Doubly-curved Shells Research Articles

Free Vibration of Graphene Nanoplatelet-Reinforced Porous Double-Curved Shells of Revolution with a General Radius of Curvature Based on a Semi-Analytical Method

Based on domain decomposition, a semi-analytical method (SAM) is applied to analyze the free vibration of double-curved shells of revolution with a general curvature radius made from graphene nanoplatelet (GPL)-reinforced porous composites. The mechanical properties of the GPL-reinforced composition are assessed with the Halpin–Tsai model. The double-curvature shell of revolution is broken down into segments along its axis in accordance with first-order shear deformation theory (FSDT) and the multi-segment partitioning technique, to derive the shell’s functional energy. At the same time, interfacial potential is used to ensure the continuity of the contact surface between neighboring segments. By applying the least-squares weighted residual method (LWRM) and modified variational principle (MVP) to relax and achieve interface compatibility conditions, a theoretical framework for analyzing vibrations is developed. The displacements and rotations are described through Fourier series and Chebyshev polynomials, accordingly, converting a two-dimensional issue into a suite of decoupled one-dimensional problems. The obtained solutions are contrasted with those achieved using the finite element method (FEM) and other existing results, and the current formulation’s validity and precision are confirmed. Example cases are presented to demonstrate the free vibration of GPL-reinforced porous composite double-curved paraboloidal, elliptical, and hyperbolical shells of revolution. The findings demonstrate that the natural frequency of the shell is related to pore coefficients, porosity, the mass fraction of the GPLs, and the distribution patterns of the GPLs.

Sound transmission loss and energy absorbing performance of stiffened doubly-curved shells with corrugated-honeycomb hybrid cores

Compared to traditional lightweight corrugation and cellular cores, the novel cellular cores auxetic metamaterials with negative and zero Poisson's ratios possess distinctive mechanical deformation traits, making them suitable for modeling lightweight sandwich structures. Therefore, the concept of combining auxetic metamaterial cellular with folded corrugation is proposed to construct a new type of corrugated honeycomb hybrid cores for studying the sound insulation and energy absorption characteristics of the stiffened sandwich doubly-curved shells, wherein the honeycomb core possesses a full range of Poisson's ratio characteristic and is composed of cellular cores exhibiting positive, negative, and zero Poisson's ratios (PPR, NPR, and ZPR). The Hamilton's principle is hired to derive the governing equations and considers fluid-structure coupling by applying normal velocities continuity conditions at the fluid-structure interface, which is further analytically solved using Navier's techniques, and the sound transmission loss (STL) is described analytically. The accuracy of these results is validated through comparisons with both experimental measurements conducted in an impedance tube and simulated outcomes generated by the COMSOL commercial software. The properties of stiffened sandwich doubly-curved shells with corrugated honeycomb hybrid cores are meticulously evaluated and compared, and the results show that the hybrid cellular core type significantly impacts the STL, wherein the average STL of the corrugation ZPR cellular hybrid cores stands at 42.06 dB within the broad low-frequency range of 380–2422 Hz, which has increased by 9.11% and 8.31% compared to the values of the corrugation NPR and traditional PPR cellular hybrid cores, the specific energy absorption (SEA) of the corrugation ZPR cellular hybrid cores is 13.06 kJ/m3, which has increased by 16.19% and 18.08% compared with the corrugation NPR and PPR cellular hybrid cores, respectively, indicating that the corrugation ZPR cellular hybrid cores have better sound insulation and energy absorption characteristics than the corrugation NPR and PPR cellular hybrid cores.

