Sector Plates Research Articles

Annular sector plates made of FG graphene origami-enabled auxetic metamaterial under bending and buckling loading: A VDQ-based approach

The behaviors of annular sector plates made of functionally graded graphene origami-enabled auxetic metamaterials (FG-GOEAMs) under the action of buckling and bending loads are investigated herein using a numerical approach. Multiple GOEAM layers with graphene origami (GOri) content are considered for the plate which changes in layer-wise patterns. Moreover, the material properties of the plate are calculated using novel genetic programming-assisted micromechanical models. In order to derive the governing equations, the Mindlin plate theory in conjunction with Hamilton’s principle is utilized within the framework of the variational differential quadrature (VDQ) method. The vector-matrix representation of the presented formulation can be beneficial from the viewpoint of implementing numerical approaches. The governing equations are then discretized and solved based on VDQ matrix differential and integral operators so as to obtain the critical buckling load and maximum lateral deflection of plates with different edge conditions. The effects of GOri content, folding degree and distribution pattern on the results are studied. It is revealed that increasing the GOri content leads to the negative Poisson’s ratio (NPR) effect which respectively reduces and increases the lateral deflection and the critical buckling load.

On the measurement of the nonlinear dynamics of sandwich sector plate surrounded by the auxetic concrete foundation: Introducing a machine learning algorithm for nonlinear problems

The measurement of the nonlinear dynamics of sandwich rotary sector plates is crucial for measurement engineers as it enables the precise analysis and understanding of the behavior of advanced composite structures under dynamic conditions. These measurements help in identifying and mitigating potential issues related to vibration, stability, and fatigue, which are critical in industries like aerospace, automotive, and civil engineering. Accurate data on nonlinear dynamics aids in the optimization of design, enhancing performance, durability, and safety. Furthermore, it supports the development of predictive maintenance strategies, reducing downtime and operational costs, and contributing to the advancement of engineering materials and techniques. So, in the current work, for the first time, nonlinear dynamics of sandwich rotary sector plate via a mathematical modeling and machine learning algorithm is presented. First, due to a lack of information on the nonlinear dynamics of sandwich rotary sector plates, a dataset for training, testing, and validating the machine learning algorithm is presented. For this purpose, using Hamilton’s principle, Von-Karman nonlinearity, and first-order shear deformation theory (FSDT), the nonlinear governing equations are obtained. Also, due to increasing stiffness and stability, an auxetic concrete foundation covers the sandwich structure. After that using the two-dimensional generalized differential quadrature method (GDQM) and Newmark’s time integration method (NTIM), the nonlinear equations are solved. This research provides valuable insights for engineers in designing advanced composite structures with improved dynamic properties. The results also contribute to the broader understanding of nonlinear dynamic interactions in complex material systems, paving the way for innovative applications in various engineering fields.

Interplay of photonic, electrical, and inertial loads on the stability of rotating sector perovskite sandwich plates with a GPL-based nanocomposite core

The bifurcation stability of sandwich sector plates, primarily constructed from lead halide perovskite skins known for their significant photostrictive and electrostrictive properties, is explored. These properties render them highly relevant for multiphysics applications. The influence of a photo-induced thermal environment on the behavior of these plates is also examined. A notable challenge, the inherent stiffness of these structures, is addressed by integrating a nanocomposite laminated core composed of a polymer matrix and graphene platelet (GPL) reinforcers. The GPLs are distributed throughout the core layers according to functionally graded models, significantly enhancing structural integrity. To effectively model the core environment, the Halpin-Tsai micromechanical rule is employed. The structural displacement field is modeled using the first-order shear deformation theory. Moreover, the von-Kármán geometrically nonlinear strain-displacement relations are applied. The constitutive relationships are governed by the theory of linear photo-thermo-electro-elasticity, providing a framework for the analysis of perovskite-based structures. The reorganization of bifurcation points from the pre-buckling route and the linearization of stability equations are performed using the adjacent-equilibrium criterion. The generalized differential quadrature (GDQ) method is utilized to solve the equilibrium equations of pre-buckling and the stability equations of buckling. This comprehensive investigation reveals the critical influence of photonic, electrical, and rotational stimuli on the stability characteristics of advanced perovskite-based sandwich sector plates, demonstrating potential advancements in multiphysics applications.

