Mechanical Design Technologies for Beam, Plate and Shell Structures

A special issue of Applied Mechanics (ISSN 2673-3161).

Deadline for manuscript submissions: closed (1 March 2022) | Viewed by 34353

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Mechanical and Materials Engineering, School of Technology and Management, Instituto Politécnico de Viana do Castelo, 4900-348 Viana do Castelo, Portugal
Interests: dynamics; vibration and damping; smart materials and structures; computational and experimental mechanics; mechatronics and structural control; structural acoustics; structural health monitoring; impact and wave propagation; composite structures; machine design; power transformers design
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Special Issue Information

Dear Colleagues,

This Special Issue will bring together theoretical studies or applied works on state-of-the-art computational modeling or experimental techniques used in the mechanical design of general structural engineering systems embodying beam, plate, and shell structural elements. Advances in fundamental theories, approximation methods, computational techniques, and experimental testing technologies, addressing modern trends and complicating effects, such as complex shapes, multi-layered structures, lattice designs, material anisotropy, structural damping treatments, smart structures, additive-manufactured parts, or complicated analysis, such as non-linear material and geometric behaviors, multi-scale approaches, dynamic analysis, and multi-physics design activities, are especially welcome.

Prof. Dr. César M. A. Vasques
Guest Editor

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Keywords

  • beam
  • plate
  • shell
  • computational methods
  • experimental techniques
  • complicating effects
  • structural analysis
  • mechanical design

Published Papers (12 papers)

