Modeling Of Composite Plates Research Articles

New analytical model for multi-layered composite plates with imperfect interfaces under thermomechanical loading

AbstractA new analytical model for thermoelastic responses of a multi-layered composite plate with imperfect interfaces is developed. The composite plate contains an arbitrary number of layers of dissimilar materials and is subjected to general mechanical loads (both distributed internally and applied on edges for each layer) and temperature changes, which can vary from layer to layer and along two in-plane directions. Each layer is regarded as a Kirchhoff plate, and each imperfect interface is described using a spring-layer interface model, which can capture discontinuities in the displacement and stress fields across the interface. Unlike existing models, the governing equations and boundary conditions are simultaneously derived for each layer by using a variational procedure based on the first and second laws of thermodynamics, which are then combined to obtain the global equilibrium equations and boundary conditions for the multi-layered composite plate. A general analytical solution is developed for a symmetrically loaded composite square plate with an arbitrary number of layers and imperfect interfaces by using a new approach that first determines the interfacial normal and shear stress components on one interface. Closed-form solutions for two- and three-layer composite square plates are obtained as examples by directly applying the general analytical solution. Numerical results for two-, three- and five-layer composite plates under different loading and boundary conditions predicted by the current model are provided, which compare well with those obtained from finite element simulations using COMSOL, thereby validating the newly developed analytical model.

Finite element analysis of the electro-mechanical coupling effects in piezoelectric laminated structures

This study utilized the COMSOL Multiphysics software to conduct finite element analysis on the piezoelectric coupling effect of the composite layer structure. The article begins by introducing the basic principles and history of the piezoelectric effect, emphasizing the importance and widespread application of piezoelectric materials in the field of smart materials. Subsequently, it defines in detail the models of bimorph piezoelectric beams and multilayer composite piezoelectric plates, and conducts potential verification. The bimorph piezoelectric beam model uses PVDF material, and the potential distribution is monitored by boundary probes, confirming the influence of the quantity and distribution of sensor electrodes on voltage distribution. The multilayer composite piezoelectric plate model combines a Si non-piezoelectric semiconductor layer with a PZT-4 piezoelectric material layer, demonstrating the in-plane distribution of potential under lateral mechanical loads. This study not only verifies the reliability of COMSOL software in piezoelectric coupling analysis but also provides an in-depth understanding of the behavior and performance of piezoelectric materials in complex environments.

Homogenised strength criterion for natural fibre-reinforced composite

A representative model for multilayer natural fibre composite (NFC) plates is introduced to investigate its homogenised strength criterion. A three-layer NFC plate model is used to analyse the local stress–strain characteristics in multi-layered NFC. Finite element analysis (FEA) is performed on the representative volume element (RVE) under various boundary conditions to investigate stress and strain at macroscopic and microscopic levels. The explicit assessment of homogenised strength requires calculating stress tensors and equivalent stresses to determine parameter values. The precise specification of homogenised strength requirements assists in comprehending the material's behaviour under various loading conditions, which affects composite application design and optimisation techniques. The study examined the effect of fibre orientation angles on NFC's mechanical behaviour. The results demonstrate that flax fibres have comparatively higher stress levels than coir fibres. This study improves the understanding of natural fibre laminate composites’ macroscopic and microscopic behaviours, that is, the material's response under different loadings. The definition of homogenised strength criterion on NFC improves their design evaluations.

Carrera Unified Formulation (CUF) for the composite plates and shells of revolution. Layer-wise models

Here, higher order layer-wise models of elastic composite multilayer plates and shells of revolution are developed using the variational principle of virtual power for the 3-D linear anisotropic theory of elasticity and generalized series in the thickness coordinates. Following the Unified Carrera Formulation (CUF), the stress and strain tensors, as well as the displacement vector, were expanded into series in terms of the coordinates of the shell thickness. The higher-order rectangular plate and cylindrical shell supported on the edges under sinusoidal loading, are considered and solved analytically using a Navier close form solution method. Also, composite axisymmetric conical, spherical, elliptical and catenoidal shell fixed at the ends are considered. Numerical calculations were performed using the computer algebra software Mathematica. The resulting equations can be used for theoretical analysis and calculation of the stress–strain state, as well as for modeling thin-walled structures used in science, engineering, and technology. The results of calculation can be used as benchmark examples for finite element analysis of the higher order composite laminate shells.

