Higher-order Theory Research Articles

In-Plane and Out-of-Plane Bending Vibration Analysis of the Laminated Composite Beams Using Higher-Order Theories

In this paper, higher-order shear deformation theories for a thorough analysis of the in-plane and out-of-plane vibrational characteristics of laminated composite beams have been presented. Through the introduction of new displacement fields and the consideration of rotary inertia and Poisson's effect, the kinetic and potential energies of the beams have been derived. This formulation, displaying significant generality, accommodates arbitrary stacking sequences. Utilizing the finite element method, a new element has been presented for calculating the beam's vibrational characteristics. Featuring three nodes, each with seven degrees of freedom, this higher-order element provides a detailed representation of complex behaviors. Mass and stiffness matrices have been derived using the energy method and apply boundary conditions through the penalty approach. The results exhibit a high degree of consistency and alignment with those obtained from the 3D commercial software ANSYS, validating the accuracy and reliability of the proposed methodology for structural analysis. This comprehensive approach contributes to advancing the understanding and modeling of laminated composite beams in diverse engineering applications. The effects of different parameters on the in-plane and out-of-plane vibration analysis of laminated composite beams have been investigated in detail.

Rapid stress prediction of additively manufactured sandwich panels with lattice cores in thermal environments

Lattice-core sandwich panels (LCSPs) with fabricated by additive manufacturing have attracted extensive interest stemming from their exceptional mechanical properties and multi-functionalities. Nevertheless, the direct correlation among stress distributions in sandwiches, external loads, and ambient environments remains unclear. This study develops an analytical predictive model capable of efficiently capturing the mechanical response of LCSPs under various temperatures. The equivalent elastic modulus of lattice cores with different unit-cell aspect ratios is first determined according to finite element (FE) results. Subsequently, the thermo-mechanical field of the homogenized sandwich in various ambient temperatures is analytically predicted based on the higher-order shear deformation theory. Finally, truss stresses within lattice cores are directly calculated using an effective displacement transition method. The prediction exhibits outstanding consistency with FE simulations. Furthermore, the impact of several key variables on the truss stress distribution is demonstrated based on parametric analysis. The results reveal that the vertical truss is the main object of bearing the major uniaxial compressive load within the body-centered cubic (BCCZ) and vertically reinforced face-centered cubic (F2CCZ) lattice cores. The increased transverse layer number/power index and/or the smaller length-to-thickness ratio contribute to a significant reduction in inclined/vertical truss stresses. In contrast, the elevated longitudinal layer number, ambient temperature, and thermal expansion of face sheets result in stress accumulation. Furthermore, the stress distributions in BCCZ LCSPs are commonly higher than those within F2CCZ LCSPs. These results can provide a useful path for the design and fabrication of additively manufactured sandwich panels with desired mechanical properties.

Guided wave propagation in a high-speed rotating concrete shell reinforced by advanced nanocomposites

This paper investigates the propagation of guided waves in a high-speed rotating concrete shell reinforced with graphene oxide powders (GOP) using higher-order shear deformation theory (HSDT). The study addresses the complexities introduced by initial hoop tension and provides a comprehensive analytical solution procedure. Concrete shells are widely used in various engineering applications due to their robustness and durability; however, their mechanical performance can be significantly enhanced by the incorporation of GOP, which improves the material properties, such as tensile strength and modulus of elasticity. The analysis begins with the formulation of the governing equations based on HSDT, which accurately captures the effects of transverse shear deformation and rotary inertia, crucial for high-speed rotating structures. The presence of initial hoop tension, resulting from the centrifugal forces in the rotating shell, is integrated into the model to reflect real-world conditions. The modified equations are then solved analytically to obtain the dispersion relations for the guided wave modes. The results reveal that the inclusion of GOP significantly alters the wave propagation characteristics, enhancing the shell’s ability to transmit high-frequency waves with minimal attenuation. The initial hoop tension is found to shift the frequencies of the guided wave modes, indicating a coupling effect between the mechanical loading and wave propagation. This study provides valuable insights into the dynamic behavior of reinforced concrete shells in high-speed rotational environments, offering a potential pathway for the design of advanced structural components in aerospace, automotive, and civil engineering applications.