Thermal buckling of the concrete structures reinforced by nanocomposites: Introducing advanced deep neural networks for thermal buckling problem

The thermal buckling behavior of concrete annular sector plates reinforced with nanocomposites is investigated in this work. The thermal buckling issue is stated using mathematical modeling, taking into account the geometric linearity and material heterogeneity caused by the nanocomposite reinforcement. The governing differential equations that are obtained from the theoretical model are solved using the discrete singular convolution (DSC) technique. To generate accurate buckling load predictions, the DSC method’s great accuracy in handling complicated boundary conditions and discontinuities is used. Furthermore, using mathematical modeling to create extensive datasets, the research aims to train deep neural networks (DNNs) to anticipate thermal buckling reactions. These datasets provide a strong basis for DNN training as they include a wide range of factors, such as geometric configurations, loading situations, and material properties. By combining DNN predictions with DSC solutions, this unique technique for solving this difficult issue seeks to improve the accuracy and efficiency of thermal buckling analysis. The findings show how well sophisticated mathematical methods and machine learning models work together, opening the door to creative solutions for the design and analysis of concrete structures reinforced with nanocomposite under complicated stress.

Dynamic stability analysis of CFRP sandwich structure reinforced by advanced nanocomposites via both machine learning method and mathematical simulation

This work introduces a quasi-3D refined theory for assessing the transient dynamic reactions of a sandwich annular sector plate subjected to mechanical shock loading. The sandwich structure has two facesheets composed of graphene origami (GOri)-enabled auxetic metal metamaterials (GOEAMs) and a core composed of carbon fiber reinforced polymer. The auxetic quality of the annular plates is mainly determined by the quantity of graphene and the level of folding in the GOri material. The elements are assessed layer by layer across the thickness of the plates. Micromechanical models supported by genetic programming may be used to predict the position-dependent Poisson’s ratio and other material parameters. The concept of Hamiltonian is used to deduce the governing equations of the structure. The equations of motion, which vary with time, are solved using the numerical solution process and the Laplace transform. A comprehensive parametric study is carried out to examine the influence of various geometric and physical parameters on the time-dependent behavior of annular sector plates. The current mathematical modeling results are being compared to the findings of previous works, as well as a machine learning technique. By using this machine learning methodology, it is feasible to computationally solve differential equations at a reduced expense, while simultaneously surmounting the challenge of formulation. To use machine learning techniques, a dependable dataset acquired from either experimental or numerical analysis is necessary. The dataset was created using the quantitative findings of the investigation. Furthermore, the machine learning technique demonstrates its capacity to provide very precise outcomes when predicting the transient behavior of the existing structure under novel loading and boundary circumstances.

Vibration analysis of quasicrystal sector plates with porosity distribution in a thermal environment

Vibration analysis of quasicrystal sector plates with porosity distribution in a thermal environment

Transverse free vibration analysis of thin sectorial plates by the weak form quadrature element method

The weak form quadrature element method is applied to free vibration analysis of thin sectorial plates with arbitrary vertex angles and boundary conditions. To tackle the strong stress singularity around the vertex, analytical displacement descriptions are introduced into the inner sectorial subdomain, while the outer annular subdomain is modeled by a single weak form quadrature thin plate element. The continuity on the interface between the two subdomains is enforced afterwards. Eventually, a generalized eigenvalue formulation is established after introducing Hamilton’s principle. The first six non-dimensional frequency parameters for various vertex angles and boundary conditions are obtained and compared with available results. Several typical free vibration modes are plotted. The accuracy, convergence rate, and computational cost of the present formulation are discussed at length.

Free vibration analysis of sandwich structure via point interpolation meshfree method based on polynomial basic function

The stability of circular and annular sector plate structures under aerodynamic pressure in supersonic conditions is crucial for aircraft components. Conventional uniform materials lead to heavy structures, which are undesirable for aircraft. This study explores the use of functionally graded materials to enhance flutter stability. It employs a refined logarithmic shear deformation theory to describe plate displacement, classical elasticity theory for constitutive equations, and Hamilton’s principle for equations of motion. Two methods, finite element, and Meshfree radial point interpolation, are used to solve these equations and verify the results. Parameter studies are conducted to assess the effects of grading index, Biot’s coefficient, span angle, and geometrical aspect ratio, revealing unexpected adverse effects of grading material on stability.