An analytical study of thermal environment’s effect on the free vibration of FGM double curved FG shells

The main objectif of this work is to examine the thermal environment’s effect of on the free vibration of double curvature shells made of functionally graded materials. A new mathematical model based on higher order shear deformation theory, is developed to incorporate the influence of dependent and independent thermal stresses, which can be uniform, linear, nonlinear, or sinusoidal on the mechanical properties of the double curvature shell. Two material couples, ( S i 3 N 4 / SUS 304 , ZrO 2 /Ti‐6Al‐4V ) , are considered as progressive materials, accounting for temperature-dependent and temperature-independent heat conduction and material properties in the thickness direction. The temperature field is assumed to be uniform across the shell surface but varies only in the thickness direction. The accuracy of the analytical results is validated by comparing them with existing literature results for functionally graded material (FGM) shells with infinite radii under dependent and independent temperature conditions. The study aims to demonstrate the thermal effects on material composition, as well as various specific geometric shapes such as plates, cylinders, spheres and ellipses and how different temperature laws influence the frequencies of vibrating double curvature FGM shells. Both existing theories accurately predict temperature-independent and temperature-dependent vibration responses of the shells. By verifying and comparing the results with the literature, a better agreement is achieved, thereby paving the way for further research in this field.

Vibrations of viscoelastic FG porous graphene-platelets reinforced doubly-curved shells via experimental characterisation of graphene platelets

This work explores the vibrations of viscoelastic functionally-graded (FG) porous graphene-platelets reinforced doubly-curved shallow shells via experimental characterisations of graphene platelets. In particular, the effects of ultrasonication time of graphene platelets, on the vibrations of graphene-platelets reinforced shells, are studied. This is of interest because graphene platelets are often ultrasonicated in solvents to achieve better dispersions during the fabrication of graphene-platelets/epoxy composite structures. In this study, geometric characteristics of the graphene platelets under different sonication times are quantitatively and qualitatively analysed through experimental characterisation techniques, including a laser diffraction particle size analyser, a scanning electron microscopy (SEM), and a scanning force microscopy (SFM). The geometric characteristics of graphene platelets are considered in the effective material properties using a micromechanics model of Halpin-Tsai. Different FG distributions of graphene platelets and closed-cell porosity are modelled. The Kelvin-Voigt viscoelastic model is used to consider the internal friction-induced energy dissipation for the polymeric composite shell. Hamilton’s variational principle and an assumed mode method are used to derive and solve the equations of motion, respectively, for the vibrations of the doubly-curved shells. The effects of graphene platelets sonication time, in combination with the effects of graphene platelets weight fraction, porosity coefficient, FG distributions, shell thickness ratio, and shell curvature radii, are scrutinised. The results show that increasing ultrasonication time reduces the shell’s out-of-plane dimensionless fundamental frequency as a result of the reduction in graphene platelets aspect ratio.

In-process textile reinforcement method for 3D concrete printing and its structural performance

3D concrete printing (3DCP) is an innovative technology for constructing complex freeform structures that are difficult or expensive to build using conventional construction methods. The printing of double-curved shells and aesthetically pleasing geometries for façade panels and roof elements requires a detailed investigation of the load-carrying capacity and failure mode during complex loading. Moreover, integrating reinforcement into printed elements is one of the major challenges in 3DCP for manufacturing structural components. Textile reinforcement has high formability and tensile strength and can be used as an in-process reinforcing method during printing. In this study, one layer of alkali-resistant glass textile was used to reinforce the 3D printed and mould-cast high-performance concrete curved members. The commonly used concrete printing nozzle was modified to allow ease in textile placement along the printing path. Further, the feasibility of the modified nozzle was evaluated by printing two different curved structures and was validated. In addition, two different curvatures of curved elements, with and without textile reinforcement were printed to study the effect of textile reinforcement and geometry when subjected to a point load in the middle. The deformation behaviour, crack development, and propagation were monitored using digital image correlation. It was observed that the textile reinforcement enhances the interlayer bonding leading to slower crack propagation and enhanced load-carrying capacity. An increase of about 10 % in the peak load-carrying capacity of 3D printed specimens was observed with the addition of textile reinforcement when compared to their mould-cast. Also, 3D printed specimens was observed to have larger deformation ductility compared to mould-cast specimens. Further, the textile aligns better with increasing curvature which enhances the resistance of membrane forces more uniformly resulting in a 15.5 % increase in the ultimate moment capacity. In addition, the first crack load and the ultimate load were predicted based on the arch equations and the results showed that the current method predicts the capacity with reasonable accuracy.

