First-order Shear Deformation Theory Research Articles

On thermo-mechanical buckling of porous bi-directional functionally graded plates using isogeometric analysis

The combined thermal and mechanical loads usually lead to buckling failure of key structures in various engineering fields. It is found that porous functionally graded structures can be used to reduce and evenly prevent potential impact on the stability of structures from extremely high temperature loads. In this paper, we employ the isogeometric analysis (IGA) method to investigate the thermo-mechanical coupling buckling behaviors of porous bi-directional functionally graded (PB-FGM) plates with porosity. The material properties such as Young's modulus, Poisson's ratio, and thermal expansion coefficient are assumed to be linearly dependent on the x-axial and z-axial coordinates. Such a gradient property can be easily realized by changing the porosity distribution. Based on the first-order shear deformation theory (FSDT), the thermo-mechanical buckling behaviors of PB-FGM rectangular and circular plates under combined thermal and mechanical loads are numerically studied. This paper elucidates the mechanical mechanism through which gradient indexes, aspect ratios, loading types, and boundary conditions influence the critical thermo-mechanical coupling-induced buckling temperature.

Precise analysis of the static bending response of functionally graded doubly curved shallow shells via an improved finite element shear model

Doubly curved shallow shells, common in aerospace and civil engineering, pose significant challenges in predicting bending responses due to their complex geometry and material properties. Therefore, this research focused on the development of an efficient eight-node quadrilateral isoparametric element model based on a new improved first-order shear deformation theory (IFSDT) to analyze the bending deflection and stresses distribution of Functionally Graded (FG) doubly curved shallow shells. The present IFSDT obviates the necessity of a shear correction factor, which has challenges in determining for FG doubly curved shallow shells, by adopting a simpler assumption about transverse shear stresses. This assumption guarantees that the model precisely predicts the parabolic shear stresses distribution throughout the thickness of the FG shell while also meeting the requirements for free traction conditions on the top and lower surfaces of the shell. In the present analysis, five distinct types of FG doubly curved shallow shells are modeled: flat plates, spherical shells, hyperbolic parabolic shells, cylindrical shells, and elliptical paraboloid shells. A power law is employed to describe the gradual changes in material properties through the thickness direction. Numerical results for displacements and stresses are obtained for various shell types, materials, power-law factors, radii of curvature, and boundary conditions under uniform and sinusoidal loads. Comprehensive comparison and convergence studies are conducted to assess the robustness and accuracy of the proposed numerical model. This study also contributes new numerical results that are valuable for future research. Ultimately, the proposed numerical model offers a robust and straightforward tool for engineers and researchers engaged in the design and analysis of complex shell structures.

Optimizing frequencies of functionally graded material plates via multi-objective genetic algorithm: Positioning point supporters for maximum performance

In the presented study, an approach is introduced for optimizing the vibrational characteristics of aerospace structures that are composed of Functionally Graded Materials (FGM). The focus is placed on the strategic positioning of point supporters to enhance the structural performance under various operational conditions. The effective elasticity properties of the FGMs are determined using the Mori-Tanaka method for homogenization. The deformation behavior of these structures is analyzed by employing the first-order shear deformation theory. Solutions are computed through the 2D Ritz method, which utilizes Chebyshev polynomials, forming the basis for the objective function of a multi-objective genetic algorithm. This algorithm is designed to optimize the positioning and the number of point supporters aimed at targeting specific vibration frequencies. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is utilized to efficiently generate Pareto optimal solutions, which illustrate the trade-offs between conflicting objectives. The validation of the solution method is achieved through comparisons with experimental data, confirming the accuracy and practical relevance of the approach. The application of the optimization framework is extended to various configurations of aerospace structures, including diverse compositions of FGM and different boundary conditions. This methodology is shown not only to enhance the operational performance of aerospace structures but also to contribute to the precise design and manufacturing of components in aircraft and satellites, aligning with the central interests of aerospace engineering.

