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Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures

A special issue of Materials (ISSN 1996-1944). This special issue belongs to the section "Advanced Materials Characterization".

Deadline for manuscript submissions: closed (20 June 2022) | Viewed by 46234

Special Issue Editors

Prof. Jarosław Jędrysiak

E-Mail Website
Guest Editor
Department of Structural Mechanics, Lodz University of Technology, al. Politechniki 6, 90-924 Lodz, Poland
Interests: microstructure; mechanical behavior of materials; mechanics of materials; mathematical modeling; engineering, applied and computational mathematics; solid mechanics; nonlinear analysis; structural analysis; structural dynamics; materials
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Izabela Lubowiecka

E-Mail Website
Guest Editor
Structural Mechanics Department, Gdańsk University of Technology, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland
Interests: engineering; applied and computational mathematics; civil engineering biomechanics; tissue engineering; mechanical properties; dynamics; finite element modeling; finite element analysis; dynamic analysis
Prof. Ewa Magnucka-Blandzi

E-Mail Website
Guest Editor
Institute of Mathematics, Poznan University of Technology, ul. Piotrowo 3A, 60-965 Poznań, Poland
Interests: difference equation; mathematical modeling; structural strength; stability of construction

Special Issue Information

Dear Colleagues,

This Special Issue deals with analytical and computational methods in the mechanics of beams, plates, and shells. The main areas of interest of this edition include linear and nonlinear models of elasticity and plasticity of these structures; thermoelasticity; problems of vibrations, wave propagation, stability of beams, plates, and shells; heat conductivity; microheterogeneous structures; layered structures; and structures made of materials with special properties – metamaterials, auxetic materials, porous materials, biomaterials, and functionally graded materials.

We invite you to submit your scientific papers on the latest research results in these aspects of the mechanics of beams, plates, and shells, with an emphasis on applications in all areas of mechanics, biomechanics, and civil engineering.

Prof. Jarosław Jędrysiak
Prof. Dr. Izabela Lubowiecka
Prof. Ewa Magnucka-Blandzi
Guest 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.

Keywords

  • Mathematical and computational modeling of beams, plates, and shells
  • Structural mechanics
  • Biomechanics
  • Dynamics
  • Thermomechanics
  • Metamaterials
  • Functionally graded beams, plates, and shells
  • Microstructure
  • Heat transfer
  • Fluid mechanics

Published Papers (24 papers)