Thermal buckling of variable stiffness composite laminates using high order plate finite elements

This paper proposes a study on the thermal buckling of Variable Angle Tow (VAT) composite plates using high-order theories. Here, the governing equations are derived via the principle of virtual work. Under the assumption of linear pre-buckling, the stability problem is reduced to a linear eigenvalue analysis considering proportional geometric stiffness. In contrast, a constant thermal load is assumed to be known along the plate thickness, and the uncoupled thermo-mechanical formulation is used, where the thermal effects are described as external loads. The plate is discretized using the Finite Element Method (FEM) and high-order theories are developed using the Carrera Unified Formulation (CUF). Using the CUF, the equations are expressed as an invariant of the plate theory approximation order. Therefore, Equivalent Single Layer (ESL) and Layer-Wise (LW) models can be easily implemented. Several geometries and lamination cases are considered for verification purposes, including different side-to-thickness ratios and fiber orientations, which result in various anisotropy effects. In addition, the effect of changing constraints and materials is evaluated. Particular attention is paid to the effect of the structural theory approximation on the evaluation of the thermal buckling load. It is shown that the correct evaluation is highly dependent on the edge-to-thickness ratio and on the anisotropy given by both the fiber orientation and the material properties. As a final remark, sensitivity analysis and best fiber angle solutions are discussed to highlight the importance of the LW modeling approach.

Free vibration analysis of laminated composite and sandwich shells using wavelet finite element method

The present work carries out free vibration analysis of laminated composite shells and panels using wavelet finite element method (WFEM). Two different wavelets, namely, Haar and B-spline wavelet on the interval (BSWI) are employed. The analysis is carried out using higher-order zigzag theory (HOZT), and the WFEM is set up according to Hamilton’s principle. The two-dimensional scaling functions are employed to substitute the interpolation functions as used in the FEM. Owing to the capability of the WFEM to work efficiently with lesser degrees of freedom compared to the traditional FEM, the proposed methodology is validated with the results available.

Consciousness: A Tangled Hierarchy

Consciousness is one of the greatest unsolved mysteries of the brain. The simple and yet fundamental question, “How do we have subjective experience?” remains a matter of great debate among neuroscientists. These debates have generated some challenges for consciousness research, namely the hard problem—do normal scientific approaches work for consciousness— and the binding problem—how are sensory inputs experienced in a unified manner? Historically, consciousness has been studied by searching for the neural correlates of consciousness which are defined as the minimal brain areas jointly necessary for conscious experience. One of the most popular experimental paradigms used to investigate the neural correlates of consciousness is binocular rivalry. In binocular rivalry, separate images are simultaneously presented to each eye and perception vacillates between them, providing a way of determining which neural changes are due to shifts in perceptual consciousness rather than changes in stimuli. As the research progressed, however, scientists realized that finding correlates of consciousness was insufficient and that explanatory theories of consciousness were needed to make further progress. This review article aims to introduce the field of consciousness research by presenting some of the core challenges to the field: tracing the search for the neural correlates of consciousness through the lens of binocular rivalry, and exploring four popular theories of consciousness. These are higher-order theory, global neuronal workspace theory, integrated information theory, and predictive processing. It concludes with a glance at the future directions of research that aim to resolve the beguiling phenomenon of consciousness.