Nonlinear thermo-electro-mechanical responses and active control of functionally graded piezoelectric plates subjected to strong electric fields

Functionally graded piezoelectric plates (FGPPs) are often exposed to extreme thermal environments and subjected to large amplitude excitation and strong electric fields. Accurately predicting the nonlinear behaviors of FGPPs under large thermo-electro-mechanical loads remains a considerable challenge. This paper proposes a comprehensive nonlinear coupled analysis model that considers geometric nonlinearity, piezoelectric nonlinearity, and the temperature dependence of piezoelectric parameters. The total Lagrangian incremental finite element equations for FGPPs under thermo-electro-mechanical loads are derived using Hamilton's principle, by employing the first-order shear deformation theory and the von Kármán nonlinear strain-displacement relationship. The accuracy of the model is validated through comparative studies. Based on this multi-nonlinear model, we further investigate the effects of geometric nonlinearity, piezoelectric nonlinearity, and temperature dependence on the nonlinear static bending, dynamic responses, and active control of FGPPs. This study demonstrates that considering these factors enables accurate prediction of the static, dynamic, and active control behaviors of FGPPs.

Physics-constrained deep learning approach for solving inverse problems in composite laminated plates

The applications of physics-informed neural networks (PINNs) in material parameters identification of composite laminates are currently research highlights. We present an efficient physics-constrained deep learning approach based on PINNs for solving material parameters of composite laminates. We explain the details of incorporating first-order shear deformation theory as physical information into designed loss functions. The performance of proposed approach is demonstrated through a numerical example of idealized composite laminated plates under uniform pressure conditions. The computational errors of material parameters are less than 0.1%. Moreover, the applicability of transfer learning (TL) has been illustrated for inversion of material parameters with few datasets. The ambition is to improve the identification efficiency of carbon and glass fiber reinforced plies material parameters across various loading conditions. Intensive studies are conducted to compare convergence time between with and without TL through a numerical example under thermal-force coupling conditions. The comparison shows PINNs with TL obtain average error of 0.144% and 0.077% in carbon and glass fiber reinforced plies, which is better than without TL of 0.472% and 0.284%, respectively. The proposed work emphasizes the effective application of PINNs-based approach that combines first-order deformation and data-driven solution features for inverse solving material parameters of composite laminates.

A nonlinear finite element analysis of laminated shells with a damage model

This paper presents a study on the development and validation of a nonlinear finite element model for laminated composite shells, that considers a first-order shear deformation theory (FSDT) and an explicit through-thickness integration. The model integrates a meso-scale damage analysis that considers progressive matrix and fiber failures. The model is compared with envelopes of experimental curves extracted from 3-point bending test coupons and shows accurate predictions.

Traveling wave vibration characteristic analysis of FRC sandwich cylindrical shells with FGP-GPLRC core under discontinuous elastic boundary conditions

In this study, a fiber-reinforced composite (FRC) sandwich cylindrical shell with a functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) core is investigated, and the traveling wave vibration characteristics of this new sandwich cylindrical shell under discontinuous elastic boundary conditions are analyzed for the first time. The influences of centrifugal and Coriolis forces are introduced into the model. By employing the first-order shear deformation theory (FSDT) and the continuity assumption of the layerwise theory, the governing equations of the rotating sandwich shell are obtained. The artificial springs are implemented at the ends of the sandwich shell to represent the discontinuous elastic boundary conditions. The natural frequency of the shell is solved via the Rayleigh-Ritz method and the state space method. Then, the approach proposed is validated by comparing the present results with those reported in the literature and the finite element method. Finally, the effects of various parameters on the traveling wave frequency of the shell are evaluated. It was found that in practical engineering, the appropriate thickness of the FGP-GPLRC core should be selected according to the boundary conditions and other factors, and the ply angle should be adjusted to obtain more stability of vibration.

A size-dependent nonlinear isogeometric approach of bidirectional functionally graded porous plates

Recent progress in materials science and fabrication technologies, such as additive manufacturing (AM) or 3D printing, has facilitated the design and production of intricate multi-directional functionally graded (FG) materials which are playing a pivotal role in interdisciplinary engineering applications. Developing mathematical modeling for such nanostructures, however, remains challenging. The primary objective of this research, therefore, is to present a mathematical model for studying the static bending characteristics considering the geometric nonlinearity of bidirectional FG nanoplates with internal pores. The mathematical formulations are established by utilizing the first-order shear deformation theory and the von-Kármán assumption within the framework of an isogeometric approach based on NURBS basis functions. To account for the influence of both strain gradient and nonlocal elasticity, we adopt the nonlocal strain gradient theory including two independent material length scale parameters to predict the geometric nonlinearity performance of structures at small-scale levels. The mechanical properties of multi-directional FG material models are assumed to be continuously graded in two directions based on power law, while internal pores can be dispersed into two typical distribution patterns. Several numerical investigations are performed to evaluate the substantial impact of certain parameters on the nonlinear deflections of bidirectional FG nanoplates with pores under various conditions. Compared to existing studies, the key contribution is to present a robust numerical model aimed at elucidating both the stiffness-softening and stiffness-hardening mechanisms of multi-directional FG nanostructures under static bending conditions with geometric nonlinearity. These findings enhance our insights into nonlinear bending performance and contribute valuable design guidelines for future small-scale engineering structures. These innovative designs have become popular and are now crucial in state-of-the-art engineering applications, such as aerospace, nuclear systems, or thermal resistance devices.