Generalized Kelvin-Voigt viscoelastic modeling and numerical study of Free-Damped vibrations in MR elastomer reinforced with graphene platelets

This study focuses on the modeling and numerical analysis of a novel composite plate, which consists of a laminated magnetorheological elastomer (MRE) reinforced with graphene platelets (GPLs). The investigation begins with the determination of the mechanical properties of the MRE, utilizing a modified generalized Kelvin-Voigt viscoelastic model. Through nonlinear regression analysis and the nonlinear least squares technique, the dependencies of the storage and loss modulus of the magnetorheological (MR) matrix are evaluated, considering factors such as the magnetic field, iron particles, and excitation frequency. The proposed model is validated by comparing the obtained results with existing experimental data from the literature, employing root mean square error and correlation coefficients as metrics of consistency. Next, the homogenization process is applied to the composite media, which involves integrating the MR elastomer matrix and GPL reinforcements using the Halpin-Tsai micromechanical approach. This procedure enables the extraction of effective material properties governing the behavior of the composite structure. The theoretical framework, encompassing third-order plate theory, linear elasticity, and viscoelasticity, is then employed to derive the dynamic equations of the composite plate, employing Hamilton's principle as a guiding principle. To solve the dynamic problem and obtain the complex frequencies characterizing the system, the generalized differential quadrature (GDQ) method is implemented. This numerical technique offers a robust and accurate solution approach, providing comprehensive insights into the vibrational behavior of the composite plate. The study conducts a thorough investigation, exploring the performance achieved by incorporating GPL reinforcements within the MRE matrix. Specifically, the effects of different volume fractions of iron particles and varying magnetic fields are comprehensively examined and analyzed. Through this comprehensive exploration, a profound understanding of the behavior of the composite plate and its response to external stimuli is attained. The findings highlight the potential advantages of integrating GPL reinforcements and offer valuable insights for optimizing the design and performance of such composite structures in practical applications. The research contributes to the advancement of knowledge in the field of composite materials and opens up new possibilities for innovative and high-performance structural designs.

On the vibro-acoustic modeling of panels excited by diffuse acoustic field (DAF)

Composite materials along with isotropic materials possess abundant applications to various engineering disciplines like aerospace and mechanical issues. The design optimization of composite materials such as sandwich panels essentially needs an accurate vibro-acoustic modeling. Such a modeling of these materials and a sound synthesis can lead to a design approach based on relevant psychoacoustic analyses. In this research, the mathematical/numerical and experimental steps required by the vibro-acoustic modeling of composite and isotropic plates excited by a diffuse acoustic field (DAF) are discussed. Herein, the analytical modeling was performed by 4th and 6th order problems adapted for the composite and isotropic plates, and moreover, the numerical modeling was carried out via the Finite Element Method (FEM). The experimental observations were also performed by means of an acoustic test cabin used for ideally generating a diffuse acoustic field (DAF). The various types of analytical and numerical simulations including synthesized sounds required by future psycho-acoustic analyses, as well as experimental observations including recorded sounds were investigated and compared. Finally, based on the various analyses, the research illustrates how such investigations and comparisons are necessary for designing and enhancing the mechanical and vibro-acoustic properties of materials.

Modeling and Vibration Control of Sandwich Composite Plates.

A finite element dynamic model of the sandwich composite plate was developed based on classical laminate theory and Hamilton's principle. A 4-node, 7-degree-of-freedom three-layer plate cell is constructed to simulate the interaction between the substrate, the viscoelastic damping layer, and the piezoelectric material layer. Among them, the viscoelastic layer is referred to as the complex constant shear modulus model, and the equivalent Rayleigh damping is introduced to represent the damping of the substrate. The established dynamics model has too many degrees of freedom, and the obtained dynamics model has good controllability and observability after adopting the joint reduced-order method of dynamic condensation in physical space and equilibrium in state space. The optimal quadratic (LQR) controller is designed for the active control of the sandwich panel, and the parameters of the controller parameters, the thickness of the viscoelastic layer, and the optimal covering position of the sandwich panel are optimized through simulation analysis. The results show that the finite element model established in this paper is still valid under different boundary conditions and different covering methods, and the model can still accurately and reliably represent the dynamic characteristics of the original system after using the joint step-down method. Under different excitation signals and different boundary conditions, the LQR control can effectively suppress the vibration of the sandwich plate. The optimal cover position of the sandwich plate is near the solid support end and far from the free-degree end. The parameters of controller parameters and viscoelastic layer thickness are optimized from several angles, respectively, and a reasonable optimization scheme can be selected according to the actual requirements.