Free vibration analysis of laminated anisotropic doubly-curved shell structures reinforced with three-phase polymer/CNT/fiber material

The present work investigates the vibrational response of laminated anisotropic doubly-curved shell structures reinforced with Carbon Nanotubes (CNTs) short fibers. The fundamental equations are derived from a curvilinear reference system of principal coordinates, employing the Equivalent Single Layer (ESL) methodology. Furthermore, a general variation in laminate thickness is considered. The unknown field variable is described using higher order theories through the unified formulation, taking into account a general interpolation of the unknown variables with Lagrange polynomials across the physical domain. The Hamiltonian Principle is adopted for the derivation of the dynamic equilibrium equations, which arediscretized numerically by using the Generalized Differential Quadrature (GDQ) method. In addition, an efficient isogeometric NURBS-based mapping is adopted for the distortion of the physical domain. The boundary conditions of the differential problem are modelled through a general distribution of linear elastic springs along the lateral surfaces of the three-dimensional doubly-curved solid. The theory is then applied to study the vibrational modes of structures with different curvatures and lamination schemes, taking into account a general distribution of CNTs along the thickness direction. The homogenized properties of CNTs layers are obtained from the Mori-Tanaka procedure, which accounts for the agglomeration effects of the dispersed nanofibers within the matrix. Unlike previous studies focusing on doubly-curved shells reinforced with composite materials and CNTs, the present formulation enables to derive the vibration characteristics of structures made of generally anisotropic materials with general orientations. Furthermore, the calibration of the parameters for the linear elastic springs’ distribution leads to general external constraints within a single element, thus reducing the computational cost of the problem.

Impact dynamic response of stiffened porous functionally graded materials sandwich doubly-curved shells with Arc-type auxetic core

The Arc-type auxetic core is based on the traditional concave hexagonal core and incorporates a bending configuration, facilitating a smooth transition of the cell elements. This modification proves highly effective in alleviating stress concentration. To extend its use in sandwich structures, the dynamic behavior of stiffened porous functionally graded materials (PFGMs) doubly-curved sandwich shell with Arc-type auxetic core under low-velocity impact is a concern that this research addresses. The material properties of external PFGM panels are controlled by two grading patterns (P-FGM and E-FGM) and has four different porosity distributions. The core layer is made of Arc-type auxetic core. A theoretical model that utilizes Hertzian elasticity theory and first-order shear deformation theory (FSDT) is proposed, and the equations of motions are derived using the Hamilton's principle. In addition, to simulate the contact force interaction in dynamic process, the spring-mass model is employed. The analytical solution is presented by using Duhamel's principle and Navier's method to anticipate the transverse displacement. The effectiveness of the obtained data is verified by comparing the findings with those of the existing literature and the numerical results established by the Abaqus commercial software. On this basis, efficient methods for optimizing the PFGM doubly-curved sandwich shell are presented by analyzing the effect of porosity, porosity distribution, gradient index, grading pattern, auxetic core inclined angle and circular arc radius on the energy absorption capability, wherein the sandwich shell of P-FGM reduces the transverse displacement by 24.5 % over E-FGM, and the corresponding gain effects for different porosity distributions are Type B > Type D > Type C > Type A.

