Layerwise Theory Research Articles

Slope stability/instability analysis of advanced nanocomposite reinforced column structure under mechanical loading via coupled Carrera unified formulation, layer-wise and Laplace transform approaches

This study presents a comprehensive investigation into the slope stability and instability of column structures made of Triply Periodic Minimal Surfaces (TPMS) under mechanical loading. TPMS structures, known for their high strength-to-weight ratio, are increasingly used in engineering applications, particularly in lightweight structures. However, their stability behavior under complex loading conditions remains largely unexplored. To address this gap, we employ a coupled approach integrating the Carrera Unified Formulation (CUF), the Layer-Wise (LW) theory, and Laplace Transform techniques. The CUF framework, known for its versatility in modeling structural behavior across different geometrical and loading configurations, is utilized to capture the mechanical response of the TPMS-based columns. The LW theory further enhances the model by accurately representing the through-thickness behavior, particularly crucial for layered or composite TPMS structures. Finally, the Laplace Transform approach is applied to efficiently solve the governing differential equations, reducing the computational complexity of time-dependent mechanical analyses. A parametric study investigates the influence of various geometrical parameters, material properties, and loading conditions on the stability of the structures. The results highlight the critical factors influencing slope stability, including the interplay between the TPMS geometry and material distribution. Moreover, the findings offer insights into failure mechanisms, providing a basis for optimizing the design of TPMS-based columns for enhanced mechanical performance. This work contributes to advancing the theoretical understanding of TPMS structures, offering novel methodologies for slope stability analysis in complex mechanical systems.

Novel High-Strength and High-Temperature Resistant Composite Material for In-Space Optical Mining Applications: Modeling, Design, and Simulation at the Polymer and Atomic/Molecular Levels.

This study explores the modeling, design, simulation, and testing of a new composite material designed for high-strength and high-temperature resistance in in-space optical mining, examining its properties at both the polymer and atomic/molecular levels. At the polymer level, the investigation includes mechanical and thermal performance analyses using COMSOL Multiphysics 6.1, employing layerwise theory, equivalent single layer (ESL) theory, and a multiple-model approach for mechanical modeling, alongside virtual thermal experiments simulating laser heating. Experimentally, porous Polyaniline (PANI) films are fabricated via electrochemical polymerization, with variations in voltage and deposition time, to study their morphology, optical performance, and electrochemical behavior. At the atomic and molecular levels, this study involves modeling the composite material, composed of Nomex, Kevlar, and Spirooxazine-Doped PANI, and simulating its behavior. The significance of this work lies in developing a novel composite material for in-space optical mining, integrating it into optical mining systems, and introducing innovative thermal management solutions, which contribute to future space exploration by improving resource efficiency and sustainability, while also enhancing the understanding of PANI film properties for in-space applications.

Progressive failure analysis of laminar composites under compression using smeared crack-band damage model and full layerwise theory

This paper presents an original finite element (FE) model that integrates the smeared crack band (SCB) approach and full layerwise plate theory (FLWT). The model enhances the computational efficiency of progressive failure analysis (PFA) of laminar composites in compression, by utilizing the layerwise approach which reduces a 3D model to a 2D one. The model distributes damage throughout the FE domain, with fracture mechanisms represented by material stiffness degradation controlled by damage variables (based on equivalent strains specifically defined for each failure mode). Mesh dependency issues are addressed by scaling fracture energy using a characteristic element length, and failure initiation and modes are determined using the 3D Hashin failure criterion.Accurately describing lamina response in fiber direction under compression requires linear-brittle softening with a stress plateau. The study showed that a model considering 30 % of residual stress accurately predicts maximum stress regardless of mesh refinement, demonstrating results’ minor dependence from the selected element size.The model accuracy has been confirmed by comparing the obtained results against experimental and benchmark data from the literature. The size effect study demonstrated a decrease in maximum stress of the open-hole laminates in compression with increasing specimen in-plane size. This trend is consistent with experimental and reference numerical observations, confirming the model accuracy and applicability even for relatively coarse meshes. Therefore, computational efficiency is improved, with preserved accuracy of conventional solid finite element models.

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.