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Research

17 pages, 11714 KiB  
Article
A 3D-Printed Honeycomb Cell Geometry Design with Enhanced Energy Absorption under Axial and Lateral Quasi-Static Compression Loads
by Marco Menegozzo, Andrés Cecchini, Frederick A. Just-Agosto, David Serrano Acevedo, Orlando J. Flores Velez, Isaac Acevedo-Figueroa and Jancary De Jesús Ruiz
Appl. Mech. 2022, 3(1), 296-312; https://doi.org/10.3390/applmech3010019 - 14 Mar 2022
Cited by 5 | Viewed by 3219
Abstract
This work presents an innovative honeycomb cell geometry design with enhanced in-plane energy absorption under quasi-static lateral loads. Numerical and experimental compression tests results under axial and lateral loads are analyzed. The proposed cell geometry was designed to overcome the limitations posed by [...] Read more.
This work presents an innovative honeycomb cell geometry design with enhanced in-plane energy absorption under quasi-static lateral loads. Numerical and experimental compression tests results under axial and lateral loads are analyzed. The proposed cell geometry was designed to overcome the limitations posed by standard hexagonal honeycombs, which show relatively low stiffness and energy absorption under loads that have a significant lateral component. To achieve this, the new cell geometry was designed with internal diagonal walls to support the external walls, increasing its stiffness and impact energy absorption in comparison with the hexagonal cell. 3D-printed unit-cell specimens made from ABS thermoplastic material were subjected to experimental quasi-static compression tests, in both lateral and axial directions. Energy absorption was compared to that of the standard hexagonal cell, with the same mass and height. Finite element models were developed and validated using experimental data. Results show that the innovative geometry absorbs approximately 15% more energy under lateral compression, while maintaining the same level of energy absorption of the standard hexagonal cell in the axial direction. The present study demonstrates that the proposed cell geometry has the potential to substitute the standard hexagonal honeycomb in applications where significant lateral loads are present. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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17 pages, 8971 KiB  
Article
Optimal Modeling of an Elevator Chassis under Crash Scenario Based on Characterization and Validation of the Hyperelastic Material of Its Shock Absorber System
by Dimitrios Giagopoulos, Alexandros Arailopoulos and Iraklis Chatziparasidis
Appl. Mech. 2022, 3(1), 227-243; https://doi.org/10.3390/applmech3010016 - 5 Mar 2022
Viewed by 1985
Abstract
A wide variety of hyperelastic rubber-like materials, exhibiting strong nonlinear stress–strain relations under large deformations, is applied in various industrial mechanical systems and engineering applications involving shock and vibration absorbers. An optimal design procedure of an elevator chassis crashing on a hyperelastic shock [...] Read more.
A wide variety of hyperelastic rubber-like materials, exhibiting strong nonlinear stress–strain relations under large deformations, is applied in various industrial mechanical systems and engineering applications involving shock and vibration absorbers. An optimal design procedure of an elevator chassis crashing on a hyperelastic shock absorber in a fail scenario, applicable in large-scale mechanical systems or industrial structures of high importance under strong nonlinear dynamic excitation, is presented in this work. For the characterization of the hyperelastic absorber, a Mooney–Rivlin material model was adopted, and a series of in-lab compression quasi-static tests were conducted. Applying a fully parallelizable state-of-the-art stochastic model updating methodology, coupled with robust, accurate and efficient Finite Element Analysis (FEA) software, the hyperelastic behavior of the shock absorber was validated under uniaxial large deformation, in order to tune all material parameters and develop a high-fidelity FE model of the shock absorber system. Next, a series of in situ full-scale experimental trials were carried out using a test-case elevator chassis, representing the crash scenario on the buffer absorber system, after a controlled free fall. A limited number of sensors, i.e., triaxial accelerometers and strain gauges, were placed at characteristic points of the real structure of the elevator chassis recording experimental data. A discrete Finite Element (FE) model of the experimentally tested arrangement involving the elevator chassis and updated buffer absorber system along with all boundary conditions was developed and used in explicit nonlinear analysis of the crash scenario. Steel material properties and the characterized updated Mooney–Rivlin material model were assigned to the elevator chassis and buffer, respectively. A direct comparison of the numerical and experimental data validated the reliability and accuracy of the methodology applied, whereas results of the analysis were used in order to redesign and optimize a new-design elevator chassis, achieving minimum design stresses and satisfying serviceability limit states. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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17 pages, 20846 KiB  
Article
On the Free Vibration and the Buckling Analysis of Laminated Composite Beams Subjected to Axial Force and End Moment: A Dynamic Finite Element Analysis
by MirTahmaseb Kashani and Seyed M. Hashemi
Appl. Mech. 2022, 3(1), 210-226; https://doi.org/10.3390/applmech3010015 - 23 Feb 2022
Cited by 3 | Viewed by 2126
Abstract
This work presents the bending–torsion coupled free vibration analysis of prestressed, layered composite beams subjected to axial force and end moment using the traditional finite element method (FEM) and dynamic finite element (DFE) techniques. Current trends in the literature, in terms of different [...] Read more.
