Mechanical Design Technologies for Beam, Plate and Shell Structures (2nd Volume)

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

Deadline for manuscript submissions: closed (15 January 2023) | Viewed by 12291

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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 follows on from the first Special Issue, entitled "Mechanical Design Technologies for Beam, Plate and Shell Structures" (https://www.mdpi.com/journal/applmech/special_issues/Beam_Plate_Shell_Structures), published in Applied Mechanics in 2021.

This Special Issue will bring together theoretical studies and applied works on state-of-the-art computational modeling and experimental techniques used in the mechanical design of general structural engineering systems embodying beam, plate, and shell structural elements. We welcome papers detailing advances in fundamental theories, approximation methods, computational techniques, and experimental testing technologies, and those 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.

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 (7 papers)

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Research

23 pages, 766 KiB  
Article
Numerical Analysis of Cracked Double-Beam Systems
by Maria Anna De Rosa and Maria Lippiello
Appl. Mech. 2023, 4(4), 1015-1037; https://doi.org/10.3390/applmech4040052 - 24 Sep 2023
Viewed by 1098
Abstract
Based on elasticity theory, this paper discusses the static analysis of a cracked double-beam system in the presence of a Winkler-type medium. It is further assumed that the double-beam system is constrained at both ends by elastically flexible springs with transverse and rotational [...] Read more.
Based on elasticity theory, this paper discusses the static analysis of a cracked double-beam system in the presence of a Winkler-type medium. It is further assumed that the double-beam system is constrained at both ends by elastically flexible springs with transverse and rotational stiffness. Using a variational formulation, the governing static equations are derived and solved using analytical and numerical approaches. In the first approach, closed-form solutions for the displacement functions are obtained based on the Euler–Bernoulli beam theory. In the second approach, the Cell Discretisation Method (CDM) is performed, whereby the two beams are reduced to a set of rigid bars connected by elastic constraints, in which the flexural stiffness of the bars is concentrated. The resulting stiffness matrix is easily deduced, and the governing equations of the static problem can be immediately solved. A comparative analysis is performed to verify the accuracy and validity of the proposed method. The study focuses on the effect of various parameters, including crack depth and position, boundary conditions, elastic medium and slenderness. The validity of the proposed analysis is confirmed by comparing the current results with those obtained from other approaches. In particular, the results obtained by closed-form solution and CDM are compared with the Finite Element Method (FEM). The accuracy of the results was assessed by making comparisons with results found in the literature and reported in the bibliography. It was shown that the proposed algorithm provides a simple and powerful tool for dealing with the static analysis of a double-beam system. Finally, some concluding remarks are made. Full article
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17 pages, 12470 KiB  
Article
Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections
by Martin Denk, Michael Jäger and Sandro Wartzack
Appl. Mech. 2023, 4(2), 476-492; https://doi.org/10.3390/applmech4020027 - 21 Apr 2023
Viewed by 1561
Abstract
The calculation of moments of area is one of the most fundamental aspects of engineering mechanics for calculating the properties of beams or for the determination of invariants in different kind of geometries. While a variety of shapes, such as circles, rectangles, ellipses, [...] Read more.
The calculation of moments of area is one of the most fundamental aspects of engineering mechanics for calculating the properties of beams or for the determination of invariants in different kind of geometries. While a variety of shapes, such as circles, rectangles, ellipses, or their combinations, can be described symbolically, such symbolic expressions are missing for freeform cross-sections. In particular, periodic B-spline cross-sections are suitable for an alternative beam cross-section, e.g., for the representation of topology optimization results. In this work, therefore, a symbolic description of the moments of area of various parametric representations of such B-splines is computed. The expressions found are then compared with alternative computational methods and checked for validity. The resulting equations show a simple method that can be used for the fast conceptual computation of such moments of area of periodic B-splines. Full article
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33 pages, 961 KiB  
Article
Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations
by László Kiss, Abderrazek Messaoudi and György Szeidl
Appl. Mech. 2023, 4(1), 254-286; https://doi.org/10.3390/applmech4010015 - 22 Feb 2023
Viewed by 1557
Abstract
It is our main objective to find the critical load for three beams with cross sectional heterogeneity. Each beam has three supports, of which the intermediate one is a spring support. Determination of the critical load for these beams leads to three point [...] Read more.
It is our main objective to find the critical load for three beams with cross sectional heterogeneity. Each beam has three supports, of which the intermediate one is a spring support. Determination of the critical load for these beams leads to three point boundary value problems (BVPs) associated with homogeneous boundary conditions—the mentioned BVPs constitute three eigenvalue problems. They are solved by using a novel solution strategy based on the Green functions that belong to these BVPs: the eigenvalue problems established for the critical load are transformed into eigenvalue problems governed by homogeneous Fredholm integral equations with kernels that can be given in closed forms provided that the Green function of each BVP is known. Then the eigenvalue problems governed by the Fredholm integral equations can be manipulated into algebraic eigenvalue problems solved numerically by using effective algorithms. It is an advantage of the way we attack these problems that the formalism established and the results obtained remain valid for homogeneous beams as well. The numerical results for the critical forces can be applied to solve some stability problems in the engineering practice. Full article
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6 pages, 1342 KiB  
Communication
Kirchhoff’s Analogy between the Kapitza Pendulum Stability and Buckling of a Wavy Beam under Tensile Loading