Soundbox-based sound insulation measurement of composite panels with viscoelastic damping

Sound transmission loss (STL), an essential index for assessing the sound insulation performance of composite laminated structures, typically relies on experimental methods to measure. The soundbox method (SBM), a straightforward technique for measuring the STL, is sensitive to microphones’ positions. Within the framework of the Chebyshev-Ritz method, a semi-analytical vibro-acoustic model extended to composite laminated panels with viscoelastic damping (VED) is proposed for the first time. Based on the developed simplified layer-wise theory, the panel is modeled using three layers: the top face layer, the VED layer, and the bottom face layer. A closed cavity is added to the model as the soundbox enclosure used in actual measurements. By employing the Hamilton's principle, the governing equation for the coupling system is derived, and the vibration and internal acoustic responses of the coupling system are calculated. A discretization strategy is introduced to address the frequency-dependent properties of the VED layer, avoiding the need to reconstruct the stiffness matrix at each frequency. To obtain the STL of the panel, sound pressures at external measurement points are calculated based on the Rayleigh integral. The proposed model is validated against numerical results from finite element analyses. The influences of the microphone position inside and outside the cavity on the measured STL are studied. Furthermore, parametric studies over the microphones' positions are performed to enhance the SBM-based evaluation of the composite panel's sound insulation performance. The optimal locations for two internal microphones and one external microphone are recommended. Finally, experimental studies are carried out to guide the implementation of the SBM.

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.

Aeroelastic analysis of a lightweight topology-optimized sandwich panel

Sandwich structures with lattice cores are novel, lightweight composite structures and are widely used in the aerospace industry. Besides, the aeroelastic behavior of sandwich panels in a supersonic flow regime still needs to be thoroughly studied. This work investigates the supersonic flutter of a sandwich panel whose core is topology-optimized. A finite element model of a sandwich panel based on the layerwise theory, coupled with the first-order piston theory, is presented. The sandwich panel core is assessed using a topology optimization approach with flutter loading constraints. The subsequent analytical homogenization scheme is developed to provide the equivalent mechanical properties of the topology-optimized panel. The modeling approach is fully validated, and the results demonstrate that the sandwich panel is capable of enlarging the flutter-free operational flight range when compared with other conventional panel designs. A parametric analysis of the topology-optimized sandwich panel regarding the critical flutter conditions is performed.

Effect of Porosity on the Free Vibration Analysis of a Rotating Pretwisted Sandwich Blade with a Functionally Graded Core in the Thermal Environment

This work deals with the investigation of the effect of porosity on the natural frequencies of the rotating pretwisted sandwich blade with a functionally graded core in the thermal environment. The top metallic and the bottom ceramic surfaces are exposed to ambient temperature and high inlet temperature, respectively. A finite element approach using a layerwise theory is developed. Two different porosity distributions are assumed here. The effect of the volume fraction index, rotational velocity, porosity model and temperature gradient on the natural frequencies of the pretwisted sandwich blade is studied.

Spectral collocation method for free vibration of sandwich plates containing a viscoelastic core

Viscoelastic constrained layer damping is a simple and efficient method for reducing noise, vibration, and fatigue in metal structures. In this work, a spectral collocation method utilizing a layer-wise plate theory was established to inspect the vibration characteristics of a sandwich plate with a viscoelastic core. The displacements of each layer satisfied the Mindlin plate theory. The core's transverse shear stress remained constant. The three layers’ transverse displacements were assumed to be identical. The displacement fields were reduced to nine variables by utilizing the interfaces’ continuity of the displacements. The equations of motion were obtained by utilizing Hamilton’s principle. The viscoelastic core’s material properties were considered as frequency-dependent. To address the complex eigenvalue problem, an iterative algorithm was used. The theoretical results were compared with published theoretical and experimental data for fully clamped rectangular sandwich plates to validate the proposed method. The modified Oberst beam method was applied by fitting the impulse response function to obtain the adhesive’s frequency-dependent storage modulus and loss factor. The natural frequencies and corresponding loss factors of three sandwich plates with different adhesives were measured by conducting impact tests. The numerical results from the present theoretical method agreed well with the measured results.