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23 pages, 70447 KiB  
Article
The Effect of the Material Periodic Structure on Free Vibrations of Thin Plates with Different Boundary Conditions
by Jarosław Jędrysiak
Materials 2022, 15(16), 5623; https://doi.org/10.3390/ma15165623 - 16 Aug 2022
Cited by 4 | Viewed by 939
Abstract
Thin elastic periodic plates are considered in this paper. Since the plates have a microstructure, the effect of its size on behaviour of the plates can play a crucial role. To take into account this effect, the tolerance modelling method is applied. This [...] Read more.
Thin elastic periodic plates are considered in this paper. Since the plates have a microstructure, the effect of its size on behaviour of the plates can play a crucial role. To take into account this effect, the tolerance modelling method is applied. This method allows us to obtain model equations with constant coefficients, which involve terms dependent of the microstructure size. Using the model equations, not only can formulas of fundamental lower-order vibration frequencies be obtained, but also formulas of higher-order vibration frequencies related to the microstructure. In this paper, the effect of the material periodic microstructure on free vibration frequencies for various boundary conditions of the plates was analysed. To obtain proper formulas of frequencies, the Ritz method is applied. Moreover, some results are compared to the results calculated using the FEM. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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16 pages, 6419 KiB  
Article
Influence of Inertial Vlasov Foundation Parameters on the Dynamic Response of the Bernoulli—Euler Beam Subjected to A Group of Moving Forces—Analytical Approach
by Magdalena Ataman and Wacław Szcześniak
Materials 2022, 15(9), 3249; https://doi.org/10.3390/ma15093249 - 30 Apr 2022
Viewed by 1381
Abstract
The subject of this study is the vibration of the Bernoulli–Euler beam on a three-parameter inertial foundation caused by a group of moving forces. The solution to the problem is obtained analytically. The influence of deformable foundation properties on the dynamic response of [...] Read more.
The subject of this study is the vibration of the Bernoulli–Euler beam on a three-parameter inertial foundation caused by a group of moving forces. The solution to the problem is obtained analytically. The influence of deformable foundation properties on the dynamic response of the beam in the case of forced vibration and the case of free vibration after the load has left the beam is analysed. The influence of velocity on the dynamic response of the beam is also investigated in both cases. The results can be used as a benchmark for calculating more complex engineering structures under moving loads caused by road or railroad vehicles. The results of the investigation are presented in the figures. It is evident that the coefficient determining the foundation inertia has a significant influence on the dynamic deflection of the beam. Taking shear into account in the Vlasov foundation model has little effect on the dynamic deflections of the beam. The equivalent damping number introduced into the Kelvin–Voigt model takes into account the structure damping and mass damping of the beam. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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21 pages, 9650 KiB  
Article
Active Control of Stiffness of Tensegrity Plate-like Structures Built with Simplex Modules
by Paulina Obara and Justyna Tomasik
Materials 2021, 14(24), 7888; https://doi.org/10.3390/ma14247888 - 20 Dec 2021
Cited by 5 | Viewed by 1588
Abstract
The aim of this study is to prove that it is possible to control the static behavior of tensegrity plate-like structures. This possibility is very important, particularly in the case of deployable structures. Here, we analyze the impact the support conditions of the [...] Read more.
The aim of this study is to prove that it is possible to control the static behavior of tensegrity plate-like structures. This possibility is very important, particularly in the case of deployable structures. Here, we analyze the impact the support conditions of the structure have on the existence of specific characteristics, such as self-stress states and infinitesimal mechanisms, and, consequently, on the active control. Plates built with Simplex modules are considered. Firstly, the presence of the specific characteristics is examined, and a classification is carried out. Next, the influence of the level of self-stress state on the behavior of structures is analyzed. A geometrically non-linear model, implemented in an original program, written in the Mathematica environment, is used. The results confirm the feasibility of the active control of stiffness of tensegrity plate-like structures characterized by the presence of infinitesimal mechanisms. In the case when mechanisms do not exist, structures are insensitive to the initial prestress level. It is possible to control the occurrence of mechanisms by changing the support conditions of the structure. Based on the obtained results, tensegrity is very promising structural concept, applicable in many areas, when conventional solutions are insufficient. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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30 pages, 7868 KiB  
Article
A Recurrent Neural Network-Based Method for Dynamic Load Identification of Beam Structures
by Hongji Yang, Jinhui Jiang, Guoping Chen, M Shadi Mohamed and Fan Lu
Materials 2021, 14(24), 7846; https://doi.org/10.3390/ma14247846 - 18 Dec 2021
Cited by 12 | Viewed by 2770
Abstract
The determination of structural dynamic characteristics can be challenging, especially for complex cases. This can be a major impediment for dynamic load identification in many engineering applications. Hence, avoiding the need to find numerous solutions for structural dynamic characteristics can significantly simplify dynamic [...] Read more.
