented herein are applicable to the nonlinear FE analysis of RC structures in general. Full article

(This article belongs to the Special Issue Advances in Structural Mechanics Modeled with FEM)

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19 pages, 9242 KiB

Open AccessArticle

Material Parameter Identification for Acoustic Simulation of Additively Manufactured Structures

by Sebastian Rothe, Christopher Blech, Hagen Watschke, Thomas Vietor and Sabine C. Langer

Materials 2021, 14(1), 168; https://0-doi-org.brum.beds.ac.uk/10.3390/ma14010168 - 31 Dec 2020

Cited by 3 | Viewed by 1972

Abstract

One possibility in order to manufacture products with very few restrictions in design freedom is additive manufacturing. For advanced acoustic design measures like Acoustic Black Holes (ABH), the layer-wise material deposition allows the continuous alignment of the mechanical impedance by different filling patterns and degrees of filling. In order to explore the full design potential, mechanical models are indispensable. In dependency on process parameters, the resulting homogenized material parameters vary. In previous investigations, especially for ABH structures, a dependency of the material parameters on the structure’s thickness can be observed. In this contribution, beams of different thicknesses are investigated experimentally and numerically in order to identify the material parameters in dependency on the frequency and the thickness. The focused material is polyactic acid (PLA). A parameter fitting is conducted by use of a 3D finite element model and it’s reduced version in a Krylov subspace. The results yield homogenized material parameters for the PLA stack as a function of frequency and thickness. An increasing Young’s modulus with increasing frequency and increasing thickness is observed. This observed effect has considerable influence and has not been considered so far. With the received parameters, more reliable results can be obtained. Full article

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17 pages, 1609 KiB

Open AccessArticle

Numerical Analysis of Bowing Phenomenon Due to Thermal Stresses in Marble Slabs

by William Hideki Ito, Anna Maria Ferrero and Paulo Ivo Braga de Queiroz

Materials 2020, 13(19), 4367; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13194367 - 30 Sep 2020

Cited by 2 | Viewed by 2044

Abstract

Bowing is a pathology known by the deformation experienced in some external covering systems in ornamental stones, especially in marble, and thermal action is one of the key factors that lead to this degradation. Previous studies presented remarkable contributions about the mechanical behavior of bowing but they were based on classical beam’s theory and improper assumptions might mislead the evaluation of internal stresses. This study proposes to evaluate internal stresses in bowing due to thermal loading considering the true deformed shape in continuum media. Finite displacement concepts are proposed to calculate stress-strain relationship and comparison with linear elastic theory is also addressed. Internal stresses not predictable in the Euler-Bernoulli beam were found in parametric analyses. Moreover, the numerical analysis accomplished in this paper indicates that transient heat flux should induce higher stresses than just considering higher gradients of temperature in steady flux which could explain the larger decohesion through width in bowing tests. Full article

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24 pages, 1997 KiB

Open AccessArticle

An Orthotropic Elastic-Plastic Constitutive Model for Masonry Walls

by Piotr Bilko and Leszek Małyszko

Materials 2020, 13(18), 4064; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13184064 - 13 Sep 2020

Cited by 14 | Viewed by 2440

Abstract

The use of a continuum structural model for the analysis of masonry structures in the plane stress state is discussed in this paper. Attention is paid to orthotropic masonry at the material level and validation of the model after its implementation in a proprietary finite element method (FEM) system via user-supplied subroutine. The constitutive relations are established in the framework of the mathematical elastoplasticity theory of small displacements and deformations. Based on the orthotropic failure criterion that was originally proposed by Hoffman in the spatial stress state, the model includes a generalization of the criterion in the plane stress. As it is the case for isotropic quasi-brittle materials, different yield surfaces are considered for tension and compression, which are both of Hoffman type. Full article

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15 pages, 4921 KiB

Open AccessArticle

Rigid Finite Element Method in Modeling Composite Steel-Polymer Concrete Machine Tool Frames

by Paweł Dunaj, Krzysztof Marchelek, Stefan Berczyński and Berkay Mizrak

Materials 2020, 13(14), 3151; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13143151 - 15 Jul 2020

Cited by 10 | Viewed by 2464

Abstract

At the stage of designing a special machine tool, it is necessary to analyze many variants of structural solutions of frames and load-bearing systems and to choose the best solution in terms of dynamic properties, in particular considering its resistance to chatter. For this reason, it is preferred to adopt a low-dimensional calculation model, which allows the user to reduce the necessary calculation time while maintaining a high accuracy. The paper presents the methodology of modeling the natural frequencies, mode shapes, and receptance functions of machine tool steel welded frames filled with strongly heterogenous polymer concrete, using low-dimensional models developed by the rigid finite elements method (RigFEM). In the presented study, a RigFEM model of a simple steel beam filled with polymer concrete and a frame composed of such beams were built. Then, the dynamic properties obtained on the basis of the developed RigFEM models were compared with the experimental results and the 1D and 3D finite element models (FEM) in terms of accuracy and dimensionality. As a result of the experimental verification, the full structural compliance of the RigFEM models (for beam and frame) was obtained, which was manifested by the agreement of the mode shapes. Additionally, experimental verification showed a high accuracy of the RigFEM models, obtaining for the beam model a relative error for natural frequencies of less than 4% and on average 2.2%, and for the frame model at a level not exceeding 11% and on average 5.5%. Comparing the RigFEM and FEM models, it was found that the RigFEM models have a slightly worse accuracy, with a dimensionality significantly reduced by 95% for the beam and 99.8% for the frame. Full article