Random thermal-vibration mechanisms of sandwich ventral fin-type plate-shell systems with porous functionally graded core

The stochastic thermal-vibration mechanisms within a sandwich ventral fin-type plate-shell system, featuring a porous functionally graded (FG) core, are exhaustively analyzed under various random loading conditions employing an innovative node-based, meshless computational approach. The studied structure is decoupled into several plates and open cylindrical panel according to the geometric characteristics, and the mechanical relationships at the structural boundaries or connection interfaces are equivalently simulated by using penalty parameters. Following the general Hamilton's principle, the meshless approach combined with the first-order shear deformation theory (FSDT) incorporating thermal effects is employed to derive the vibration equations of the sandwich ventral fin-type plate-shell systems. Also, the pseudo excitation method (PEM) is introduced to calculate stationary and nonstationary random responses. In order to verify the accuracy of the meshless algorithm in this study, the convergence and correctness are studied comprehensively. And then, the effects of some parameters such as temperature variation, porosity parameters, power-law index and random excitations on the thermal vibration characteristics of the sandwich ventral fin-type plate-shell systems with porous FG core are presented. The results show that the power-law index and temperature can increase the frequency parameter of the structure. The smooth power spectral density (PSD) excitation only affects the amplitude of the response curve, and does not affect the frequency corresponding to the peak. In the analysis of non-stationary random vibration, the influence of modulation parameters on response is very significant.

Vibration analysis and suppression of axially moving composite laminated plates with modified energy method and piezoelectric shunt damping circuits

This paper presents a modified variational modeling method and develops an electro-mechanical coupling based vibration control method for moving composite plate structures. Unlike the stationary structures, movement will introduce new challenges for both vibration analysis and control of the laminated plate. Based on the modified variational method, electromechanically coupled dynamic models for the moving plate with piezoelectric patches and control circuits are developed. To release limitations to the admissible functions, modified variational principles are derived for the interface and boundary constraints in both directions of the moving plate. On the basis of first-order shear deformation theory (FSDT), the energy functional expressions of the axially moving laminated plates are formulated and the governing equations are obtained. To suppress the vibration, a piezoelectric shunt damping circuit (PSDC) with negative capacitance is proposed and the control circuit parameters are optimized using the differential evolution (DE) algorithm. Through numerous numerical examples, the high accuracy, good efficiency, and flexibility in constructing admissible functions of the proposed modeling method are demonstrated. The developed PSDC possesses much better vibration suppression properties for the moving laminated plates than the series R-L PSDC. Effects of the moving speed and negative capacitance on the optimal circuit parameters are also examined. The appropriate values of the negative capacitance are shown to be near the capacitance of the patches.

Symmetric and asymmetric vibration and buckling of a thermal rotating annular-plate with Pasternak foundation

This paper studies the symmetric and asymmetric vibration and buckling modes of a rotating thermal annular plate resting on a Pasternak foundation. With considering the von Kármán geometric nonlinearity and the first-order shear deformation theory, the governing equations of the system are established via Hamilton's principle, and then solved by using the differential quadrature method. With both inner and outer boundaries constrained, the modes of the rotating system vary differently depending on the mode symmetry. The symmetric modes are mainly affected by the generated centrifugal force, while the asymmetric ones are affected by both centrifugal and Coriolis forces. The additional Coriolis, with mainly two directions, strengthens the forward travelling parts of the asymmetric modes, but makes the backward counterparts buckled more easily. Also, the thermal effect, as well as boundary elasticity and foundation coefficients, are also investigated from the viewpoint of mode symmetry. Results show that the temperature rise can shift the fundamental vibration mode from the symmetric one to the asymmetric one and backward travelling waves for rotation, which also adds to the complexity of mode variation with joint parameters. For the joint effect of the temperature rise and rotating, the annular plate tends to buckle more readily while the effects of the two factors are linearly superimposed.