The determination of structural dynamic characteristics can be challenging, especially for complex cases. This can be a major impediment for dynamic load identification in many engineering applications. Hence, avoiding the need to find numerous solutions for structural dynamic characteristics can significantly simplify dynamic load identification. To achieve this, we rely on machine learning. The recent developments in machine learning have fundamentally changed the way we approach problems in numerous fields. Machine learning models can be more easily established to solve inverse problems compared to standard approaches. Here, we propose a novel method for dynamic load identification, exploiting deep learning. The proposed algorithm is a time-domain solution for beam structures based on the recurrent neural network theory and the long short-term memory. A deep learning model, which contains one bidirectional long short-term memory layer, one long short-term memory layer and two full connection layers, is constructed to identify the typical dynamic loads of a simply supported beam. The dynamic inverse model based on the proposed algorithm is then used to identify a sinusoidal, an impulsive and a random excitation. The accuracy, the robustness and the adaptability of the model are analyzed. Moreover, the effects of different architectures and hyperparameters on the identification results are evaluated. We show that the model can identify multi-points excitations well. Ultimately, the impact of the number and the position of the measuring points is discussed, and it is confirmed that the identification errors are not sensitive to the layout of the measuring points. All the presented results indicate the advantages of the proposed method, which can be beneficial for many applications. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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21 pages, 844 KiB  
Article
Comparison of the Natural Vibration Frequencies of Timoshenko and Bernoulli Periodic Beams
by Łukasz Domagalski
Materials 2021, 14(24), 7628; https://doi.org/10.3390/ma14247628 - 11 Dec 2021
Cited by 8 | Viewed by 1904
Abstract
This paper deals with the linear natural vibrations analysis of beams where the geometric and material properties vary periodically along the beam axis. In contrast with homogeneous prismatic beams, the frequency spectra of such beams are irregular as there exist enlarged intervals between [...] Read more.
This paper deals with the linear natural vibrations analysis of beams where the geometric and material properties vary periodically along the beam axis. In contrast with homogeneous prismatic beams, the frequency spectra of such beams are irregular as there exist enlarged intervals between some adjacent frequencies. Presented here are two averaged models of beams based on the tolerance modelling approach. The assumptions of classical Euler–Bernoulli and Timoshenko–Ehrenfest beam theories are adopted as the foundations. The resulting mathematical models are systems of differential equations with constant, weight-averaged coefficients. This makes it possible to apply any classical method of solution suitable for homogeneous beams, such as Galerkin orthogonalization. Here, emphasis is placed on the comparison of natural frequencies neighbouring the frequency band-gaps that are obtained from these two theories. Two basic cases of material and geometric property distribution in a periodicity cell are studied, and the natural frequencies and mode shapes are obtained for a simply supported beam. The results are supported by a comparison with the finite element method and partially exact solutions. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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18 pages, 1939 KiB  
Article
Buckling Analysis of Functionally Graded Sandwich Plates under Both Mechanical and Thermal Loads
by Dongdong Li, He Zhu and Xiaojing Gong
Materials 2021, 14(23), 7194; https://doi.org/10.3390/ma14237194 - 25 Nov 2021
Cited by 6 | Viewed by 1342
Abstract
This paper presents an analytical solution for the thermomechanical buckling of functionally graded material (FGM) sandwich plates. The solution is obtained using a four-variable equivalent-single-layer (ESL) plate theory. Two types of sandwich plates are included: one with FGM facesheets and homogeneous core, and [...] Read more.
This paper presents an analytical solution for the thermomechanical buckling of functionally graded material (FGM) sandwich plates. The solution is obtained using a four-variable equivalent-single-layer (ESL) plate theory. Two types of sandwich plates are included: one with FGM facesheets and homogeneous core, and vice versa for the other. The governing equations are derived based on the principle of minimum total potential energy. For simply supported boundary conditions, these equations are solved via the Navier method. The results on critical buckling load and temperature increment of simply supported FGM sandwich plates are compared with the available solutions in the literature. Several results are presented considering various material and geometrical parameters as well as their effect on the thermomechanical buckling response of FGM sandwich plates. The relationship between the mechanical load and the temperature increment for uniform/linear temperature rise of FGM sandwich plates under combined mechanical and thermal loads is studied. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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22 pages, 3589 KiB  
Article
Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions
by Wenhao Huang, Kai Xue and Qiuhong Li
Materials 2021, 14(22), 7088; https://doi.org/10.3390/ma14227088 - 22 Nov 2021
Cited by 10 | Viewed by 1768
Abstract
Functionally graded materials (FGMs) structures are increasingly used in engineering due to their superior mechanical and material properties, and the FGMs plate with cutouts is a common structural form, but research on the vibration characteristics of FGMs plate with cutouts is relatively limited. [...] Read more.
Functionally graded materials (FGMs) structures are increasingly used in engineering due to their superior mechanical and material properties, and the FGMs plate with cutouts is a common structural form, but research on the vibration characteristics of FGMs plate with cutouts is relatively limited. In this paper, the three-dimensional exact solution for the vibration analysis of FGMs rectangular plate with circular cutouts subjected to general boundary conditions is presented based on the three-dimensional elasticity theory. The displacement field functions are expressed as standard cosine Fourier series plus auxiliary cosine series terms satisfying the boundary conditions in the global coordinate system. The plate with circular cutout is discretized into four curve quadrilateral sub-domains using the p-version method, and then the blending function method is applied to map the closed quadrilateral region to the computational space. The characteristic equation is obtained based on the Lagrangian energy principle and Rayleigh–Ritz method. The efficiency and reliability of proposed method are verified by comparing the present results with those available in the literature and FEM methods. Finally, a parametric study is investigated including the cutout sizes, the cutout positions, and the cutout numbers from the free vibration characteristic analysis and the harmonic analysis. The results can serve as benchmark data for other research on the vibration of FGMs plates with cutouts. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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16 pages, 1432 KiB  