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.

Linear Bending Analysis of Functionally Graded Sandwich Shells With the Meshless Method Based on the Layer-Wise Theory

Linear Bending Analysis of Functionally Graded Sandwich Shells With the Meshless Method Based on the Layer-Wise Theory

Mathematical modeling and dynamic analysis of carbon fiber reinforced plastic shaft-disk-bearing system considering internal damping effect

The internal damping has significant influence on the dynamic characteristics of carbon fiber reinforced plastic drive shaft. In this paper, a dynamic model of the single-span multi-disk carbon fiber reinforced plastic shaft with elastic support is established based on layer-wise theory, damping specific capacity model, and Euler–Bernoulli beam theory. The model takes into account physical factors such as rigid body displacement caused by elastic support deformation, gyroscopic effect of concentrated mass disk, viscous internal damping of the carbon fiber reinforced plastic shaft, and lamination parameters. The model is used to analyze the natural angular frequency and critical instability speed of carbon fiber reinforced plastic shaft-disk-bearing system. The analysis results are compared with those obtained from the equivalent modulus beam theory, equivalent single layer theory, simplified homogenized beam theory, and quadrature element method. All the results demonstrate the accuracy of the proposed model, thereby validating its effectiveness. Furthermore, the model is utilized to investigate the influence of lamination parameters and mass ratio on the natural angular frequency and critical instability speed. This study provides valuable insights for the dynamics and stability design of the carbon fiber reinforced plastic shaft-disk-bearing system.

A layer-wise theory for the dynamic analysis of functionally graded composite nanobeams under thermal environment using nonlocal boundary conditions and Chebyshev collocation technique

In this study, a layer-wise theory satisfying displacement continuity at each layer’s interface and the Chebyshev collocation technique are adopted to analyze the vibration behavior of functionally graded composite nanobeams under non-uniform temperature variation in the thickness direction. The temperature-dependent mechanical properties vary according to the rule of mixture. Boundary conditions are modified by including the effect of size parameter and named as nonlocal boundary conditions. These nonlocal boundary conditions along with Eringen’s nonlocal elasticity theory are developed to capture the effect of size-dependency for such a nanobeam based on the first-order shear deformation theory (FSDT) and physical neutral plane. The energy principle and the variational approach are used to obtain force-moment equilibrium equations, which lead to governing differential equations and local boundary conditions. Two types of sandwich constructions are considered, namely, Type 1 (functionally graded-homogeneous-functionally graded) and Type 2 (homogeneous-functionally graded-homogeneous), by maintaining the material continuity at the interfaces. Natural frequencies are analyzed in the fundamental mode for various values of volume fraction index, thickness of the layers, size scale parameter, and thermal environment. The convergence rate of the Chebyshev collocation technique is also shown over the differential quadrature method.

Efficient zigzag theory-based spectral element model for guided waves in composite structures containing delaminations

Lamb wave-based structural health monitoring offers excellent potential for real-time delamination detection in laminated structures. It necessitates fast and accurate numerical simulation of guided wave interaction with delaminations. Towards this objective, we present an efficient layerwise zigzag theory (ZIGT) based time-domain spectral element for wave propagation analysis of composite beam- and panel-type structures (strips) containing delamination at arbitrary locations. The ZIGT delivers accuracy like layerwise theories by allowing slope discontinuities in the in-plane displacement field at layer interfaces while maintaining computational efficiency like equivalent single-layer (ESL) theories, making it ideal for such analyses. The high-order elemental nodes at Lobatto points have only four displacement variables, irrespective of the number of layers in the laminate. Delamination is modelled using the region approach, adapting the recently proposed hybrid point-least squares continuity method to satisfy the nonlinear displacement field continuity at the delamination fronts. The model’s efficacy is examined vis-à-vis elasticity-based elements, ESL theory-based elements, and the ZIGT-based standard finite element for free vibration and guided wave propagation responses of composite strips featuring multiple delaminations. The present model shows superior overall efficiency, accuracy, and convergence. An application of the model is also explored for identifying delamination locations from Lamb wave velocity fields.