This work presents the bending–torsion coupled free vibration analysis of prestressed, layered composite beams subjected to axial force and end moment using the traditional finite element method (FEM) and dynamic finite element (DFE) techniques. Current trends in the literature, in terms of different types of modeling techniques and constraints, were briefly examined. The Galerkin-type weighted residual method was applied to convert the coupled differential equations of motion into a discrete problem using a polynomial interpolation function in the finite element method. In the dynamic finite element method, trigonometric shape functions were implemented to describe the equations in terms of nodal displacements. The eigenvalue problem resulting from the discretization along the length of the beam was solved in order to determine the system’s natural frequencies and modes. The results, showing the effects of axial load, end moment, and combined loading on natural frequencies, are discussed and are followed by some concluding remarks. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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18 pages, 2049 KiB  
Article
Dynamic Finite Element Modelling and Vibration Analysis of Prestressed Layered Bending–Torsion Coupled Beams
by MirTahmaseb Kashani and Seyed M. Hashemi
Appl. Mech. 2022, 3(1), 103-120; https://doi.org/10.3390/applmech3010007 - 16 Jan 2022
Cited by 6 | Viewed by 3750
Abstract
Free vibration analysis of prestressed, homogenous, Fiber-Metal Laminated (FML) and composite beams subjected to axial force and end moment is revisited. Finite Element Method (FEM) and frequency-dependent Dynamic Finite Element (DFE) models are developed and presented. The frequency results are compared with those [...] Read more.
Free vibration analysis of prestressed, homogenous, Fiber-Metal Laminated (FML) and composite beams subjected to axial force and end moment is revisited. Finite Element Method (FEM) and frequency-dependent Dynamic Finite Element (DFE) models are developed and presented. The frequency results are compared with those obtained from the conventional FEM (ANSYS, Canonsburg, PA, USA) as well as the Homogenization Method (HM). Unlike the FEM, the application of the DFE formulation leads to a nonlinear eigenvalue problem, which is solved to determine the system’s natural frequencies and modes. The governing differential equations of coupled flexural–torsional vibrations, resulting from the end moment, are developed using Euler–Bernoulli bending and St. Venant torsion beam theories and assuming linear harmonic motion and linearly elastic materials. Illustrative examples of prestressed layered, FML, and unidirectional composite beam configurations, exhibiting geometric bending-torsion coupling, are studied. The presented DFE and FEM results show excellent agreement with the homogenization method and ANSYS modeling results, with the DFE’s rates of convergence surpassing all. An investigation is also carried out to examine the effects of various combined axial loads and end moments on the stiffness and fundamental frequencies of the structure. An illustrative example, demonstrating the application of the presented methods to the buckling analysis of layered beams is also presented. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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28 pages, 1641 KiB  
Article
Formulation of Shell Elements Based on the Motion Formalism
by Olivier Bauchau and Valentin Sonneville
Appl. Mech. 2021, 2(4), 1009-1036; https://doi.org/10.3390/applmech2040059 - 10 Dec 2021
Cited by 2 | Viewed by 2468
Abstract
This paper presents a finite element implementation of plates and shells for the analysis of flexible multibody systems. The developments are set within the framework of the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, [...] Read more.
This paper presents a finite element implementation of plates and shells for the analysis of flexible multibody systems. The developments are set within the framework of the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, (2) couples their displacement and rotation components by recognizing that configuration and motion are members of the Special Euclidean group, and (3) resolves all tensors components in local frames. The formulation based on the motion formalism (1) provides a theoretical framework that streamlines the formulation of shell elements, (2) leads to governing equations of motion that are objective, intrinsic, and present a reduced order of nonlinearity, (3) improves the efficiency of the solution process, (4) circumvents the shear locking phenomenon that plagues shell formulations based on classical kinematic descriptions, and (5) prevents the occurrence of singularities in the treatment of finite rotation. Numerical examples are presented to illustrate the advantageous features of the proposed formulation. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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20 pages, 4774 KiB  
Article
A Box-Girder Design Using Metaheuristic Algorithms and Mathematical Test Functions for Comparison
by Károly Jármai, Csaba Barcsák and Gábor Zoltán Marcsák
Appl. Mech. 2021, 2(4), 891-910; https://doi.org/10.3390/applmech2040052 - 21 Oct 2021
Cited by 2 | Viewed by 2255
Abstract
In engineering, metaheuristic algorithms have been used to solve complex optimization problems. This paper investigates and compares various algorithms. On one hand, the study seeks to ascertain the advantages and disadvantages of the newly presented heuristic techniques. The efficiency of the algorithms is [...] Read more.