An improved mathematical model for static and dynamic analysis of functionally graded doubly-curved shells

An improved mathematical model for static and dynamic analysis of functionally graded doubly-curved shells

A novel arc-type auxetic cellular doubly-curved shells with negative Poisson's ratio for broadband low-frequency sound insulation

The novel cellular cores auxetic metamaterials with negative Poisson's ratio (NPR) have unique mechanical deformation characteristics compared to conventional cellular cores, which can be further applied to modeling lightweight sandwich structures. The Arc-type cellular core is based on the traditional re-entrant cellular core and incorporates a bending configuration, facilitating a smooth transition of the cell elements. Based on that, the sound transmission characteristics of sandwich doubly-curved shells with NPR arc-type auxetic cellular core layer is studied in this article. The Hamilton's principle is applied to derive the governing equations and considers fluid-structure coupling by applying normal velocities continuity conditions at the fluid-structure interface, which is further analytically solved using Navier's method, and the sound transmission loss (STL) is described analytically. The correctness of the proposed formula is verified by comparing the theoretical solution with the calculation results of the commercial software COMSOL and the experimental results of impedance tube sound insulation. Based on the theoretical model, it is calculated that the average STL of the arc-type cellular is 6.61% higher than that of the traditional re-entrant cellular within the broad low-frequency range of 100–2448Hz. Then the effect of key parameters on the STL of sandwich structure is systematically analyzed, and the results show that the first frequency of the sandwich shell decreases with the increase of the rib thickness, but increases with the increase of the arc radius. Notably, a smaller arc radius and a larger rib thickness exhibit superior sound insulation properties across a broad frequency range. In addition, when the core layer thickness increases from 0.007m to 0.009m, the average STL of sandwich structures is reduced by 7.38% in a broad low-frequency range of 100–2448Hz.

Geometrical and material optimization of the functionally graded doubly-curved shell by metaheuristic optimization algorithms

This paper presents the simultaneous geometrical and material optimization of functionally graded doubly-curved shells under static load and free vibration. The weak form of governing equations is derived from third-order shear and normal deformation theory. Bending and free vibration analyses were conducted using the finite element method. The functionally graded material (FGM) is composed of metal and ceramic, and Voigt’s rule of mixtures is applied to capture the characteristics of FGMs throughout the shell thickness direction. In this regard, two multi-objective optimization algorithms (i.e., multi-objective particle swarm optimization and multi-objective cuckoo search optimization algorithms are employed. The objective functions combine minimizing the maximum normalized displacement and mass and maximizing the first dimensionless frequency. The results show that where minimizing the mass of the FG shell structure was considered an objective function, the value of the power index is equal to zero for almost all studied cases.

Broadband low-frequency sound insulation of stiffened sandwich PFGM doubly-curved shells with positive, negative and zero Poisson's ratio cellular cores

Compared to the conventional cellular cores, the cellular cores auxetic metamaterials with negative and zero Poisson's ratios have unique mechanical deformation characteristics, which can be further applied to modeling lightweight sandwich structures. Based on that, the sound transmission characteristics of a novel stiffened sandwich porous functionally graded materials (PFGM) doubly-curved shells with full Poisson's ratio characteristic range cellular cores are investigated in this study. The adjustment of material properties of PFGM face sheets in the thickness direction is achieved through power law based on component volume fraction, and the core layer consists of cellular cores with positive, negative, and zero Poisson's ratios (PPR, NPR, and ZPR). Two common types of stiffened sandwich shell types, namely, the shell with PFGM face sheets and metal-rich cellular cores (type-A), and the ceramic-rich cellular cores (type-B), are discussed, and the Hamilton's principle is used to derive the governing equations. By applying normal velocities continuity conditions at the fluid-structure interface to consider fluid-structure coupling, which is further analytically solved using Navier's technology, and the average sound transmission loss (STL) with broadband low-frequency is described. The effectiveness of the established theoretical model is confirmed by comparing it with previously published results, experimental and simulated results obtained by impedance tube and COMSOL commercial software. A systematic comparison is conducted on the performance of stiffened sandwich PFGM doubly-curved shells with full Poisson's ratio characteristic range cellular cores, and the results show superior performance in the sound insulation for the sandwich shell with ZPR cellular cores, considerably at a broad low-frequency range of 220–2040 Hz, in comparison with the sandwich shell with NPR cellular cores and conventional PPR cellular cores types. This work's findings can serve as a benchmark for future studies and help to design and create engineering sandwich structures with improved sound insulation properties.