Austenitizing Temperature Effects on the Martensitic Transformation and its Influence on Simulated Welding Residual Stresses in a Microalloyed-Steel

This study focused on the effects of different peak (austenitizing) temperatures (Tp) over the martensite start temperature (Ms) and its influence on the final residual stresses after welding simulation. For this purpose, the expansion coefficients obtained through physical (dilatometric) simulations of a high-strength low-alloy steel were considered for three peak temperatures: 1300 °C, 1150 °C, and 920 °C and a cooling rate of 25 °C/s. Aiming at clarifying the physical phenomenon behind GTAW welding, one carried out nonlinear transient thermomechanical finite-element (FE) analyses to reconstitute the welding process and simulate the subsequent formation of residual stresses in the HAZ. Once the heat source simulation was calibrated, four material models were created, one for each Tp, and a fourth model considering a constant expansion coefficient, without considering the martensite transformation for comparison. A Three-bar model was evaluated to isolate the effects of Tp (Ms) in the residual stresses. A composite plate model was also considered, in which the sheet HAZ was subdivided according to the reached peak temperature, and the respective material models were applied. The results show the importance of martensite transformation on the welding-induced residual stress and a clear trend of decreasing tensions with lowering the Tp, especially over HAZ.

Modeling and analysis of composite plates and their implementation in transportation.

The article describes the process of creating and comparing composite structures using 3D models created in the graphical program ANSYS Workbench in the ACP (Ansys Composite Pre-Postprocessing) module. The research is a contribution in the field of transportation, where it is appropriate to use a lightweight yet sufficiently strong material, which is mainly influenced by the distribution of reinforcing fibers.

Acoustic sources localization for composite pate using arrival time and BP neural network

This paper presents a machine learning approach to localizing a five-peak narrow-band modulated sinusoidal signal excitation source within a composite panel. In particular, the Back Propagation (BP) neural network is used. The idea is to use the arrival time of the first wave packet in a five-peak wave signal to locate their source. Specifically, this paper divides the composite material board into multiple regions, designs 8 receiving points to receive the signal from the excitation source, and finds the region where each source is located. The COMSOL numerical simulation platform is used to build a composite plate model and simulate the propagation of five-peak waves to train and test the machine learning network. Correspondingly, carry out experimental verification and use a scanning laser Doppler vibrometer (SLDV) to build a non-contact experimental platform to obtain the wave field information in the composite material plate. The results show that BP neural networks can learn to map signal features to their sources in both contexts.

DAMAGE CHARACTERIZATION OF COMPOSITE STIFFENED PANELS UNDER IMPACT LOADING IN AIRCRAFT APPLICATION

Composite Materials have becomesa popular due to itshigh specificstrength and high stiffness to weight ratio. They found extensive applications in automobile, aerospace, defence equipment’s and other critical components. Composite plates are predominantly used as alternative materials to regular materials. In order to provide even better strength and resistance to deformation, stiffeners are attached to the composite plates thereby increasing the bending stiffness to a large extent. These stiffened panels have found principal application in aircraft wings, ship hulls and bridge decks. In this project, low velocity impact on composite plate and composite stiffened panel has been studied. Numerical models of composite plates and stiffened panels are impacted with different energies (4J, 9J, 16J) and are analysed by finite element software ABAQUS explicit and four different oblique impact angles 90◦, 60◦, 45◦and 30◦ are analysed. Different parameters such as displacement, contact force, energy absorbed were compared for both composite plates and stiffened panels. It was noted that stiffened panels offer more resistance to deformation and absorb more energy due to high stiffness. Keywords:Stiffened Panels, low-velocity impact, FE Model, ABAQUS Explicit.