In engineering, metaheuristic algorithms have been used to solve complex optimization problems. This paper investigates and compares various algorithms. On one hand, the study seeks to ascertain the advantages and disadvantages of the newly presented heuristic techniques. The efficiency of the algorithms is highly dependent on the nature of the problem. The ability to change the complexity of the problem and the knowledge of global optimal locations are two advantages of using synthetic test functions for algorithm benchmarking. On the other hand, real-world design issues may frequently give more meaningful information into the effectiveness of optimization strategies. A new synthetic test function generator has been built to examine various optimization techniques. The objective function noisiness increased significantly with different transformations (Euclidean distance-based weighting, Gaussian weighting and Gabor-like weighting), while the positions of the optima remained the same. The test functions were created to assess and compare the performance of the algorithms in preparation for further development. The ideal proportions of the primary girder of an overhead crane have also been discovered. By evaluating the performance of fifteen metaheuristic algorithms, the optimum solution to thirteen mathematical optimization techniques, as well as the box-girder design, is identified. Some conclusions were drawn about the efficiency of the different optimization techniques at the test function and the transformed noisy functions. The overhead travelling crane girder design shows the real-life application. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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14 pages, 6163 KiB  
Article
Study on Establish a Brittle Fracture Prediction Considering Different Crack Opening Modes Using Mixed-Mode Ratio
by Takuya Akahoshi, Koji Azuma, Tsutomu Iwashita and Toshiomi Itatani
Appl. Mech. 2021, 2(4), 849-862; https://doi.org/10.3390/applmech2040049 - 18 Oct 2021
Cited by 5 | Viewed by 2410
Abstract
In this study, we propose a method for predicting the occurrence of brittle fractures in the beam-to-column joints of steel structures, considering different crack opening modes. We conducted experiments on beam-to-diaphragm joint specimens with varying plastically constrained cracks to reproduce brittle fractures. The [...] Read more.
In this study, we propose a method for predicting the occurrence of brittle fractures in the beam-to-column joints of steel structures, considering different crack opening modes. We conducted experiments on beam-to-diaphragm joint specimens with varying plastically constrained cracks to reproduce brittle fractures. The experiments’ results demonstrated the effectiveness of the toughness scale model and the Weibull stress approach. In addition, we propose the mixed-mode ratio, which is a quantitative index of the mode difference, and we applied it to the finite element models of the specimens. In this study, we evaluate the validity of the mixed-mode ratio and explore the differences in crack opening modes, as they pertain to the occurrence of brittle fractures. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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23 pages, 17268 KiB  
Article
Steady-State Harmonic Vibrations of Viscoelastic Timoshenko Beams with Fractional Derivative Damping Models
by Michael Klanner, Marcel S. Prem and Katrin Ellermann
Appl. Mech. 2021, 2(4), 797-819; https://doi.org/10.3390/applmech2040046 - 11 Oct 2021
Cited by 7 | Viewed by 2695
Abstract
Due to growing demands on newly developed products concerning their weight, sound emission, etc., advanced materials are introduced in the product designs. The modeling of these materials is an important task, and a very promising approach to capture the viscoelastic behavior of a [...] Read more.
Due to growing demands on newly developed products concerning their weight, sound emission, etc., advanced materials are introduced in the product designs. The modeling of these materials is an important task, and a very promising approach to capture the viscoelastic behavior of a broad class of materials are fractional time derivative operators, since only a small number of parameters is required to fit measurement data. The fractional differential operator in the constitutive equations introduces additional challenges in the solution process of structural models, e.g., beams or plates. Therefore, a highly efficient computational method called Numerical Assembly Technique is proposed in this paper to tackle general beam vibration problems governed by the Timoshenko beam theory and the fractional Zener material model. A general framework is presented, which allows for the modeling of multi-span beams with general linear supports, rigid attachments, and arbitrarily distributed force and moment loading. The efficiency and accuracy of the method is shown in comparison to the Finite Element Method. Additionally, a validation with experimental results for beam systems made of steel and polyvinyl chloride is presented, to illustrate the advantages of the proposed method and the material model. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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11 pages, 4209 KiB  
Article
Paint Coating Removal by Heating for High-Strength Bolted Joints in Steel Bridge and Its Influence on Bolt Axial Force
by Tomonori Nakahara, Mikihito Hirohata, Shinsuke Kondo and Toru Furuichi
Appl. Mech. 2021, 2(4), 728-738; https://doi.org/10.3390/applmech2040042 - 30 Sep 2021
Cited by 4 | Viewed by 2717
Abstract
A series of experiments were carried out for developing a paint coating removal method for high-strength bolted joints in steel bridges. The paint-coated bolted joint specimens were heated to the target temperature of 200 °C by using a sheet-type ceramic heater. The maximum [...] Read more.
A series of experiments were carried out for developing a paint coating removal method for high-strength bolted joints in steel bridges. The paint-coated bolted joint specimens were heated to the target temperature of 200 °C by using a sheet-type ceramic heater. The maximum temperature of specimens could be controlled within 10% of the target value. The paint coating was easily removed by using general tools after heating. The behaviour of bolts with thermal expansion and shrinkage was monitored by strain gauges attached to the bolts during heating. It was estimated that the axial forces of the bolts were reduced by 2.6% of the initially installed axial forces, on average. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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14 pages, 4753 KiB  