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30 pages, 2393 KiB

Open AccessArticle

Homogenization and Equivalent Beam Model for Fiber-Reinforced Tubular Profiles

by Daniel Gnoli, Sajjad Babamohammadi and Nicholas Fantuzzi

Materials 2020, 13(9), 2069; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13092069 - 30 Apr 2020

Cited by 6 | Viewed by 2439

Abstract

The current work presents a study on hollow cylinder composite beams, since hollow cylinder cross-sections are one of the principal geometry in many engineering fields. In particular, the present study considers the use of these profiles for scaffold design in offshore engineering. Composite beams cannot be treated as isotropic ones due to couplings mainly present among traction, torsion, bending and shear coefficients. This research aims to present a simple approach to study composite beams as they behave like isotropic ones by removing most complexities related to composite material design (e.g., avoid the use of 2D and 3D finite element modeling). The work aims to obtain the stiffness matrix of the equivalent beam through an analytical approach which is valid for most of the laminated composite configurations present in engineering applications. The 3D Euler–Bernoulli beam theory is considered for obtaining the correspondent isotropic elastic coefficients. The outcomes show that negligible errors occur for some equivalent composite configurations by allowing designers to continue using commercial finite element codes that implement the classical isotropic beam model. Full article

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20 pages, 7783 KiB

Open AccessArticle

FE Analyses of Hyperelastic Solids under Large Bending: The Role of the Searle Parameter and Eulerian Slenderness

by Federico Oyedeji Falope, Luca Lanzoni and Angelo Marcello Tarantino

Materials 2020, 13(7), 1597; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13071597 - 01 Apr 2020

Cited by 14 | Viewed by 2012

Abstract

A theoretical model concerning the finite bending of a prismatic hyperelastic solid has been recently proposed. Such a model provides the 3D kinematics and the stress field, taking into account the anticlastic effects arising in the transverse cross sections also. That model has been used later to extend the Elastica in the framework of finite elasticity. In the present work, Finite Element (FE) analyses of some basic structural systems subjected to finite bending have been carried out and the results have been compared with those provided by the theoretical model performed previously. In the theoretical formulation, the governing equation is the nonlinear local relationship between the bending moment and the curvature of the longitudinal axis of the bent beam. Such a relation has been provided in dimensionless form as a function of the Mooney–Rivlin constitutive constants and two kinematic dimensionless parameters termed Eulerian slenderness and compactness index of the cross section. Such parameters take relevance as they are involved in the well-known Searle parameter for bent solids. Two significant study cases have been investigated in detail. The results point out that the theoretical model leads to reliable results provided that the Eulerian slenderness and the compactness index of the cross sections do not exceed fixed threshold values. Full article

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14 pages, 1632 KiB

Open AccessArticle

Material-Oriented Shape Functions for FGM Plate Finite Element Formulation

by Wojciech Gilewski and Jan Pełczyński

Materials 2020, 13(3), 803; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13030803 - 10 Feb 2020

Cited by 9 | Viewed by 3303

Abstract

A four-noded finite element of a moderately thick plate made of functionally graded material (FGM) is presented. The base element is rectangular and can be extended to any shape using a transformation based on NURBS functions. The proposed 2D shape functions are consistent with the physical interpretation and describe the states of element displacement caused by unit displacements of nodes. These functions depend on the FGM’s material parameters and are called material-oriented. The shape function matrix is based on a superposition displacement field of two plate strips with 1D exact shape functions. A characteristic feature of the proposed formulation is full coupling of the membrane and bending states in the plate. The analytical form of the stiffness matrix and the nodal load vector was obtained, which leads to the numerical efficiency of the formulation. The element has been incorporated into Abaqus software with the use of Maple program. The finite element shows good convergence properties for different FGM models in the transverse direction to the middle plane of the plate. During derivation of the 2D plate element the formally exact 1D finite element for transverse nonhomogeneous FGM plate strip was developed. Full article

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13 pages, 6291 KiB

Open AccessArticle

Rate-Dependent Cohesive Zone Model for Fracture Simulation of Soda-Lime Glass Plate

by Dong Li and Demin Wei

Materials 2020, 13(3), 749; https://0-doi-org.brum.beds.ac.uk/10.3390/ma13030749 - 06 Feb 2020