Dynamic responses of functionally graded origami-enabled auxetic metamaterial sector plate induced by mechanical shock: Application of innovative machine learning algorithm

For the first time, in the current work, the quasi-3D new refined theory (Q3D-NRT) is used to analyze the dynamic reactions of functionally graded (FG) annular sector plates made of graphene origami (GOri)-enabled auxetic metal metamaterials to the mechanical shock loading. The auxetic property of the annular plates is effectively controlled by graphene content and GOri folding degree that is graded across the thickness direction of the annular plates in a layer-wise manner, as Poisson’s ratio and other material properties are position-dependent and can be estimated by genetic programming-assisted micromechanical models (MM). Hamilton’s concept is used to find the structure’s governing equations. The differential quadrature technique and the Laplace transform are used at design sites to solve the time-varying equations of motion. The system response is translated from the Laplace domain to the time domain using a modified version of the Dubner and Abate approach. To investigate the impact of different geometrical and physical factors on the dynamic reactions of the annular sector plates, thorough parametric research is conducted. The findings of the present mathematical modeling are compared with those of the earlier publications and also with those of the machine learning approach. Utilizing this learning strategy, differential equations may be solved with very cheap computer costs while also overcoming formulation complexity. It needs a valid dataset from experimental or numerical analysis to use machine learning techniques. This dataset was compiled using the study’s numerical findings. Additionally, the machine learning approach demonstrates the capacity to deliver findings with a high degree of accuracy when predicting the mechanical characteristics of the existing structure under novel loading and boundary circumstances.

Review of solution methodologies for structural analysis of composites

This article reviews state-of-art solution methodologies for structural analysis of composites. The use of composites and advance composite in the design of structures has contributed to significant development in modeling and analysis of composite structures. Various modeling approaches as well as solution methodologies had been developed in the past for accurate and efficient response prediction of these structures. Our study focuses on the review of solution methodologies adopted for examined the bending, buckling and free vibrations of composites. These solution methodologies are classified as analytical, semi-analytical and numerical methods. While analytical solutions are restricted to specific set of boundaries and loading conditions, the numerical solutions find applications in complex geometries and general boundary conditions. With the development of computational technologies, the numerical solutions have gained popularity over a period of last three decades. In this article, the analytical approaches are reviewed in the framework of Navier technique, Levy Method, and symplectic superposition method while the numerical approaches are reviewed in the framework of Rayleigh–Ritz method, finite element method (FEM), meshfree methods, wavelets-based methods and differential quadrature method. The laminated composite plates/shells, CNT reinforced composite, FGM plates, circular and annular sector or sector plates have been studied in this review. An overview of mathematical formulation for the numerical methods is also presented.

Nonlinear large-amplitude vibration analysis of annular sector plates made of FGMs subjected to cooling shock

A numerical approach is developed in the present article to study the geometrically nonlinear vibrations of annular sector plates made of functionally graded materials (FGMs) due to being exposed to cooling shock. The first-order shear deformation plate theory (FSDT) is used in the modeling of plate, and the governing equations of motion are derived based on Hamilton's principle considering von Kármán nonlinear kinematic relations. It is also considered that the properties of FGMs are dependent on temperature and distribution of materials. According to the uncoupled thermoelasticity theory, the temperature distribution is obtained via 1D Fourier-type transient heat conduction equation. To numerically solve the problem, the generalized differential quadrature (GDQ) method and Newmark-beta integration scheme are utilized. Considering two different types of thermal loading as cooling shock, the effects of various parameters including thermal load rapidity time, geometry, magnitude of thermal load and material properties on the large-amplitude vibrations of annular sector plates are investigated.

Dynamic Analysis of Multilayered Piezoelectric Quasicrystal Three-Dimensional Sector Plates with Imperfect Interfaces

Piezoelectric quasicrystals have attracted extensive attention due to their unique physical and mechanical properties. This paper studies the dynamic response of multilayered two-dimensional decagonal piezoelectric quasicrystal sector plates with imperfect interfaces. Based on the quasicrystal linear elasticity, partial differential state equations along the thickness direction are derived by using the state-space method. Then, by virtue of the differential quadrature method and the Fourier series expansions, this boundary-value problem with mixed boundary conditions and imperfect interfaces is solved. In addition, via the joint coupling matrix, the field quantities in the interior of the structure are connected to those on the external surfaces with numerical instability. Finally, parameter studies on the effects of angular spans, imperfect interfaces, and mixed boundary conditions are numerically investigated where the dimensionless frequencies and modes are exhibited.

Buckling simulation of eccentrically rotating nanocomposite sector plates in thermal environment using the 2D Chebyshev collocation method

The present paper investigates the inertial stability of a graphene platelet (GPL) reinforced nanocomposite sector plate eccentrically rotating with a constant angular velocity. The axis of spinning is perpendicular to the plate and parallel to the transverse direction of origin. It is considered at a distance and angle to the plate coordinate origin. A uniform thermal environment is considered that affects the plate response. The nanocomposite is regarded as a laminated plate in which the GPLs in each layer are orientated and dispersed equally and randomly. The volume fraction of particles varies from layer to layer based on functionally graded (FG) linear models suitable for studying the buckling phenomenon. The pre-buckling and stability paths are separated by utilizing the adjacent equilibrium criterion. Both paths are solved by implementing the Chebyshev Collocation (CC) technique. The consequences of geometrical parameters, nanocomposite characteristics, and eccentric angle and distance on the stability of the current system are investigated. It will be revealed that the eccentric distance, according to its angle, can significantly increase or decrease the critical speed of the fabrication.