3D wave dispersion analysis of graphene platelet-reinforced ultra-stiff double functionally graded nanocomposite sandwich plates with metamaterial honeycomb core layer

This research addresses the three-dimensional thermomechanical wave propagation behavior in sandwich composite nanoplates with a metamaterial honeycomb core layer and double functionally graded (FG) ultra-stiff surface layers. Due to its potential for high-temperature applications, pure nickel (Ni) is preferred for the honeycomb core layer, and an Al2O3/Ni ceramic-metal matrix is preferred for the surface layers. The functional distribution of graphene platelets (GPLs) in three different patterns, Type-U, Type-X, and Type-O, in the metal-ceramic matrix with a power law distribution provides double-FG properties to the surface layers. The mechanical and thermal material characteristics of the core and surface layers, as well as the reinforcing GPLs, are temperature-dependent. The pattern of temperature variation over the plate thickness is considered to be nonlinear. The sandwich nanoplate’s motion equations are obtained by combining the sinusoidal higher-order shear deformation theory (SHSDT) with nonlocal integral elasticity and strain gradient elasticity theories. The wave equations are established by using Hamilton’s principle. Parametric simulations and graphical representations are performed to analyze the effects of honeycomb size variables, wave number, the power law index, the GPL distribution pattern, the GPL weight ratio, and the temperature rise on three-dimensional wave propagation in an ultra-stiff sandwich plate. The results of the analysis reveal that the 3D wave propagation of the sandwich nanoplate can be significantly modified or tuned depending on the desired parameters and conditions. Thus, the proposed sandwich structure is expected to provide essential contributions to radar/sonar stealth applications in air, space, and submarine vehicles in high or low-temperature environments, protection of microelectromechanical devices from high noise and vibration, soft robotics applications, and wearable health and protective equipment applications.

Three-dimensional thermomechanical wave propagation analysis of sandwich nanoplate with graphene-reinforced foam core and magneto-electro-elastic face layers using nonlocal strain gradient elasticity theory

This article investigates the propagation of bending, longitudinal, and shear waves in a smart sandwich nanoplate with a graphene platelet (GPL)-reinforced foam core and magneto-electro-elastic (MEE) surface layers using sinusoidal higher-order shear deformation theory (SHSDT). The suggested nanoplate is comprised of a Ti–6Al–4V foam core placed between MEE surface layers. The MEE surface layers are composed of a volumetric combination of cobalt-ferrite (CoFe2O4) and barium-titanate (BaTiO3). The foam core and MEE face layers’ material characteristics are temperature dependent. In this study, three different core types are considered: metallic solid core (Type-I), GPL-reinforced solid core (Type-II) and GPL-reinforced foam core (Type-III), as well as three different foam distributions: symmetrical foam I (S-Foam I), symmetrical foam II (S-Foam II) and uniform foam (U-Foam). To derive the nanoplate's equations of motion and determine the system response, Hamilton's principle and Navier's method are employed. The effects of various parameters such as the wave number, nonlocal parameter, foam void coefficient and distribution pattern, GPL volume fraction, and thermal, electric, and magnetic charges, on the phase velocity and wave frequency are investigated via analytical calculations. The findings of the research indicate that the 3-D wave propagation characteristics of the sandwich nanoplate can be considerably modified or tuned with respect to external loads and material parameters. Thus, the proposed sandwich structure is expected to provide important contributions to radar stealth applications, protection of nanoelectromechanical devices from high frequency and temperature environments, advancement of smart nanoelectromechanical sensors characterized by lightweight and temperature sensitivity and wearable health equipment applications.

A study on graphene-reinforced magneto-electro-elastic laminated nanoplate's thermomechanical vibration behaviour based on a higher-order plate theory