Article
Three-Dimensional Bending Analysis of Multi-Layered Orthotropic Plates by Two-Dimensional Numerical Model
by Piotr Pluciński, Jan Jaśkowiec and Maciej Wójtowicz
Materials 2021, 14(22), 6959; https://doi.org/10.3390/ma14226959 - 17 Nov 2021
Cited by 1 | Viewed by 1508
Abstract
The paper presents effective numerical modelling of multi-layered plates with orthotropic properties. The method called the FEM23 is employed to construct the numerical model. The approach enables a full 3D analysis to be performed while using a 2D finite element mesh. The numerical [...] Read more.
The paper presents effective numerical modelling of multi-layered plates with orthotropic properties. The method called the FEM23 is employed to construct the numerical model. The approach enables a full 3D analysis to be performed while using a 2D finite element mesh. The numerical model for a multi-layered plate is constructed by an assembling procedure, where each layer with orthotropic properties is added to the global numerical model. The paper demonstrates that the FEM23 method is very flexible in defining the multilayered plate, where the thickness of each layer as well as its mechanical orthotropic properties can be defined independently. Several examples of three-layered or nine-layered plates are analyzed in this paper. The results obtained by the FEM23 method coincide with the ones taken from the published papers or calculated with the standard 3D FEM approach. The orthotropic version of the FEM23 can be quite easily applied for other kinds of problems including thermo-mechanics, free vibrations, buckling analysis, or delamination. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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18 pages, 6702 KiB  
Article
Research of Vibrations of an Armoured Personnel Carrier Hull with FE Implementation
by Zdzisław Hryciów, Jerzy Małachowski, Piotr Rybak and Andrzej Wiśniewski
Materials 2021, 14(22), 6807; https://doi.org/10.3390/ma14226807 - 11 Nov 2021
Cited by 3 | Viewed by 1831
Abstract
Modern wheeled armoured vehicles can perform a variety of tasks, making the development of weapon systems that can be safely and effectively integrated with the vehicle structure an area of interest. Due to the cost of implementing new models, it is more economical [...] Read more.
Modern wheeled armoured vehicles can perform a variety of tasks, making the development of weapon systems that can be safely and effectively integrated with the vehicle structure an area of interest. Due to the cost of implementing new models, it is more economical to test potential configurations using numerical methods, such as the finite element method. The numerical model has been validated to confirm the reliability of the obtained results. Modal tests were also performed using four configurations to identify the frequency and mode shape of natural vibrations occurring within the support structure. In an experimental setting, hull vibrations were forced using the modal hammer testing method. The modal assurance criterion (MAC) and the authors’ procedure were used to confirm the experimental and numerical test results. Additional testing in the form of impact loads was carried out for turret-containing structures. Structural strain at indicated points and forces transmitted by brackets to the bottom of the hull were compared. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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14 pages, 6701 KiB  
Article
Numerical Models of the Connection of Thin-Walled Z-Profile Roof Purlins
by Přemysl Pařenica, Petr Lehner, Jiří Brožovský and Martin Krejsa
Materials 2021, 14(21), 6573; https://doi.org/10.3390/ma14216573 - 01 Nov 2021
Cited by 4 | Viewed by 1906
Abstract
High thin-walled purlins of Z cross-section are important elements in steel wide-span structures. Their behaviour is influenced by many variables that need to be examined for every specific case. Their practical design thus requires extended knowledge of their behaviour for the possible configurations [...] Read more.
High thin-walled purlins of Z cross-section are important elements in steel wide-span structures. Their behaviour is influenced by many variables that need to be examined for every specific case. Their practical design thus requires extended knowledge of their behaviour for the possible configurations and dimensions. Numerical analysis verified by experimental investigation can thus enrich such knowledge. Numerical models have the advantage of repeatability and the ability to offer parametric changes. The parametric study presented shows a detailed description of a finite element model of thin-walled cross-sectional roof purlins connected to other roof elements. Models include various approaches to modelling bolt connection. Two schemes of purlins, with and without cleats, are presented. The results of different approaches in numerical modelling are compared with the results of a physical test on a real structure. The article shows a significant agreement in the case of specific approaches and points out the differences with others. The results can be helpful in terms of how to approach the modelling of thin-walled structures and the effective approach to experimental preparation. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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25 pages, 3176 KiB  
Article
Application of Variational Method to Stability Analysis of Cantilever Vertical Plates with Bimodular Effect
by Xuan-Yi Xue, Da-Wei Du, Jun-Yi Sun and Xiao-Ting He
Materials 2021, 14(20), 6129; https://doi.org/10.3390/ma14206129 - 15 Oct 2021
Cited by 3 | Viewed by 1488
Abstract
In the design of cantilevered balconies of buildings, many stability problems exist concerning vertical plates, in which reaching a critical load plays an important role during the stability analysis of the plate. At the same time, the concrete forming vertical plate, as a [...] Read more.