by Rahul Ramachandran and Michael Nosonovsky
Appl. Mech. 2023, 4(1), 248-253; https://doi.org/10.3390/applmech4010014 - 21 Feb 2023
Viewed by 1445
Abstract
The Kirchhoff analogy between the oscillation of a pendulum (in the time domain) and the static bending of an elastic beam (in the spatial domain) is applied to the stability analysis of an inverted pendulum on a vibrating foundation (the Kapitza pendulum). The [...] Read more.
The Kirchhoff analogy between the oscillation of a pendulum (in the time domain) and the static bending of an elastic beam (in the spatial domain) is applied to the stability analysis of an inverted pendulum on a vibrating foundation (the Kapitza pendulum). The inverted pendulum is stabilized if the frequency and amplitude of the vibrating foundation exceed certain critical values. The system is analogous to static bending a wavy (patterned) beam subjected to a tensile load with appropriate boundary conditions. We analyze the buckling stability of such a wavy beam, which is governed by the Mathieu equation. Micro/nanopatterned structures and surfaces have various applications including the control of adhesion, friction, wettability, and surface-pattern-induced phase control. Full article
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32 pages, 643 KiB  
Article
An Intuitive Derivation of Beam Models of Arbitrary Order
by Hart Honickman
Appl. Mech. 2023, 4(1), 109-140; https://doi.org/10.3390/applmech4010008 - 28 Jan 2023
Viewed by 2180
Abstract
This article presents a new beam model that employs a recursive derivation procedure that enables the user to set the order of the governing differential equations as an input parameter, without the need for ad hoc assumptions or methodologies. This article employs a [...] Read more.
This article presents a new beam model that employs a recursive derivation procedure that enables the user to set the order of the governing differential equations as an input parameter, without the need for ad hoc assumptions or methodologies. This article employs a novel system of kinematic variables, section constants, and section functions that facilitate the development of higher-order beam models that retain a clear philosophical link to classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory. The present beam model is a type of equivalent single layer beam model, wherein section constants are used to model the global stiffness characteristics of the beam, and section functions are used to recover sectional fields of displacements, strains, and stresses. The present beam model is solved for several example beams, and the results are compared to the results of finite element analyses. It is shown that the present beam model can accurately predict the deformed shapes and stress fields of each of the example beams. This article also reveals an interesting peculiarity of the elastic potential energy that pertains to any unidimensional beam model that is governed by differential equations that are of finite order. Full article
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13 pages, 3760 KiB  
Article
Analytical Model for the Prediction of Instantaneous and Long-Term Behavior of RC Beams under Static Sustained Service Loads
by Bassel Bakleh, Hala Hasan and George Wardeh
Appl. Mech. 2023, 4(1), 31-43; https://doi.org/10.3390/applmech4010003 - 9 Jan 2023
Cited by 1 | Viewed by 1749
Abstract
A great number of reinforced concrete structures are approaching the end of their service life and they are strongly affected by progressive deterioration processes due to insufficient maintenance. A fundamental understanding of all damage phenomena acting together on reinforced concrete, RC, structures under [...] Read more.
A great number of reinforced concrete structures are approaching the end of their service life and they are strongly affected by progressive deterioration processes due to insufficient maintenance. A fundamental understanding of all damage phenomena acting together on reinforced concrete, RC, structures under service loads is a crucial step toward more sustainable structures. The present work aims to study the creep of RC beams in the cracked state. To achieve this objective, an analytical model was developed based on Bernoulli’s theory and the global equilibrium of the RC beam. A Newton–Raphson algorithm was also proposed to solve the non-linear equilibrium equations related to the non-linearity in the adopted materials models. The proposed model allows predicting the instantaneous and long-term behavior under any loading level up to the steel yielding, and it takes into consideration the effect of creep on the behavior of concrete both in tension and compression. In addition to the evolution of the deflection with time, the model is also able to follow the height of the compression zone as well as the evolution of crack’s height and width under any sustained service load. The comparison between analytical and experimental results found in the literature for long-term loaded beams showed a good agreement. Full article
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16 pages, 2194 KiB  
Article
Undamped Free Vibration Analysis of Functionally Graded Beams: A Dynamic Finite Element Approach
by Aaron Gee and Seyed M. Hashemi
Appl. Mech. 2022, 3(4), 1223-1239; https://doi.org/10.3390/applmech3040070 - 7 Oct 2022
Cited by 2 | Viewed by 1950
Abstract
A Dynamic Finite Element (DFE) method for coupled axial–flexural undamped free vibration analysis of functionally graded beams is developed and subsequently used to investigate the system’s natural frequencies and mode shapes. The formulation is based on the Euler–Bernoulli beam theory and material grading [...] Read more.
A Dynamic Finite Element (DFE) method for coupled axial–flexural undamped free vibration analysis of functionally graded beams is developed and subsequently used to investigate the system’s natural frequencies and mode shapes. The formulation is based on the Euler–Bernoulli beam theory and material grading is assumed to follow a power law variation through the thickness direction. Using the closed-form solutions to the uncoupled segments of the system’s governing differential equations as the basis functions of approximation space, the dynamic, frequency-dependent, trigonometric interpolation functions are developed. The interpolation functions are used with the weighted residual method to develop the DFE of the system. The resulting nonlinear eigenvalue problem is then solved to determine the coupled natural frequencies. Example elements using DFE, Finite Element Method (FEM) and the Dynamic Stiffness Method (DSM) are implemented in MATLAB for testing, verification, and validation. Good agreement was observed and the DFE formulation exhibited superior convergence performance compared to the FEM. Full article
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