Article
An Economical and Mechanical Investigation on Local Post-Weld Heat Treatment for Stiffened Steel Plates in Bridge Structures
by Mikihito Hirohata, Shuhei Nozawa and Károly Jármai
Appl. Mech. 2021, 2(4), 714-727; https://doi.org/10.3390/applmech2040041 - 29 Sep 2021
Cited by 4 | Viewed by 2560
Abstract
A heat treatment is effective for reducing the residual stress of the welded structures. A post-weld heat treatment (PWHT) requires a large heating apparatus (furnace). It requires a high energy, a long time, and a high cost. For examining the possibility of cost [...] Read more.
A heat treatment is effective for reducing the residual stress of the welded structures. A post-weld heat treatment (PWHT) requires a large heating apparatus (furnace). It requires a high energy, a long time, and a high cost. For examining the possibility of cost and energy saving in PWHT work, an economical and mechanical investigation of the local PWHT to stiffened plate members in steel bridges was conducted. The expense of apparatus for the furnace PWHT was 1.5 times higher than that of local PWHT by sheet-type ceramic heaters. When the number of heater units was reduced and were repeatedly used, the expense for the apparatus became lower. However, it took longer to complete the heat treatment than with the furnace PWHT or the local PWHT with full heater units. The thermal elastic-plastic finite element (FE) analysis examined the effect of local PWHT. The tendency of the stress distribution after the local PWHT differed from the welding residual stress or the stress after the furnace PWHT because of the temperature difference between the heated and the non-heated parts of the local PWHT. However, the effect of residual stress relief by the local PWHT could be almost the same as that of the furnace PWHT. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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13 pages, 25185 KiB  
Article
Modal Analysis of Optimized Trapezoidal Stiffened Plates under Lateral Pressure and Uniaxial Compression
by Zoltán Virág and Sándor Szirbik
Appl. Mech. 2021, 2(4), 681-693; https://doi.org/10.3390/applmech2040039 - 28 Sep 2021
Cited by 4 | Viewed by 2802
Abstract
This paper deals with the modal analysis of optimized trapezoidal stiffened plates with simple supported conditions on the four edges of the base plate. The main objective of the finite element analysis is to investigate the natural frequencies and mode shapes of some [...] Read more.
This paper deals with the modal analysis of optimized trapezoidal stiffened plates with simple supported conditions on the four edges of the base plate. The main objective of the finite element analysis is to investigate the natural frequencies and mode shapes of some stiffened structures subjected to lateral pressure and uniaxial compression in order to identify any potentially dangerous frequencies and eliminate the failure possibilities. The natural frequencies and mode shapes are important parameters in the design of stiffened plates for dynamic loading conditions. In this study, the numerical analysis is performed for such a design of this kind of welded plates which have already been optimized for lateral pressure and uniaxial compression. The objective function of the optimization to be minimized performed with the Excel Solver program is the cost function which contains material and fabrication costs for Gas Metal Arc Welding (GMAW) welding technology. In this study, the eigenvalue extraction used to calculate the natural frequencies and mode shapes is based on the Lanczos iteration methods using the Abaqus software. The structure is made of two grades of steel, which are described with different yield stress while all other material properties of the steels in the isotropic elastic model remain the same. Drawing the conclusion from finite element analysis, this circumstance greatly affects the result. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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36 pages, 806 KiB  
Article
On the Generation of Harmonics by the Non-Linear Buckling of an Elastic Beam
by Luiz M. B. C. Campos and Manuel J. S. Silva
Appl. Mech. 2021, 2(2), 383-418; https://doi.org/10.3390/applmech2020022 - 15 Jun 2021
Cited by 1 | Viewed by 3044
Abstract
The Euler–Bernoulli theory of beams is usually presented in two forms: (i) in the linear case of a small slope using Cartesian coordinates along and normal to the straight undeflected position; and (ii) in the non-linear case of a large slope using curvilinear [...] Read more.
The Euler–Bernoulli theory of beams is usually presented in two forms: (i) in the linear case of a small slope using Cartesian coordinates along and normal to the straight undeflected position; and (ii) in the non-linear case of a large slope using curvilinear coordinates along the deflected position, namely, the arc length and angle of inclination. The present paper starts with the exact equation in a third form, that is, (iii) using Cartesian coordinates along and normal to the undeflected position like (i), but allowing exactly the non-linear effects of a large slope like (ii). This third form of the equation of the elastica shows that the exact non-linear shape is a superposition of linear harmonics; thus, the non-linear effects of a large slope are equivalent to the generation of harmonics of a linear solution for a small slope. In conclusion, it is shown that: (i) the critical buckling load is the same in the linear and non-linear cases because it is determined by the fundamental mode; (ii) the buckled shape of the elastica is different in the linear and non-linear cases because non-linearity adds harmonics to the fundamental mode. The non-linear shape of the elastica, for cases when powers of the slope cannot be neglected, is illustrated for the first four buckling modes of cantilever, pinned, and clamped beams with different lengths and amplitudes. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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