Nonlinear active control of thermally induced pyro-coupled vibrations in porous-agglomerated CNT core sandwich plate with magneto-piezo-elastic facings

In this article, the damped nonlinear transient response of a smart sandwich plate (SSP) comprising of agglomerated CNT-reinforced porous nanocomposite core with multifunctional magneto-piezo-elastic (MPE) facesheets, subjected to the thermal environment, is numerically investigated. The synergistic influence of agglomeration, porosity and pyro-coupling on vibration control is studied for the first time under the finite element framework. The attenuation of the vibrations is caused by active constrained layer damping (ACLD) treatment. The kinematics of the plate is based on the layer-wise shear deformation theory and von-Karman’s nonlinearity. The viscoelastic properties of the ACLD patch and CNT agglomeration of the core are mathematically modelled using Golla–Hughes–McTavish and Eshelby–Mori–Tanaka methods, respectively. A comprehensive examination of the inter-related effects of different agglomeration states, porosity distributions and thermal loading profiles has been performed. The new insights on controlling pyro-coupled induced vibrations of smart sandwich plates by supplying control voltage directly to the MPE facesheets without ACLD treatment have been discussed thoroughly. The numerical analysis confirms the significant effects of pyro-coupling associated with active vibration control response of SSP.

Effects of size and location of magnetorheological segments on random vibration response of laminated composite beams using an N-layer of layerwise theory

Laminated composite beams are widely used in engineering applications, including wind turbine blades and automobile, where the structures are highly subjected to non-deterministic random loadings, requiring a reliable technique to ensure the stability of the structure during operation. Recently, to mitigate the effects of random loadings on the structural stability of the structure, segments of magnetorheological (MR) fluids have been embedded in the laminated beams (MR-laminated beams). In this work, the effects of the size and location of MR-fluid segments on random vibration characteristics are investigated. A laminated beam is considered in which several layers/segments are filled with MR fluids and are subjected to several random loads. An N-layer model of layerwise theory (LWT) developed by the present authors in previous work is considered for computational purposes. A finite element model based on LWT is developed to study the numerical examples. MR-laminated beams consist of five sections; two MR-fluid sections and three composite sections have been studied using LWT. To justify the numerical results, the first three natural frequencies of a laminated beam without an MR layer are solved using a 3D model in COMSOL software which shows a close match with the results of LWT. An in-house experimental setup has been developed to verify the simulation results. The simulation results are then compared with the first-order shear deformation theory (FSDT) and verified by several experimental tests. The effects of MR fluid segments on the dynamic response of MR-laminated beams for six different configurations have been investigated. In addition, the effects of thicknesses of MR fluid section on the dynamic behavior of structures have been investigated. Effects of magnetic fields on statistical properties, correlation, and autocorrelation on MR-laminated beams made of E-glass and fiber-carbon have been investigated. As a case study, the vibration response of a wind turbine blade made of an MR-laminated beam has been investigated using a narrow band process.

Design, fabrication, nonlinear analysis, and experimental validation for an active sandwich beam in strong electric field and thermal environment

In the present work, an efficient one-dimensional finite element (1D-FE) framework considering layerwise mechanics with full electro-mechanical coupling has been developed for the laminated smart sandwich beams submitted to active damping. Nonlinear constitutive relations of piezo-thermo-elasticity at large electric field with temperature-dependent material properties have been considered. The efficient layerwise theory (ELWT) considers the normal deformation of the piezoelectric sensing/actuating patches/layers due to the more significant value of piezoelectric strain coefficient d33. The electric potential variation across the thickness of the PZT sensor/actuator has been assumed quadratic. The state space format of the dynamical system has been constructed based on a reduced order model in modal space. The feedback linearization approach has been applied to the nonlinear system of equations to design an equivalent linear optimal control strategy. An experimental facility has been developed to test the accuracy of the present nonlinear FE model. This facility consists of a thermal chamber with a heating system, air gun, actuation & sensing units with band-pass filters, a smart sandwich beam equipped with PZT-SP5H patches, a data acquisition system, and a computer with LabVIEW software. Open- and closed-loop responses from the present 1D-FE model have been compared with those obtained through experimentation at different temperatures. It has been observed that the current nonlinear FE model correctly captures the dynamic behavior of the vibrating smart sandwich beam at different operating temperatures and strong electric field. The study shows a strong dependence of the PZT materials on thermal chamber temperature and actuation field. New results for a smart sandwich beam are also presented to study the performance of PZT-SP5H patches as sensors/actuators for nonlinear active shape and vibration control in a thermal environment. The effect of piezoelectric actuator/sensor thickness, patch size, position, and applied mechanical load on the active shape and vibration control has been discussed.