On mechanics of piezocomposite shell structures

This study presents an original and novel investigation into the mechanics of piezo-flexo-magneto-elastic nanocomposite doubly-curved shells (PFMDCSs) and the ability to detect the lower and higher levels of electro-magnetic fields. In this context, by utilizing the first-order shear deformation shell model, stresses and strains are acquired. By imposing Hamilton's principle and the von Kármán approach, the governing equations have been obtained. The intelligent shell model consists of size-dependent influences, viz., strain gradients. This will take place via Mindlin's strain gradient elasticity theory and the subsequent re-establishing of the mathematical framework by incorporating this concept. The strain gradient results in a flexoelectric/flexomagnetic effect. The converse effect of the magnetic field on the basis of a close circuit has been assumed. The developed bending equations have been transferred into the algebraic ones by substituting an analytical technique based on homogeneous immovable simple support for the four edges. The problem has been solved according to the Newton-Raphson iteration scheme, and transverse deflections have been computed. For researching the rightness and precision of the shell models together with the solution process, a comparison is prepared by the finite element method (FEM) results for simplified shells, and a good correlation has been observed. At last, by examining several factors governing the problem, the conditions under which the magnetic effects can be noticeable and dominant in doubly-curved shells have been sought. This study could serve as a benchmark reference for piezoceramic-DCSs, as the presented governing equations are original. The most interesting outcome of this research is that the electro-magnetic response of intelligent structures can be entirely geometry-dependent.

Equivalent layer-wise theory for the hygro-thermo-magneto-electro-elastic analysis of laminated curved shells

The paper presents a multifield formulation involving five different physical problems under the equilibrium thermodynamic conditions for laminated doubly-curved shell structures. More specifically, the study focuses on the coupling between the mechanical elasticity and the thermo-hygrometric problem, while also considering the magneto-electricity of the solid. The configuration variables are described with a generalized formulation based on the Equivalent Layer Wise (ELW) approach, taking into account higher order polynomial interpolations along the thickness direction. The fundamental relations are derived from the Master Balance principle and solved using the Navier's method. Furthermore, the three-dimensional response of the doubly-curved shell solid in terms of primary and secondary variables is recovered from the two-dimensional solution with a methodology based on the three-dimensional multifield balance equations and the Generalized Differential Quadrature (GDQ) numerical technique. Some examples are then presented in which panels of different curvatures and lamination schemes are investigated. The results are compared with success to those coming from three-dimensional numerical models developed with a commercial software. It is shown that the present analytical solution is a valid tool for modelling multifield problems for the evaluation of the response of doubly-curved shells under generalized external actions and pre-determined values of the configuration variables.

Thermo-Mechanical analysis of laminated Doubly-Curved Shells: Higher order Equivalent Layer-Wise formulation

The paper presents a refined two-dimensional formulation for the thermo-mechanical analysis of laminated doubly-curved shell structures under thermodynamic equilibrium conditions. Both the kinematic configuration variables and the temperature variation with respect to the natural equilibrium state are described with a generalized formulation, following the Equivalent Layer-Wise (ELW) approach employing higher order polynomials, along with some proper zigzag functions. The governing equations are derived from the stationary configuration of the Helmholtz free energy of the system, and a semi-analytical solution is found. In the post-processing phase, the Fourier-based Generalized Differential Quadrature (F-GDQ) is applied to recover the actual three-dimensional response of the doubly-curved shell solid, and very accurate results are obtained for the quantities of both mechanical and heat conduction problems. In addition, the integrals occurring in the theory are performed numerically with the Taylor-based Generalized Integral Quadrature (GTIQ), showing a high level of accuracy with a reduced number of sample points. The model is validated in some case studies, where the accuracy of the model is shown, and the numerical predictions are successfully compared with those ones from refined three-dimensional numerical simulations. After that, an extensive set of parametric investigations is reported, pointing out the effects of the panel curvature, lamination schemes and different levels of coupling on the thermo-mechanical structural behavior of the investigated panels.