Sandwich nanostructures incorporating piezoelectric and magneto-electro-elastic properties have emerged as promising candidates for next-generation smart devices and composites. Due to their exceptional design, fabrication, and energy conversion capabilities, these structures are extensively utilised as sensors and actuators in nano-electromechanical systems. Accordingly, in this article, the free vibration behaviour of a multifunctional laminated (MFL) nanoplate with piezoelectric PZT5-H and magnetostrictive CoFe2O4 (cobalt-ferrite) face layers and a graphene-reinforced core layer is investigated by applying a higher-order sinusoidal shear deformation theory (HSDT). In addition, two different material cases consisting of Ti6Al4V and ZrO2 materials and two foam models, uniform and symmetric, are considered for the foam core layer. Hamilton's principle is used to obtain the plate's governing equations. Navier's solution approach is utilised to get the natural frequencies of the laminated nanoplate under thermal load and electric and magnetic fields. A parametric study is performed to determine the effects of volumetric graphene content, the foam model and its pore ratio, face/core material content, external electric and magnetic potential, and thermal load on the free vibration response of the MFL nanoplate. The obtained numerical results can be a reference point for future research on layered porous MEE structures, especially for micro/nano-sized systems.

Coupled higher-order layerwise mechanics and finite element formulations for laminated composite beams with active SMA layers

This study proposes a thermo-elastic coupled nonlinear finite element (FE) model for laminated composite beams with active SMA layers based on a higher-order layerwise theory and Brinson's model of SMA's phase transformation constitutive relations. The developed FE Model is further discretized by using the Newton-Raphson time integration scheme to update SMA's phase transformation progress step by step. This new model can be used for thermal-mechanical behavior analysis of hybrid SMA-composite laminated beams, which especially enables accurate prediction for static response of moderately thick to thick beams, large deformation analysis, through-thickness variations of interlaminar stresses and strains. The accuracy and effectiveness of the proposed approach are verified by several numerical examples, and the results are compared with those obtained from corresponding alternative solutions and experimental tests. Using the developed FEM, the effects of temperature, geometrical nonlinearity, pre-strain of SMA, and stacking sequence of composite laminates on the static response of hybrid SMA-composite beams are studied.

Numerical analysis of uncertain frequency of rotating composites using NURBS-based isogeometric HSDT approach: Rim-driven configuration

This study delves into the impact of material and fabrication uncertainties on the natural frequencies of rim-driven rotating structures. Utilizing a higher-order shear deformation theory (HSDT), an isogeometric analysis (IGA) model predicts these frequencies. Sensitivity analysis via a radial basis function network (RBFN) model, validated with Monte Carlo simulation, highlights parameter influence. Parametric investigations unveil sensitivity patterns and influential parameters. Employing a stochastic approach, the study compares the effects of random material properties on the free vibration response of rotating and non-rotating plates. Additionally, the RBFN-based surrogate model assesses reliability parameters concerning resonance failure in rim-driven rotating composite structures.

Stability and dynamic analyses of hybrid laminates using refined higher-order zigzag theory

This article presents a comparative study on the stability and dynamic response of hybrid laminated composite plates over monolithically produced laminated composite plates. A Refined Higher-order Zigzag Theory (RHZT) is formulated and implemented using finite element method for the analysis of hybrid laminates. This formulation considers both the interlaminar shear stress continuity and shear-free boundary conditions at surfaces of the plates. The numerical implementation employs C 0 continuous eight-noded isoparametric plate elements considering geometric nonlinearity. The element stiffness matrix is formulated to consider both the linear and nonlinear terms of the strain-displacement equations. Derivation of the consistent mass matrix for a plate element is presented following the approximation of total kinetic energy and utilising Hamilton’s principle. Numerical examples are provided to demonstrate buckling and free vibration analyses (as eigenvalue problems). The results are numerically verified and validated using data from published literature. Finally, parametric studies are presented to demonstrate the effectiveness of fibre hybridisation approach on the buckling and free vibration behaviour of laminated composites.