Effects of base material and magnetic field on the dynamic response of MR-laminated composite structures

Stability and vibration control are major challenges for applications in which laminated composite beams are being used. Using composite base materials with higher strength and/or using appropriate layout orientation are the two potential methods to improve the dynamic performance of laminated composite structures. However, using composite materials with higher strength significantly increases the manufacturing cost. Recently, layers/segments of Magnetorheological (MR) fluids have been added to the common laminated beams, the so-called MR-laminated beam, to improve the dynamic characteristics of such structures. The present work investigates the effect of base materials and applied magnetic field on the dynamic response of MR-laminated beams. Different composite materials, including E-glass, carbon fiber, and Kevlar, have been used as base materials to build the sandwich MR-laminated beam. The hollow spaces of the sandwich beam are filled with MR fluid to fabricate a testing sample for experimental purposes. A modified layerwise theory, N-layer, has been used to determine the vibration response of the structures. It is concluded that applying a magnetic field increases the natural frequency of the MR-laminated beam. In fact, applying 1400-Gauss magnetic fields to a low-cost material like E-glass provides the same natural frequency as that of the fiber-carbon without magnetic fields.

Non-polynomial hybrid models for the bending of magneto-electro-elastic shells

This paper presents different non-polynomial hybrid models in the framework of Carrera’s Unified Formulation for the bending of a magneto-electric shell with variable radii of curvature. The shell’s middle surface is graphed by a parametric surface. Differential Geometry is employed for evaluating the Lamé Parameters and Radius of Curvature. The mechanical displacements are modeled in the context of an equivalent single layer by sinusoidal, hyperbolic, and tangential models. The electrical and magnetic scalar potential functions are written by a polynomial thickness function in the framework of Layerwise theory. The shell panels are subjected to mechanical, electrical, and magnetic loads. The governing equations are obtained by the Principle of Virtual Displacement. The correspondent partial differential equations are discretized by Chebyshev-Gauss-Lobatto grid distribution and solved by the so-called Differential Quadrature Method. The classical Lagrange polynomial is employed as the basis function for the method. The stresses, electrical displacement, and magnetic induction are recovered by the three-dimensional (3D) equilibrium equations. A comparative analysis with 3D solutions provided in the literature is performed for a square plate and a doubly curved shallow shell panel and remarkable results are obtained. So, the validated models are further used to study shells with variable radii of curvature; specifically, for helicoid, ellipsoid, and catenoid panels.

Vibration analysis of thermally loaded isotropic and composite beam and plate structures

This work proposed the use of the Carrera Unified Formulation (CUF) for the vibration and buckling analysis of structures subjected to thermal loads. In detail, the variation of natural frequencies for progressively large thermal loads is investigated. Here, particular attention is focused on the study of buckling thermal loads as degenerate cases of the vibration analysis and on the mode aberration caused by thermal stresses. From this standpoint, the use of CUF for the development of high-order beam and plate models is fundamental. Indeed, Lagrange-like (LE) polynomials are considered for developing the kinematic expansion and Layerwise (LW) theories are employed to characterize the complex phenomena that may appear in composite structures. A linearized formulation to study the natural frequencies variation as a function of the progressive increasing thermal loadings is adopted. Different isotropic and laminated composite structures have been analyzed and compared with the Abaqus solution to validate the presented methodology and provide some benchmark solutions. In addition, a parametric study was conducted to evaluate the stacking sequence and thickness effect in the vibration modes and thermal buckling loads. The results document the excellent accuracy and reliability of the presented methodology and show the potentialities of this numerical tool able to analyze cases that are difficult to study experimentally.