Cost-effective and accurate interlaminar stress modeling of composite Kirchhoff plates via immersed isogeometric analysis and equilibrium

Abstract The interest for composites has constantly grown in recent years, especially in the aerospace and automotive industries, as they can be moulded in complex form and geometry, as well as exhibit enhanced engineering properties. Nevertheless, despite the accelerated diffusion of laminated composites, the design of these materials is often restrained by the lack of cost-effective modeling techniques. In fact, the existing numerical strategies allowing for cheap simulations of laminated structures usually fail to directly capture out-of-plane through-the-thickness stresses, which are typically responsible for failure modes such as delamination. In this context, a stress recovery approach based on equilibrium has been recently shown to be an efficient modeling strategy in the framework of isogeometric analysis. Since immersed approaches like the finite cell method have been proven to be a viable alternative to mesh-conforming discretization for dealing with complex/dirty geometries as well as trimmed surfaces, we herein propose to extend the stress recovery approach combining the finite cell method, isogeometric analysis and equilibrium to model the out-of-plane behavior of Kirchhoff laminated plates. Extensive numerical tests showcase the effectiveness of the proposed approach.

Distributed strain monitoring for different composites structures with high resolution based on optical fiber sensing

Distributed strain monitoring for different composites structures has been accomplished with high resolution based on optical fiber frequency domain reflectometry (OFDR) system. The dynamic measurement range and spatial resolution of the system can be adjusted according to the objects to be monitored. In order to verify the reliability of the system, theoretical and experimental studies have been carried out. The physical model structures have been established. The sensing fiber was pasted onto the physical structure. The finite element analysis software ANSYS has been used to build 3D models of the structures in experiments, including the aluminum alloy cantilever beam model and the carbon fiber reinforced composite plate model. The simulated strain curves have been acquired based on the composite material analysis and the static analysis of module simulation according to the actual load. The experimental strain curves have been obtained by the established OFDR system. The theoretical and experimental results show that the system can achieve the spatial resolution of 1.3 mm within the measurement range of 50 m. Under certain load conditions, the maximum error between the experimental measurement results and the theoretical simulation results of the strain distribution is 2.62% for the aluminum alloy cantilever beam, and that is 2.65% for the carbon fiber reinforced composite sheet. The results verified the reliability of the OFDR system for distributed monitoring of strain.

Finite element analysis of smart composite plate structures coupled with piezoelectric materials: Investigation of static and vibration responses

This research presents a generalized-energy-based finite element modeling of smart composite plates with distributed piezoelectric materials for the static and vibration responses under electrical and mechanical loading. The zigzag kinematics in conjunction with a non-polynomial higher-order shear deformation theory is used to derive the model. The plate theory accounts for the non-linear variations of the transverse shear strains across the thickness of the plates and also accommodates the inter-laminar continuity effects of transverse shear stresses at the interfaces. Eight noded isoparametric serendipity elements are used to discretize the physical domain. The solutions in the time domain are obtained from the discretized system of ordinary differential equations with Newmark’s time integration scheme. Several numerical examples are solved for different types of smart composite plates with various piezoelectric materials, boundary conditions, static and dynamic loadings. The classical negative feedback controller is used for deriving the suppressed and controlled vibration responses of the smart composite plates with distributed actuators and sensors. A comparison of the present FE solutions with the elasticity and other analytical and numerical solutions shows good agreement, thereby ensures the applicability of the present finite element model for studying the coupled electromechanical problems of piezoelectricity.

Numerical study on the dynamic progressive failure due to low-velocity repeated impacts in thin CFRP laminated composite plates

In this paper, the mechanical response of Carbon Fibre Reinforced Polymer (CFRP) plates subjected to repeated low-velocity impacts is numerically investigated. 3D models of composite plates subjected to repeated low-velocity impacts were developed in Abaqus/Explicit software. The numerical models were validated using experimental data obtained from impact tests on CFRP plates using drop weight tower methodology through the comparison of commonly used parameters (i.e., maximum contact force, maximum impactor displacement, and energy absorption). Damage is intended as several modes for intralaminar failure such us fibre or matrix breakage and interlaminar failure (i.e., delamination). Puck failure criterion with linear strain softening was employed for acknowledging intralaminar failure. Additionally, the bi-linear traction–separation cohesive zone model was employed to account for interlaminar damage by defining zero thickness cohesive elements at the interfaces. A sequence of impacts was applied to the composite plate at three different energy levels. It was found that the impact time and the peak force increase in the sequential impacts which indicates a change in the stiffness of the laminate in sequential impacts. The analyses of the results of the damage accumulation and delamination in CFRP plates showed that most of the intra-laminar and interlaminar damage is limited to a few initial impacts in a repeated impact scenario.