In the design of cantilevered balconies of buildings, many stability problems exist concerning vertical plates, in which reaching a critical load plays an important role during the stability analysis of the plate. At the same time, the concrete forming vertical plate, as a typical brittle material, has larger compressive strength but lower tensile strength, which means the tensile and compression properties of concrete are different. However, due to the complexities of such analyses, this difference has not been considered. In this study, the variational method is used to analyze stability problems of cantilever vertical plates with bimodular effect, in which different loading conditions and plate shapes are also taken into account. For the effective implementation of a variational method, the bending strain energy based on bimodular theory is established first, and critical loads of four stability problems are obtained. The results indicate that the bimodular effect, as well as different loading types and plate shapes, have influences on the final critical loads, resulting in varying degrees of buckling. In particular, if the average value of the tensile modulus and compressive modulus remain unchanged, the introduction of the bimodular effect will weaken, to some extent, the bending stiffness of the plate. Among the four stability problems, a rectangular plate with its top and bottom loaded is most likely to buckle; next is a rectangular plate with its top loaded, followed by a triangular plate with its bottom loaded. A rectangular plate with its bottom loaded is least likely to buckle. This work may serve as a theoretical reference for the refined analysis of vertical plates. Plates are made of concrete or similar material whose bimodular effect is relatively obvious and cannot be ignored arbitrarily; otherwise the greater inaccuracies will be encountered in building designs. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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16 pages, 4892 KiB  
Article
Experimental Research of Ratio between Residual and Elastic Strains εres/εE in High-Strength Concrete Beams Subjected to Bending
by Hydayatullah Bayat, Andrzej Ubysz, Marek Maj, Marek Chalecki, Jarosław Wójt and Ashot Tamrazyan
Materials 2021, 14(20), 6007; https://doi.org/10.3390/ma14206007 - 12 Oct 2021
Cited by 2 | Viewed by 1510
Abstract
In the mechanics of concrete constructions, one distinguishes between residual and elastic strains. Cyclic loadings evoke changes mainly in the elastic strains; however, the total strains are decided by the sum of the residual and elastic strains. The knowledge of the ratio between [...] Read more.
In the mechanics of concrete constructions, one distinguishes between residual and elastic strains. Cyclic loadings evoke changes mainly in the elastic strains; however, the total strains are decided by the sum of the residual and elastic strains. The knowledge of the ratio between the residual and total strains allows to predict the total deformations of a construction assuming it is made from an ideally elastic material. This paper presents the effect of the load level at the values of the residual strains for beams made of high-strength concretes and subjected to bending. The investigations showed that the share of residual strains for these concretes differed from the share of residual strains for concretes of lower classes. The investigations were made for cyclically loaded concrete samples and ferroconcrete beams for various relative load levels. The ratio between the residual and total strains was presented in the form of a dependence on the relative load level of the element. An important conclusion was that, after the crack formation, the share of residual stresses reduced, along with the increase in the concrete strength and elastic features of the construction which started to predominate. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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19 pages, 6829 KiB  
Article
Numerical Prediction of Local Instability in Double Corrugated Profiles
by Artur Piekarczuk and Przemysław Więch
Materials 2021, 14(20), 6002; https://doi.org/10.3390/ma14206002 - 12 Oct 2021
Cited by 1 | Viewed by 1819
Abstract
The technological process of forming the double-corrugated structures of the K-span system causes deep transverse embossing on the surface of the profiles. Such profile geometry makes it difficult to apply classical theories related to plastic failure mechanisms to identify the formation of local [...] Read more.
The technological process of forming the double-corrugated structures of the K-span system causes deep transverse embossing on the surface of the profiles. Such profile geometry makes it difficult to apply classical theories related to plastic failure mechanisms to identify the formation of local instabilities. This article presents an original method for the prediction of local instabilities of double-corrugated structures. The method was developed on the basis of a hierarchical validated FEM model. The geometrically and materially nonlinear analysis method was adopted to perform numerical calculations. The results of calculations enabled the determination of reference equilibrium paths for the eccentrically compressed shell element. Based on the analysis of nonlinear equilibrium paths, a method for predicting the beginning and the end of the appearance of local instabilities in the elastoplastic pre-buckling range was developed. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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15 pages, 6659 KiB  
Article
The Stability Analysis of Periodic Beams Interacting with Periodic Elastic Foundation with the Use of the Tolerance Averaging Technique
by Jakub Marczak and Jarosław Jędrysiak
Materials 2021, 14(20), 5923; https://doi.org/10.3390/ma14205923 - 09 Oct 2021
Cited by 3 | Viewed by 1132
Abstract
In this paper a stability analysis of microperiodic beams resting on the periodic inhomogeneous foundation is carried out. The main issue of this considerations, which is the analytical solution to the governing equations characterised by periodic, highly oscillating and non-continuous coefficients, is overwhelmed [...] Read more.