A four-node rectangular plate finite element using Airy functions with transverse shear

PurposeAmong different types of engineering structures, plates play a significant role. Their analysis necessitates numerical modeling with finite elements, such as triangular, quadrangular or sector plate elements, owing to the intricate geometrical shapes and applied loads. The scope of this study is the development of a new rectangular finite element for thin plate bending based on the strain approach using Airy's function. It is called a rectangular plate finite element using Airy function (RPFEUAF) and has four nodes. Each node had three degrees of freedom: one transverse displacement (w) and two normal rotations (x, y).Design/methodology/approachEquilibrium conditions are used to generate the interpolation functions for the fields of strain, displacements and stresses. The evolution of the Airy function solutions yielded the selection of these polynomial bi-harmonic functions. The variational principle and the analytical integration approach are used to evaluate the basic stiffness matrix.FindingsThe numerical findings for thin plates quickly approach the Kirchhoff solution. The results obtained are compared to the analytical solution based on Kirchhoff theory.Originality/valueThe efficiency of the strain based approach using Airy's function is confirmed, and the robustness of the presented element RPFEUAF is demonstrated. Because of this, the current element is more reliable, better suited for computations and especially intriguing for modeling this kind of structure.

Free vibration analysis of the sandwich structured composite annular plates: Numerical and experimental investigation

Sandwich structures are interesting structural elements due to their high stiffness-to-weight ratio, high fatigue resistance, and excellent vibration characteristics. The aerospace industry relies heavily on these types of structures considering the different optimized materials and shapes available for sandwich construction. In the present study, vibration aspects of annular sandwich structures with composite laminates and a 3D printed honeycomb core are investigated in both the numerical and experimental methods. Amongst the various shapes of sandwich structures, annular sector plates are predominantly used in the construction of modern bridges, aircrafts, and automobile parts. Furthermore, the investigation of annular sandwich plates featuring GFRP facesheet and 3D printed PLA cores are studied in a very limited extent. In order to obtain the sector plates experimentally, Glass Fiber Reinforced Polymer (GFRP) laminates are fabricated by hand layup techniques, and the 3D printing Poly-lactic Acid (PLA) honeycomb core is manufactured using Fused Deposition Modelling (FDM). The material properties of honeycomb core and composite skins are estimated with the help of Gibson formulation and rule of mixture, respectively. Based on available literature, the analysis approach is validated through numerical analysis using ANSYS Finite Element (FE) software. Also, the frequency responses of annular sandwich plate were measured in both experimental and numerical analysis and the results showed good agreement. However, in order to describe the effectiveness of annular composite sandwich plates, parametric studies are carried out in terms of natural frequencies and mode shapes with different configurations of core geometry, ply orientation, boundary constraints, and inner to outer radius ratio. The research outcome highlights that the optimum angle ply orientation, core height of 12.5 mm with clamped–clamped condition and inner to outer radius of 0.75 mm yields better structural stiffness.

Influence of Fiber Angle on the Steady State Periodic Response of Annular Sectorial Plates

Structural elements in the form of annular sectorial plates are widely used in aeronautical, biomedical, and marine engineering. When these components are exposed to dynamic load, large-amplitude vibrations occur. The vibration response analysis based on the linear strain-displacement relation typically yields a conservative estimate and can be used as a first approximation to the actual solution for thin structural elements. As a result, geometric nonlinearity must be incorporated for the efficient and fail-proof design of such elements. This paper shows non-linear and linear steady-state forced vibration responses of the annular sectorial plates. The governing equations of motion have been solved in the time domain by using a modified shooting method and an arc-length/pseudo-arc length continuation technique at the bifurcation point to obtain the complete response curve comprised of stable and unstable branches. This work investigates the effect of fibre angle on the non-linear steady-state forced vibration response of annular sectorial plates. The strain/stress fluctuation throughout the thickness of the laminated annular sectorial plate is determined to explain why hardening nonlinearity has increased. The cyclic fluctuation of the non-linear steady-state normal stress during a time period at the centre of the top and bottom surface is also provided in relation to the forcing frequency ratio of peak amplitude in the non-linear response. Due to the change in restoring forces, the frequency spectra reveal much increased harmonic involvement along with the fundamental harmonic for all fibre angles.