An investigation of vibration responses for bolted composite flanged-cylindrical shells considering material and joint nonlinearity

In this paper, a thorough investigation into the vibration response of bolted composite flanged-cylindrical shell structures, considering the material nonlinearity of carbon fiber-reinforced polymer composites (CFRP) and the joint nonlinearity of bolt connections, is presented. Firstly, a general semi-analytical modeling method for bolted composite flanged-cylindrical shell is developed based on the first-order shear deformation theory (FSDT) and the energy method. In this method, material nonlinearity is introduced by accounting for the frequency-strain dependency of material parameters. A joint model with non-uniform distribution parameters and dynamic boundaries is proposed to simulate the interface pressure distribution and nonlinear mechanical behavior of bolted joints. Then, for the general numerical model that incorporates both types of nonlinearities, the ability to accurately predict the nonlinear vibration behavior of a bolted composite flanged-cylindrical shell is demonstrated through experimental testing. Finally, an in-depth discussion is conducted on the influence of fiber layup patterns and bolt numbers on the nonlinear vibration response of the bolted composite flanged-cylindrical shells. The conducted analysis indicates that the proposed method can offer utility to designers, empowering them with the insights necessary for the dynamic optimization of such structures.

Free vibration analysis of functionally graded composite plates reinforced with linearly and nonlinearly distributed carbon nanotubes in hygrothermal environments

This article presents a novel investigation of the free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates under hygrothermal environments. It explores both uniform and non-uniform (functionally graded) distributions of CNTs across the plate thickness for the first time. The effective material properties of the CNTRC, considering temperature and moisture dependence, are determined using the extended rule of mixture. First-order shear deformation theory (FSDT) is employed to derive the governing equations incorporating hygro-elastic and thermo-elastic relations. These equations are solved using the finite element method. A validation study verifies the accuracy of the employed approaches. Subsequently, a comprehensive parametric study investigates the influence of plate geometry (length-to-width and width-to-thickness ratios), CNTs volume fraction, boundary conditions, linear and non-linear CNTs distributions, and hygrothermal environments on the free vibration behavior of polymeric nanocomposite plates reinforced with CNTs fillers is conducted. The results reveal that the increase in temperature and moisture leads to a decrease in the effective stiffness of the FG-CNTRC plates.

Semi-analytical vibration modeling of complex axisymmetric shells using shifted Legendre series

This paper presents a semi-analytical approach based on the shifted Legendre series for vibration modeling of complex axisymmetric shells. This method divides the structure along its generator into complex axisymmetric shells comprised solely of conical and spherical shell segments. A global cylindrical coordinate system is established to unify the coordinate system of complex axisymmetric shells. Coupling between segments and the simulation of arbitrary boundary conditions are achieved using artificial spring technology. Based on the first-order shear deformation theory (FSDT), the energy functional of each segment is derived. The circumferential displacement is expanded using Fourier series, while the meridional displacement is expanded using the shifted Legendre series at shifted Gauss-Lobatto nodes. Utilizing the inner product matrix and differential matrix of the shifted Legendre series, the integration and differentiation processes in the vibration characteristic equation are simplified into a product form, significantly enhancing computational efficiency. Through convergence analysis and comparison of the computational results of the present method with numerical simulation results, experimental results and literature results demonstrate the advantages of high convergence, high accuracy and fast solution speed of this solution method. On this basis, the vibration characteristics of ring-stiffened double-layer hemispherical shells are investigated. The results demonstrate the great applicability of this method for vibration modeling of complex axisymmetric shells in engineering.

Vibration analysis of Ti-SiC composite airfoil blade based on machine learning

In this study, machine learning (ML) methods are integrated with Rayleigh-Ritz method and first-order shear deformation theory (FSDT) to predict the vibration properties of Ti-SiC fiber-reinforced composite airfoil blade. The natural vibration characteristics of airfoil blade are largely determined by various geometric and material parameters, which leads to the high computational cost of numerical methods. Therefore, the low-cost ML models in conjunction with Ti-SiC fiber-reinforced composite material is developed to replace traditional numerical methods in order to predict the vibration characteristics of airfoil blade. Random Forest (RF), Gradient Boosting Decision Tree (GBDT) and Back Propagation (BP) neural network models are utilized to compare the predicted results with existing data. Among these models, the BP neural network demonstrates superior performance. Additionally, the SHapley Additive exPlanation (SHAP) method is utilized to elucidate BP neural network model, facilitating the prioritization of input features. This approach offers a feasible auxiliary solution for investigating the vibration characteristics of airfoil blade.