In this paper a stability analysis of microperiodic beams resting on the periodic inhomogeneous foundation is carried out. The main issue of this considerations, which is the analytical solution to the governing equations characterised by periodic, highly oscillating and non-continuous coefficients, is overwhelmed by the application of the tolerance averaging technique. As a result of such application, the governing equation is transformed into a form with constant coefficients which can be solved using well-known mathematical methods. In several calculation examples, the convergence of the results of two derived averaged models is examined, as well as the convergence of the lowest value of the critical force parameter derived from the averaged models with the FEM model. The results prove the superiority of the presented analytical solution over the FEM analysis in the optimisation process. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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20 pages, 55561 KiB  
Article
Probabilistic Approach to Limit States of a Steel Dome
by Paweł Zabojszcza, Urszula Radoń and Waldemar Szaniec
Materials 2021, 14(19), 5528; https://doi.org/10.3390/ma14195528 - 24 Sep 2021
Cited by 8 | Viewed by 1529
Abstract
In this paper, Numpress Explore software, developed at the Institute of Fundamental Technological Research of the Polish Academy of Sciences (IPPT PAN), was used to conduct reliability analyses. For static-strength calculations, the MES3D module, designed by the authors, was employed. Ultimate limit state [...] Read more.
In this paper, Numpress Explore software, developed at the Institute of Fundamental Technological Research of the Polish Academy of Sciences (IPPT PAN), was used to conduct reliability analyses. For static-strength calculations, the MES3D module, designed by the authors, was employed. Ultimate limit state was defined as condition of non-exceedance of the capacity value, resulting from the stability criterion of the bent and compressed element. The serviceability limit state was defined as the condition of non-exceedance of allowable vertical displacement. The above conditions constitute implicit forms of random variable functions; therefore, it was necessary to build an interface between the Numpress Explore and MES3D programs. In the study, a comparative analysis of two cases was carried out. As regards the first case, all adopted random variables had a normal distribution. The second case involved a more accurate description of the quantities mentioned. A normal distribution can be adopted for the description of, e.g., the randomness in the location of the structure nodes, and also the randomness of the multiplier of permanent loads. In actual systems, the distribution of certain loads deviates substantially from the Gaussian distribution. Consequently, adopting the assumption that the loads have a normal distribution can lead to gross errors in the assessment of structural safety. The distribution of loads resulting from atmospheric conditions is decidedly non-Gaussian in character. The Gumbel distribution was used in this study to describe snow and wind loads. The modulus of elasticity and cross-sectional area were described by means of a log-normal distribution. The adopted random variables were independent. Additionally, based on an analysis of the elasticity index, the random variables most affect the failure probability in the ultimate limit state and serviceability limit state were estimated. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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13 pages, 1627 KiB  
Article
Parameter Interval Uncertainty Analysis of Internal Resonance of Rotating Porous Shaft–Disk–Blade Assemblies Reinforced by Graphene Nanoplatelets
by Yi Cai, Zi-Feng Liu, Tian-Yu Zhao and Jie Yang
Materials 2021, 14(17), 5033; https://doi.org/10.3390/ma14175033 - 03 Sep 2021
Cited by 5 | Viewed by 1654
Abstract
This paper conducts a parameter interval uncertainty analysis of the internal resonance of a rotating porous shaft–disk–blade assembly reinforced by graphene nanoplatelets (GPLs). The nanocomposite rotating assembly is considered to be composed of a porous metal matrix and graphene nanoplatelet (GPL) reinforcement material. [...] Read more.
This paper conducts a parameter interval uncertainty analysis of the internal resonance of a rotating porous shaft–disk–blade assembly reinforced by graphene nanoplatelets (GPLs). The nanocomposite rotating assembly is considered to be composed of a porous metal matrix and graphene nanoplatelet (GPL) reinforcement material. Effective material properties are obtained by using the rule of mixture and the Halpin–Tsai micromechanical model. The modeling and internal resonance analysis of a rotating shaft–disk–blade assembly are carried out based on the finite element method. Moreover, based on the Chebyshev polynomial approximation method, the parameter interval uncertainty analysis of the rotating assembly is conducted. The effects of the uncertainties of the GPL length-to-width ratio, porosity coefficient and GPL length-to-thickness ratio are investigated in detail. The present analysis procedure can give an interval estimation of the vibration behavior of porous shaft–disk–blade rotors reinforced with graphene nanoplatelets (GPLs). Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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19 pages, 9771 KiB  
Article
Experimental Study of Lateral-Torsional Buckling of Class 4 Beams at Elevated Temperature
by Piotr Woźniczka
Materials 2021, 14(17), 4825; https://doi.org/10.3390/ma14174825 - 25 Aug 2021
Cited by 1 | Viewed by 2078
Abstract
The results of experimental research on lateral-torsional buckling of steel plate girders with slender web subjected to fire conditions are presented in this paper. The scope of the research covers four girders, three of which have been tested under high temperature conditions. The [...] Read more.