Cited by 9 | Viewed by 2678

Abstract

In this paper, rate-dependent cohesive zone model was established to numerical simulate the fracture process of soda-lime glass under impact loading. Soda-lime glass is widely used in architecture and automobile industry due to its transparency. To improve the accuracy of fracture simulation of soda-lime glass under impact loading, strain rate effect was taken into consideration and a rate-dependent cohesive zone model was established. Tensile-shear mixed mode fracture was also taken account. The rate-dependent cohesive zone model was implemented in the commercial finite element code ABAQUS/Explicit with the user subroutine VUMAT. The fracture behavior of a monolithic glass plate impacted by a hemispherical impactor was simulated. The simulation results demonstrated that the rate-dependent cohesive zone model is more suitable to describe the impact failure characteristics of a monolithic glass plate, compared to cohesive zone model without consideration of strain rate. Moreover, the effect of the strain rate sensitivity coefficient C, the mesh size of glass plate and the impact velocity on the fracture characteristics were studied. Full article

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30 pages, 7705 KiB

Open AccessArticle

Free Vibrations of Sandwich Plates with Damaged Soft-Core and Non-Uniform Mechanical Properties: Modeling and Finite Element Analysis

by Michele Bacciocchi, Raimondo Luciano, Carmelo Majorana and Angelo Marcello Tarantino

Materials 2019, 12(15), 2444; https://0-doi-org.brum.beds.ac.uk/10.3390/ma12152444 - 31 Jul 2019

Cited by 21 | Viewed by 3118

Abstract

The paper aims to investigate the natural frequencies of sandwich plates by means of a Finite Element (FE) formulation based on the Reissner-Mindlin Zig-zag (RMZ) theory. The structures are made of a damaged isotropic soft-core and two external stiffer orthotropic face-sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. A non-uniform distribution of the reinforcing fibers is assumed along the thickness of the skin and is modeled analytically by means of peculiar expressions given as a function of the thickness coordinate. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution of the straight fibers, stacking sequence, and mass fraction of the constituents. Some final remarks are presented to provide useful observations and design criteria. Full article

(This article belongs to the Special Issue Advances in Structural Mechanics Modeled with FEM)

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19 pages, 9646 KiB

Open AccessArticle

Investigation of the Flow Properties of CBM Based on Stochastic Fracture Network Modeling

by Bo Zhang, Yong Li, Nicholas Fantuzzi, Yuan Zhao, Yan-Bao Liu, Bo Peng and Jie Chen

Materials 2019, 12(15), 2387; https://0-doi-org.brum.beds.ac.uk/10.3390/ma12152387 - 26 Jul 2019

Cited by 25 | Viewed by 2955

Abstract

Coal contains a large number of fractures, whose characteristics are difficult to describe in detail, while their spatial distribution patterns may follow some macroscopic statistical laws. In this paper, several fracture geometric parameters (FGPs) were used to describe a fracture, and the coal seam was represented by a two-dimensional stochastic fracture network (SFN) which was generated and processed through a series of methods in MATLAB. Then, the processed SFN image was able to be imported into COMSOL Multiphysics and converted to a computational domain through the image function. In this way, the influences of different FGPs and their distribution patterns on the permeability of the coal seam were studied, and a finite element model to investigate gas flow properties in the coal seam was carried out. The results show that the permeability of the coal seam increased with the rising of fracture density, length, aperture, and with the decrease of the angle between the fracture orientation and the gas pressure gradient. It has also been found that large-sized fractures have a more significant contribution to coal reservoir permeability. Additionally, a numerical simulation of CBM extraction was carried out to show the potential of the proposed approach in the application of tackling practical engineering problems. According to the results, not only the connectivity of fractures but also variations of gas pressure and velocity can be displayed explicitly, which is consistent well with the actual situation. Full article

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22 pages, 3927 KiB

Open AccessArticle

An Efficient Beam Element Based on Quasi-3D Theory for Static Bending Analysis of Functionally Graded Beams

by Hoang Nam Nguyen, Tran Thi Hong, Pham Van Vinh and Do Van Thom

Materials 2019, 12(13), 2198; https://0-doi-org.brum.beds.ac.uk/10.3390/ma12132198 - 08 Jul 2019

Cited by 36 | Viewed by 3621

Abstract

In this paper, a 2-node beam element is developed based on Quasi-3D beam theory and mixed formulation for static bending of functionally graded (FG) beams. The transverse shear strains and stresses of the proposed beam element are parabolic distributions through the thickness of the beam and the transverse shear stresses on the top and bottom surfaces of the beam vanish. The proposed beam element is free of shear-looking without selective or reduced integration. The material properties of the functionally graded beam are assumed to vary according to the power-law index of the volume fraction of the constituents through the thickness of the beam. The numerical results of this study are compared with published results to illustrate the accuracy and convenience rate of the new beam element. The influence of some parametrics on the bending behavior of FGM beams is investigated. Full article

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