An isogeometric analysis of solar panels with a bio-inspired substrate

We in this paper propose a high-performance design using bio-inspired metamaterials for multilayered perovskite solar cell (MPSC) plates. The static bending and free vibrational responses of the newly designed MPSC panels with the presence of the triply periodic minimal surface (TPMS) substrate are subsequently investigated numerically. The displacements of the present plate model are then approximated by five-variable higher-order shear deformation theories (HSDTs). The weak forms are established for both the static bending and free vibration problems and subsequently derive the discrete forms using the NURBS-based isogeometric approach. To enhance the operational efficiency of solar panels in challenging environments, we integrate advanced lightweight architectures based on bio-inspired TPMS structures as a substrate layer into the original solar panel design. In this research, three widely employed TPMS structures: Primitive, Gyroid, and I-graph and Wrapped Package-graph (IWP), are examined in conjunction with two functional grading patterns implemented through the thickness direction. For the first time, the static bending performance of MPSC plates integrated into a TPMS-based substrate layer and subjected to wind pressure as well as thermal conditions is comprehensively studied. In addition, the influence of several significant factors on the free vibration behavior of MPSC plates is also elucidated. The findings show a promising and intriguing design avenue, particularly in the application of high-performance metamaterials to address contemporary challenges in renewable energy usage and environmental protection.

Vibration and aeroelastic instability analysis in GPL-porous multi-layered beam with the rotation effect

This research studies the vibrations and instability of a rotating three-layer beam under aerodynamic forces consisting of two functionally graded (FG) composite surfaces and a porous intermediate layer. Linear poroelasticity theory is used for modeling the porous layer while Young’s modulus and density vary along the thickness. Equivalent coefficients of the graphene nanoplatelets-reinforced composite (GPLs) are extracted by modified Halpin-Tsai theory, according to five different configurations. The equations of motion in the GPL-porous multi-layered beam are derived using the Euler–Bernoulli beam (EBB), Timoshenko beam (TB), and Reddy’s higher-order shear deformation theory (HSDT) theories, as well as the energy method and Hamilton’s principle. The most important results show the effect of reinforcements and their different configurations, porosity and its distribution, speed of rotation on natural frequency, critical flutter point, and loss factor for a GPL-porous multi-layered beam. The unique properties of GPL-reinforced porous materials facilitate the design of components capable of effectively managing dynamic loads and resisting aeroelastic instabilities. This results in more efficient, reliable, and durable systems across various industries.

Measurement of phase velocity in the functionally graded concrete systems via improved higher-order shear deformation theory

The measurement of phase velocity (PV) in concrete systems is critically important for civil engineers as it provides essential insights into the material properties and structural integrity of concrete. PV, which refers to the speed at which a wave phase propagates through a medium, is directly related to the stiffness and density of the material. By accurately measuring PV, civil engineers can assess the quality and homogeneity of concrete, detect potential flaws, and predict the material’s behavior under various load conditions. This information is crucial for ensuring the safety and durability of concrete structures, from bridges and buildings to pavements and dams. Moreover, understanding PV helps in the optimization of mix designs and the development of new, advanced concrete materials, ultimately leading to more resilient and cost-effective construction practices. For this issue, in this work, for the first time, the measurement of PV in the concrete doubly curved panel reinforced by graphene oxide powders (GOPs) via improved higher-order shear deformation theory is presented. Hamilton’s principle and analytical method are used for extracting and solving the higher-order equations. Finally, some recommendations for improving the efficiency and stability of the concrete structures are presented for related engineering industries. The findings underscore the potential of combining state-of-the-art theoretical models with cutting-edge material reinforcements to push the boundaries of structural engineering and material performance.

Vibration and flutter analysis of piezoelectric plates in an electrothermal field using higher order theories

Vibration and flutter analysis of piezoelectric plates in an electrothermal field using higher order theories

An intelligent computational iBCMO-DNN algorithm for stochastic thermal buckling analysis of functionally graded porous microplates using modified strain gradient theory