Numerical modeling of vibration and damping of higher-order magnetorheological elastomer polar orthotropic composite sectorial/annular plates

This study contributes to the modeling and analysis of damping and vibration in the innovative composite sector and annular plates composed of a magnetorheological elastomer (MRE) reinforced with glass fibers. These plates are formed of laminate construction. For the purpose of this investigation, polar orthotropic laminas are used. The generalized Maxwell constitutive law is employed in order to describe the tunable viscoelastic properties of the MR elastomer, including storage and modal loss factor. The application of a magnetic field enables one to exert control over the storage and loss moduli of these materials. In addition, the effective mechanical properties of the MRE composite (MREC) are determined through a modified version of the Voigt micromechanical rule and the Halpin–Tsai rule. In order to define the displacement field of the plate, a hyperbolic higher-order shear deformation approach is used. By adopting Hamilton’s principle, one may get the equations describing the motion as well as the relevant boundary and continuity conditions. In order to solve this system of highly coupled partial differential equations (PDEs), the 2D generalized differential quadrature (GDQ) approach is exploited. A comparison was made between the developed model and those available in the literature to validate the accuracy and convergence quality of the solution technique and formulation. A complete investigation is carried out into the influence of the magnetic field on the free-damped response of the MREC sector and annular plates. In addition, the effects of the composite and geometric properties of the structure on the natural frequencies and modal loss factors of the structure have been examined.

Free vibration analysis of pre-stretched hyperelastic micromorphic continua with arbitrary shapes

A novel numerical strategy is developed in this article to study the free vibrations of hyperelastic micromorphic continua under bending load. In the proposed approach, the variational differential quadrature (VDQ) method and the idea of position transformation are used. The 3D micromorphic hyperelasticity is first formulated via vector-matrix relations which can be readily utilized in the coding process of numerical methods. The present numerical approach is able to address problems with irregular domains. To this end, the domain of elements is transformed into a regular one by the technique of mapping of position field based on the finite element shape functions. Being locking-free, simple implementation, computational efficiency and fast convergence rate are other features of the present variational approach. Three numerical examples including rectangular, sector and circular plates under bending load are considered whose free vibration behavior is analyzed. It is shown that the method is capable of predicting the relation between natural frequencies of micromorphic hyperelastic continua with load factor in an efficient way. The effects of internal length scale, scale-transition parameter and mode transition on the results are investigated.

On the asymmetric dynamic response of viscoelastic sector plate made of FG polymer foam

This work provides an analytical investigation of the damped forced vibration behavior of viscoelastic annular sector plates made of porous polymer foam. For this aim, the motion equations are obtained through first-order shear deformation theory (FSDT) in conjunction with the energy method and the calculus of variations. Three distinct types of pore distribution are explored in the plate thickness such as porosity symmetric distribution type 1 (PSDT1), porosity symmetric distribution type 2 (PSDT2), and porosity non-symmetric distribution (PND). Then, the obtained relations are extended to constitutive equations by considering the standard linear solid (SLS) viscoelastic model. The perturbation technique and Fourier series are employed to solve the system of equations with variable coefficients. The equations with variable coefficients are changed to a system with constant coefficients by inserting a new variable, and the asymmetrically dynamic response is computed analytically in a closed-form solution. Then, the transient dynamic behavior of viscoelastic functionally graded porous (VFGP) annular sector plates is detailed for various types of radial and asymmetric circumferential loadings. Furthermore, a user-defined field (USDFLD) code is developed for evaluating the reliability of the analytical findings using finite element (FE) software. Finally, we have benchmarked the effectiveness of our framework by investigating several geometrical parameters, material properties, and loadings types.

Effects of Lamination Schemes on the Periodic Response of the Annular Sectorial Plates

A broad variety of aeronautical, biomedical, and military applications make use of structures in the form of annular sectorial plates. When in use, they are subjected to stress fluctuations and vibrations with considerable amplitudes. Geometric non-linearity is necessary for efficient design of such components, as the vibration responses obtained using the linear strain–displacement relation are often conservative and can only be utilized to approximate the genuine response. This study examined the influence of different lamination schemes on a non-linear/linear steady-state forced vibration response of annular sectorial plates. Both the modified shooting approach and the arc-lengthalgorithm technique were used for solving the governing equations of motion in the time domain. Frequency-response curves were drawn in their entirety, including both the stable and unstable portions. Sectorial plates of varying layer numbers are studied by analyzing their non-linear dynamic behavior by means of frequency response curves, periodic stress variation, phase plane plots, and frequency spectra. The number of layers shown to have an impact on steady-state responsiveness. In a hardening non-linear manner, the annular sector plates show a peak linear displacement amplitude that is significantly larger than the corresponding values in the non-linear analysis.