On the Importance of the Recovery Procedure in the Semi-Analytical Solution for the Static Analysis of Curved Laminated Panels: Comparison with 3D Finite Elements.

The manuscript presents an efficient semi-analytical solution with three-dimensional capabilities for the evaluation of the static response of laminated curved structures subjected to general external loads. A two-dimensional model is presented based on the Equivalent Single Layer (ESL) approach, where the displacement field components are described with a generalized formulation based on a higher-order expansion along the thickness direction. The fundamental equations are derived from the Hamiltonian principle, and the solution is found by means of Navier's approach. Then, an efficient recovery procedure, derived from the three-dimensional elasticity equations and based on the Generalized Differential Quadrature (GDQ) method, is adopted for the derivation of the three-dimensional solution. Some examples of investigation are presented, where the numerical predictions of refined three-dimensional Finite-Element-based models are matched with a high level of accuracy. The model is validated for both straight and curved panels, taking into account different lamination schemes and load shapes. Furthermore, it is shown that the numerical solution to the elasticity problem in the recovery procedure is determining and accurately predicting the three-dimensional static response of the doubly-curved shell solid.

Effect of porosity on the modal response of doubly-curved laminated shell structures made of functionally graded materials employing higher order theories

The manuscript investigates the modal response of laminated anisotropic doubly-curved shell structures of variable thickness made of Functionally Graded Materials (FGM), according to an efficient equivalent single layer strategy where the displacement field is described employing a condensed unified formulation, accounting for a higher order through-the-thickness expansion. A generalized power law distribution is adopted for the assessment of the FGM layers, whereas the presence of voids is considered starting from different homogenization assumptions. Unlike previous works which presented a variation of the homogenized material properties within the shell solid, in this paper the problem of material porosity is addressed, therefore a general distribution of the volume fraction of the constituent materials is considered, along with the presence of voids. To this end, both linear and trigonometric through-the-thickness distributions are here assumed. The fundamental governing equations are derived starting from a proper set of curvilinear principal coordinates, while a generalized set of blending functions accounts for arbitrarily shaped structures. Non-conventional boundary conditions are, here, modelled with a distribution of linear springs along the shell edges. The numerical implementation of the problem is performed with the generalized differential quadrature method. A systematic set of validating examples is presented, whose results are compared to predictions based on refined models, as well as some experimental evidence. After a validation step, an extensive parametric analysis points out the sensitivity of the porosity parameters on the modal response of structures with different curvatures and external constraints, with valid findings for engineering design purposes.

ПРЕОБРАЗОВАНИЕ СХЕМЫ ФОРМООБРАЗОВАНИЯ ОБТЯЖКОЙ НА ПРИНЦИПАХ СИММЕТРИИ

We assume that the concept of symmetry plays an important role in improving the theory and practice of the forming process by covering load-bearing thin-sheet shells of double curvature, which guarantees the production of contour-forming parts of the skin of modern aircraft with an exact geometric shape and minimal variation in thickness. To understand our assumption, it is necessary to remember that the complexity of the theory of plastic shells lies in the geometric and physical nonlinearity and the need to take into account shear stresses and deformations along the surface of the shell and its variability in curvature, therefore there is still no unified approach to the analysis of the formative processes of covering from sheet material. This assumption applies only to thin-sheet shells of double curvature, providing a different isometric position (curved surfaces one on top of the other) of the open surface as a whole, and not closed like a sphere. Therefore, the process of shaping a sheet blank into a shell part of an aircraft has some form of symmetry with respect to a given set of surface transformations, unless certain properties or relationships, the so-called invariants of the set of transformations, change when they are performed.