The results of experimental research on lateral-torsional buckling of steel plate girders with slender web subjected to fire conditions are presented in this paper. The scope of the research covers four girders, three of which have been tested under high temperature conditions. The fourth girder has been used to determine the critical load resulting in lateral-torsional buckling of the considered element at room temperature. All the considered elements had identical cross sections and lengths; however, they differed in external temperatures applied and magnitude of measured geometrical imperfections. It has to be highlighted, that the experiments have been conducted subject to the anisothermal conditions, taking into account the uneven distribution of temperature in the cross section. An approach of this type represents a more accurate modelling of the structural component behaviour, when subjected to fire, as compared to the experiments conducted under isothermal conditions. Complete information on the development of research stand, conduct and results of particular tests are presented in this paper. The temperature–time curves for girder components, results of imperfection measurements and mechanical properties of steel are presented. The obtained critical temperatures and graphs of girder top flange horizontal deflection versus temperature are also included. The computer models developed for analysed girders are described in the paper as well. The results obtained with these models have been compared with experimental results. The computational models validated in this way constitute a basis for further parametric studies of lateral-torsional buckling in the domain of steel plate girders with slender web when subjected to fire conditions. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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20 pages, 5372 KiB  
Article
Experimental and Numerical Study of the Elastic SCF of Tubular Joints
by Mostafa Atteya, Ove Mikkelsen, John Wintle and Gerhard Ersdal
Materials 2021, 14(15), 4220; https://doi.org/10.3390/ma14154220 - 28 Jul 2021
Cited by 3 | Viewed by 2176
Abstract
This paper provides data on stress concentration factors (SCFs) from experimental measurements on cruciform tubular joints of a chord and brace intersection under axial loading. High-fidelity finite element models were generated and validated against these measurements. Further, the statistical variation and the uncertainty [...] Read more.
This paper provides data on stress concentration factors (SCFs) from experimental measurements on cruciform tubular joints of a chord and brace intersection under axial loading. High-fidelity finite element models were generated and validated against these measurements. Further, the statistical variation and the uncertainty in both experiments and finite element analysis (FEA) are studied, including the effect of finite element modelling of the weld profile, mesh size, element type and the method for deriving the SCF. A method is proposed for modelling such uncertainties in order to determine a reasonable SCF. Traditionally, SCF are determined by parametric formulae found in codes and standards and the paper also provides these for comparison. Results from the FEA generally show that the SCF increases with a finer mesh, 2nd order brick elements, linear extrapolation and a larger weld profile. Comparison between experimental SCFs indicates that a very fine mesh and the use of 2nd order elements is required to provide SCF on the safe side. It is further found that the parametric SCF equations in codes are reasonably on the safe side and a detailed finite element analysis could be beneficial if small gains in fatigue life need to be justified. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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19 pages, 59855 KiB  
Article
Numerical Simulation of Vehicle–Lighting Pole Crash Tests: Parametric Study of Factors Influencing Predicted Occupant Safety Levels
by Paweł Baranowski and Krzysztof Damaziak
Materials 2021, 14(11), 2822; https://doi.org/10.3390/ma14112822 - 25 May 2021
Cited by 9 | Viewed by 2900
Abstract
In this paper, numerical simulations of the EN 12767 test procedure for a vehicle–lighting pole crash are presented. A representative soil–vehicle–lighting pole model is first developed. The Geo Metro vehicle model is used, and significant attention is given to representing the soil and [...] Read more.
In this paper, numerical simulations of the EN 12767 test procedure for a vehicle–lighting pole crash are presented. A representative soil–vehicle–lighting pole model is first developed. The Geo Metro vehicle model is used, and significant attention is given to representing the soil and its interaction with the traffic pole. Soil is represented using smoothed particle hydrodynamics (SPH) coupled with finite elements (FEs). A parametric study is carried out to investigate the key factors influencing the outcomes and consequently the estimation of the occupant safety levels during crash scenario described in EN 12767. First, a sensitivity study of lighting pole mesh is conducted As a result, the optimal mesh size is used for further studies regarding physical parameters such as soil properties and friction coefficient in vehicle–pole interfaces. Friction and mesh size are found to have a considerable influence on the acceleration severity index (ASI), theoretical head impact velocity (THIV), post-impact velocity and vehicle behavior during the lighting pole crash scenario. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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14 pages, 2783 KiB  
Article
Analytical Prediction for Nonlinear Buckling of Elastically Supported FG-GPLRC Arches under a Central Point Load
by Zhicheng Yang, Airong Liu, Jie Yang, Siu-Kai Lai, Jiangen Lv and Jiyang Fu
Materials 2021, 14(8), 2026; https://doi.org/10.3390/ma14082026 - 17 Apr 2021
Cited by 25 | Viewed by 2122
Abstract
In this paper, we present an analytical prediction for nonlinear buckling of elastically supported functionally graded graphene platelet reinforced composite (FG-GPLRC) arches with asymmetrically distributed graphene platelets (GPLs). The effective material properties of the FG-GPLRC arch are formulated by the modified Halpin–Tsai micromechanical [...] Read more.
In this paper, we present an analytical prediction for nonlinear buckling of elastically supported functionally graded graphene platelet reinforced composite (FG-GPLRC) arches with asymmetrically distributed graphene platelets (GPLs). The effective material properties of the FG-GPLRC arch are formulated by the modified Halpin–Tsai micromechanical model. By using the principle of virtual work, analytical solutions are derived for the limit point buckling and bifurcation buckling of the FG-GPLRC arch subjected to a central point load (CPL). Subsequently, the buckling mode switching phenomenon of the FG-GPLRC arch is presented and discussed. We found that the buckling modes of the FG-GPLRC arch are governed by the GPL distribution pattern, rotational restraint stiffness, and arch geometry. In addition, the number of limit points in the nonlinear equilibrium path of the FG-GPLRC arch under a CPL can be determined according to the bounds of successive inflexion points. The effects of GPL distribution patterns, weight fractions, and geometric configurations on the nonlinear buckling behavior of elastically supported FG-GPLRC arches are also comprehensively discussed. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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19 pages, 2039 KiB  