The authors propose an intelligent computational method using the deep feedforward neural network integrated with an improved balance composite motion optimization algorithm to formulate a so-called iBCMO-DNN for solving the stochastic thermal buckling problems of functionally graded porous microplates. In the present approach, the deterministic behaviors of the functionally graded porous microplates were firstly analyzed by the combination of a unified higher-order shear deformation theory, modified strain gradient theory, and Ritz-type series solutions, and then stochastic responses under uncertainty of material properties are obtained by the iBCMO-DNN algorithm. The deep neural network with the long short-term memory model is used as a surrogate method to replace the time-consuming computational model, while the improved balance composite motion optimization is used to search for the optimal solutions. The obtained numerical results for various boundary conditions, uncertainty parameters, and three types of temperature distribution indicated that the proposed method achieves its accuracy and effectiveness in predicting stochastic thermal buckling of the functionally graded porous microplates. The improved balance composite motion optimization algorithm demonstrates a computational time ∼1.7 times faster than its predecessor. Furthermore, integrating a deep neural network into the improved algorithm reduces computational time to about 2/5 compared to the method without it.

A size-dependent electro-mechanical buckling analysis of flexoelectric cylindrical nanoshells

In this paper, a buckling analysis for flexoelectric cylindrical nanoshells under axial compression is performed by considering the higher-order shear deformation theory and non-uniform pre-buckling deformation. Size-dependent critical buckling stresses and buckling mode shapes are obtained by the Galerkin's method with newly proposed displacement functions. Numerical results are compared with existing solutions and excellent agreements are observed. Furthermore, a comprehensive parametric study of boundary conditions, geometrical parameters and applied electric voltage is carried out to reveal the influence of flexoelectric effect on the size-dependent buckling characteristics of flexoelectric cylindrical nanoshells.

Nonlinear transient response of rotating graphene platelets reinforced metal foams blades with initial geometric imperfection

In this paper, a new mechanical model including initial geometric imperfection is developed to investigate the nonlinear transient response of graphene platelets reinforced metal foams (GPLRMF) blades subjected to blast load. Combined with higher-order shear deformation plate theory (HSDT) and von-Karman geometric nonlinearity, the nonlinear motion equations are established, in which the Coriolis force, centrifugal force as well as initial geometric imperfection are simulated. Considering cantilever boundary condition, the partial differential equations are transformed into a series of ordinary differential equations by Galerkin discretization. Using the four order Runge-Kutta algorithm, the nonlinear transient response is numerically researched, and the time histories and phase trajectories are obtained. In addition, the effectiveness of the current research is validated by comparing the results with the existing valuable literatures. The influences of rotating speed, presetting angle, initial geometric imperfection, material property, damping coefficient, and blast load parameter on the dynamic deflection and instantaneous speed are presented. Numerical results reveal that the nonlinear transient dynamics of the composite blades under blast load are significantly influenced by initial geometric imperfection.

Vibration analysis of sandwich functionally graded material plate with cut-outs using artificial neural network technique

In the present article, the effect of geometric discontinuities on the vibrational response of porous sandwich functionally graded material (SFGM) plates with double FGM facesheets has been investigated using the artificial neural network (ANN) technique. Generalized governing equations for the SFGM plate have been derived based on nonpolynomial based higher-order shear deformation theory (HSDT). Geometric discontinuities have been incorporated in terms of cut-outs in the SFGM plates. The FGM layers integrate a porosity model, while the core layer is considered a ceramic layer within the SFGM plate structure. Further, a C° continuous isoparametric finite element formulation with a four-noded, isoparametric quadrilateral element with seven degrees of freedom (DOFs) per node has been employed to accomplish the results. The accuracy of the present results has been demonstrated through convergence and validation studies. A comprehensive study has been carried out to investigate the influence of volume fraction index, even and uneven porosity distribution and cut-outs on the frequency parameter of SFGM plates. However, the finite element method (FEM) is computationally challenging. Therefore, the motivation behind adopting ANN technique to develop a predictive model for reasonable accuracy with less computational time. The ANN technique is proposed to predict the NDFP of the SFGM plate using cut-outs under various conditions using numerical simulation datasets. An optimised ANN model has been developed with an architecture of (6–5–10–5–1), exhibits best performance based on mean error value, which accurately predicts the Non-Dimensional Frequency Parameter (NDFP) of the SFGM plate.