Functionally graded doubly-curved shell with temperature dependent material properties and surface-mounted MEE layers

In the present work, the geometrically nonlinear behavior of a simply supported functionally graded doubly curved shell with a surface-mounted magneto-electro-elastic layer is investigated based on Donnell’s theory. Kirchoff’s assumption and von Kármán’s strain-displacement relationship are used to obtain the governing differential equations. The through-the-thickness shell temperature is computed using Fourier’s heat conduction equation. Elastic material properties are assumed to be temperature-dependent and follow the power-law distribution function of the constituent ceramic-metal volume fractions. The magneto-electro-elastic layer is polarized along the thickness direction, which is subjected to electric and magnetic potentials. Gauss’s laws for electrostatics and magnetostatics are satisfied for magneto-electric materials. Nonlinear partial differential equations of motion are reduced to ordinary differential equations by introducing a stress function and using a single-term time-dependent assumed displacement function. Nonlinear free vibration response is obtained by direct numerical integration. After comparing the derived model with published literature results, numerical studies on the effects of applied electric and magnetic coupled fields of surface-mounted magneto-electro-elastic layers on shell vibration are reported. The nonlinear frequency ratios with respect to specified displacement for both spherical and cylindrical shells with thin Piezoelectric BaTiO 3 and Piezomagnetic CoF e 2 O 4 panels across material compositions, the radius of curvature, and thermal conduction are studied.

Higher order theories for the modal analysis of anisotropic doubly-curved shells with a three-dimensional variation of the material properties

The manuscript investigates the dynamic properties of doubly-curved shell structures laminated with innovative materials employing the Generalized Differential Quadrature (GDQ) method. A higher order generalized expression of the displacement field variable is assumed following the Equivalent Single Layer (ESL) approach. The geometrical description of the structures follows the differential geometry basics, whereas arbitrarily-shaped domains are distorted by means of generalized isogeometric blending functions. A three-dimensional generally anisotropic elastic constitutive behaviour is assumed within each layer of laminates, and a smooth variation of the material properties is implemented. In particular, a two-dimensional distribution alongside the physical domain is considered, whereas a through-the-thickness dispersion of the material properties is associated to each layer, taking into account both polynomial and non-polynomial analytical expressions. The fundamental equations are derived from the Hamiltonian principle, and they are solved directly in strong form via the GDQ method taking into account a non-uniform discrete computational grid. After some preliminary validating examples, some parametric investigations are performed systematically, showing the influence of the variation of the material properties on the modal response of the structures characterized by different lamination schemes, curvatures and boundary conditions. The proposed model allows for the dynamic analysis of the structures of different curvatures characterized by very complicated dispersions of the material properties following a simple and accurate methodology.

Novel mechanism for subsiding destructive consequences of simultaneous exertion of mechanical shock on the nanocomposite structures using 3D-flexibility theory and data-driven solution

Doubly-curved shells due to their extreme stiffness and small weight are innovative structures for applications in civil, biomedical, and other engineering fields. For the first time, with the aid of a time-dependent wave propagation approach, free and forced vibrations of graphene platelets-reinforced doubly curved panel is presented. 3D-flexibility theory, equilibrium condition, and space-state differential equations expressed in the Laplace and spatial domain are used to model the current work’s motion equations. Half-sine loading with a specific duration time is presented as the external mechanical loading on the current curved open-type shell structure. Due to a wide range of applications such as encountering some curved parts with external loading, it is essential to improve the mechanical properties. To improve the mechanical properties of the open-type shell structure, graphene nanoplatelet (GPL) reinforcement is presented. The machine learning model is developed using data-driven solutions and mathematical simulation (MS). Initially, the MS analyzes the composite panels analytically under different situations. The data-driven model is then trained using the Levenberg-Marquardt approach using the outputs of the MS model (410 configurations). The impact of different parameters on the composite panel's amplitude motion is then assessed using a data-driven model. The results of the current study are useful suggestions for designing composite systems such as composite panels under external shock.