Article
Dynamics of Space-Fractional Euler–Bernoulli and Timoshenko Beams
by Paulina Stempin and Wojciech Sumelka
Materials 2021, 14(8), 1817; https://doi.org/10.3390/ma14081817 - 07 Apr 2021
Cited by 5 | Viewed by 2007
Abstract
This paper investigates the dynamics of the beam-like structures whose response manifests a strong scale effect. The space-Fractional Euler–Bernoulli beam (s-FEBB) and space-Fractional Timoshenko beam (s-FTB) models, which are suitable for small-scale slender beams and small-scale thick beams, respectively, have been extended to [...] Read more.
This paper investigates the dynamics of the beam-like structures whose response manifests a strong scale effect. The space-Fractional Euler–Bernoulli beam (s-FEBB) and space-Fractional Timoshenko beam (s-FTB) models, which are suitable for small-scale slender beams and small-scale thick beams, respectively, have been extended to a dynamic case. The study provides appropriate governing equations, numerical approximation, detailed analysis of free vibration, and experimental validation. The parametric study presents the influence of non-locality parameters on the frequencies and shape of modes delivering a depth insight into a dynamic response of small scale beams. The comparison of the s-FEBB and s-FTB models determines the applicability limit of s-FEBB and indicates that the model (also the classical one) without shear effect and rotational inertia can only be applied to beams significantly slender than in a static case. Furthermore, the validation has confirmed that the fractional beam model exhibits very good agreement with the experimental results existing in the literature—for both the static and the dynamic cases. Moreover, it has been proven that for fractional beams it is possible to establish constant parameters of non-locality related to the material and its microstructure, independent of beam geometry, the boundary conditions, and the type of analysis (with or without inertial forces). Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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24 pages, 2534 KiB  
Article
Stress-Based FEM in the Problem of Bending of Euler–Bernoulli and Timoshenko Beams Resting on Elastic Foundation
by Zdzisław Więckowski and Paulina Świątkiewicz
Materials 2021, 14(2), 460; https://doi.org/10.3390/ma14020460 - 19 Jan 2021
Cited by 7 | Viewed by 2698
Abstract
The stress-based finite element method is proposed to solve the static bending problem for the Euler–Bernoulli and Timoshenko models of an elastic beam. Two types of elements—with five and six degrees of freedom—are proposed. The elaborated elements reproduce the exact solution in the [...] Read more.
The stress-based finite element method is proposed to solve the static bending problem for the Euler–Bernoulli and Timoshenko models of an elastic beam. Two types of elements—with five and six degrees of freedom—are proposed. The elaborated elements reproduce the exact solution in the case of the piece-wise constant distributed loading. The proposed elements do not exhibit the shear locking phenomenon for the Timoshenko model. The influence of an elastic foundation of the Winkler type is also taken into consideration. The foundation response is approximated by the piece-wise constant and piece-wise linear functions in the cases of the five-degrees-of-freedom and six-degrees-of-freedom elements, respectively. An a posteriori estimation of the approximate solution error is found using the hypercircle method with the addition of the standard displacement-based finite element solution. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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19 pages, 3941 KiB  
Article
Parametric Formula for Stress Concentration Factor of Fillet Weld Joints with Spline Bead Profile
by Yixun Wang, Yuxiao Luo and Seiichiro Tsutsumi
Materials 2020, 13(20), 4639; https://doi.org/10.3390/ma13204639 - 17 Oct 2020
Cited by 19 | Viewed by 3104 | Correction
Abstract
The existing parametric formulae to calculate the notch stress concentration factor of fillet welds often result in reduced accuracy due to an oversimplification of the real weld geometry. The present work proposes a parametric formula for the evaluation of the notch SCF based [...] Read more.
The existing parametric formulae to calculate the notch stress concentration factor of fillet welds often result in reduced accuracy due to an oversimplification of the real weld geometry. The present work proposes a parametric formula for the evaluation of the notch SCF based on the spline weld model that offers a better approximation of the real shape of the fillet weld. The spline model was adopted in FE analyses on T-shape joints and cruciform joints models, under different loading conditions, to propose a parametric formula for the calculation of the SCF by regression analysis. In addition, the precision of parametric formulae based on the line model was examined. The magnitude of the stress concentration was also analyzed by means of its probability distribution. The results show that the line model is not accurate enough to calculate the SCF of fillet weld if the weld profile is considered. The error of the SCF by the proposed parametric formulae is proven to be smaller than 5% according to the testing data system. The stress concentration of cruciform joints under tensile stress represents the worst case scenario if assessed by the confidence interval of 95% survival probability. Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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4 pages, 181 KiB  
Correction
Correction: Wang et al. Parametric Formula for Stress Concentration Factor of Fillet Weld Joints with Spline Bead Profile. Materials 2020, 13, 4639
by Yixun Wang, Yuxiao Luo and Seiichiro Tsutsumi
Materials 2021, 14(9), 2433; https://doi.org/10.3390/ma14092433 - 07 May 2021
Cited by 1 | Viewed by 1112
Abstract
The authors wish to revise the following from pages 16–18 in the text of Appendix B [...] Full article
(This article belongs to the Special Issue Modeling and Analysis of Static, Dynamic, and Thermal Behavior of Shell, Plate, and Beam Structures)
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