Free Vibration of Joined Spherical–Conical Panel and Shells Using the 2D-GDQ Method

The free vibration analysis of joined conical–spherical panels and shells of revolution is the primary aim of this investigation. The equations of motion are derived by considering Donnell’s kinematic assumptions and the first-order shear deformation theory (FSDT), which considers the effects of shear deformation as well as rotational inertia. The equations of motion are discretized by using the two-dimensional generalized differential quadratic (2D-GDQ) method in the [Formula: see text] and [Formula: see text] directions for conical and spherical panels and shells, respectively. Natural frequencies of joined conical–spherical shells and panels are determined for different boundary conditions. The accuracy of results has been compared with the results of the other researchers and those obtained using Abaqus and Ansys, which showed good agreement. Moreover, the effects of length, thickness, and the angle of the semi-vertex of the conical shell on the dynamic behavior of joined spherical–conical panels/shells are investigated.

Buckling load optimization of laminated composite plates with elliptical hole under different non-uniform edge loads using bonobo optimizer algorithm

This present work investigates the buckling load optimization of the laminated composite plates with the elliptical hole under different non-uniform edge loads. The design objective is the maximization of the critical buckling load by determining the optimum fiber orientations in the layers. The stability equations are derived based on the first-order shear deformation theory (FSDT) of the laminated plates. The critical buckling loads are calculated using the finite element method with the nine noded rectangular element having five degrees of freedom per node. The bonobo optimizer (BO) algorithm is employed to optimize the laminated composite plates with the elliptical hole. The computer programming is developed in the MATLAB environment. Besides, the parametric studies are conducted for different types of the non-uniform edge loads, boundary conditions, cutout radius ratio and aspect ratios and the obtained numerical results are compared. Finally, the optimum results show that these factors play an imperative role in the optimum pattern and stacking sequence of the laminated composite plates with hole. The new significant findings can aid the designers in the structural design, and other industrial applications.

Flutter in functionally graded conical shell under follower force

Truncated conical shells are essential components of rocket booster nozzles and thrust vector control (TVC) systems for the propulsion of multi-stage launch vehicles. The TVCs assist the ascent of launch vehicles by directing the resultant thrust from the boosters, acting as a follower force that might trigger instability. Previous studies on the instability of aerospace structures have mostly focused on beams, plates, and cylindrical shells. This study analyses a truncated conical shell under a follower force of constant magnitude, considering thickness-wise gradation of material properties employed for thermal management. The governing equations are derived following Hamilton's principle, considering first-order shear deformation theory, and solved using the finite element method. Clamped and free boundaries are assumed at the small and large ends. The influence of mass and stiffness proportional damping is considered. Although strong flutter appears as the dominant instability mode, instances of erratic weak instabilities are also observed for undamped and lightly damped cases. Damping enhances stability, but its effect becomes saturated. The flutter loads are presented for varying non-dimensional parameters, characterizing the shell geometry and material properties.

Burst pressure performance comparison of type V hydrogen tanks: Evaluating various shapes and materials

Hydrogen, as a clean energy carrier, presents a significant step toward sustainable energy solutions but faces challenges in storage due to its low energy density and high volatility. This study addresses the optimization of Type V hydrogen storage tanks by investigating the burst pressure performance of spherical, cylindrical, and toroidal shapes. Using finite element analysis (FEA) and first-order shear deformation theory, we examined how these geometries impact burst pressure outcomes across a range of composite materials and layup configurations. The materials tested included carbon T700/epoxy, Kevlar/epoxy, E-glass fiber/epoxy, and basalt/epoxy. Results demonstrate that the toroidal shape significantly outperforms spherical and cylindrical designs in stress distribution and burst pressure, with basalt/epoxy composites exhibiting superior burst pressure performance (12.7 MPa) compared to Kevlar/epoxy (10.8 MPa), E-glass fiber/epoxy (11.4 MPa), and carbon T700/epoxy (8.9 MPa). Kevlar/epoxy toroidal tanks outperform other materials in weight performance, having a structural performance index of 0.0305 Mpa.m3/kg and hydrogen density per unit mass of 0.0251 kg H2/kg. The stacking sequence [-45/45]s optimized stress distribution for the toroidal shape across all materials. The findings highlight that toroidal designs offer significant advantages for high-pressure hydrogen storage, providing efficient stress management and improved safety. This paper underlines the potential of toroidal vessels for enhancing hydrogen storage efficiency and emphasizes the importance of material selection and stacking sequences in achieving optimal burst pressure performance for international organization for standardization (ISO) certification.

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.