Dynamic Analysis of Multi-Stepped Functionally Graded Carbon Nanotube Reinforced Composite Plate with General Boundary Condition

This study presents the multi-stepped functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate model for the first time, and its free and forced vibration is analyzed by employing the domain decomposition method. The segmentation technique is employed to discretize the structure along the length direction. The artificial spring technique is applied to the structural boundary and piecewise interface for satisfying the boundary conditions and the combined conditions between subplates. Based on this, the boundary conditions of subdomains could be considered as a free boundary constraint, reducing the difficulty in constructing the allowable displacement function. Since all the structures of subdomains are identical, the allowable displacement functions of them can be uniformly constructed using the two-dimensional ultraspherical polynomial expansion. The potential energy function of the plate is derived from the first-order shear deformation theory (FSDT). The allowable displacement function is substituted into the potential energy function, and then the natural frequencies and mode shapes of the multi-stepped FG-CNTRC plate are decided by using the Rayleigh–Ritz method. The accuracy and reliability of the proposed method are confirmed by the results of the previous literature and finite element method (FEM). On this basis, the influences of the geometric and material parameters on free and forced vibration of the multi-stepped FG-CNTRC plate are also studied.

Elastic buckling of composite webs in back-to-back cold-formed steel built-up columns-Part II: Design formula

Elastic buckling of the composite webs in cold-formed steel (CFS) back-to-back built-up columns was investigated in this paper. The built-up members were fabricated from two identical C-section components and were assembled with self-drilling screws on their webs. The new buckling modes of screw composite plates with simply supported on four sides (SS) have been determined by previous experiments and numerical simulations. In this paper, the instability mechanism was analyzed based on the small deflection theory to study the elastic buckling behavior of SS screw composite plates. Immediately, a calculation model of SS screw composite plates was established considering the shear slip and the screw restraint. The analytic formula of elastic critical stresses was deduced based on the calculation model. However, the critical stress is affected by the ratio of the web length to the depth of the web, the screw diameter and the screw spacing. The proposed formula was modified using previous results obtained by extensive finite element parametric analyzes to increase the applicability for the proposed analytical formula in SS screw composite plates. Eventually, the applicability and accuracy of the design formula were validated using the previous experimental results. Therefore, a new stability calculation theory and a design formula considering the influence of shear slip were proposed to solve the defects in solving the buckling problem of screw composite plates using the classical stability theory of the single plate.

Optimization algorithms for composite beam as smart active control of structures using genetic algorithms

The principles of productive active and semi-active civil and infrastructure engineering structural control date back 40 years and significant progress has been recorded in those four decades. Smart structures typically have some control systems that enable them to deal with perturbations. The active vibration management techniques have been applied numerically and experimentally in order to reduce the vibrational levels of lightweight economic composite structures. Smart composite beams and plates have been produced and tested with surface-based piezoelectric sensors and actuators. It has been found that an effective model of smart composite plates can predict the dynamic characteristics. Utilizing Genetic Algorithm (GA) was designed and implemented. Two regression model as root mean square (RMSE) and determination coefficient (R2) were used. The first and second bending modes are operated effectively by a beam, and simultaneous vibration levels are significantly reduced for the conductive plates by the simultaneous operation of the bending and twisting modes. Vibration management is realized by using efficient control. GA could show better performance for managing linear feedback laws under given assumptions.

An analytical stress model for composite multi-pinned plates considering the combination effects of pin load and bypass load in different positions

Multi-pin joints are commonly used in engineering due to their high loading capacity. However, affected by coupling relationships between pin load and bypass load, the evaluation of stress state is difficult for composite multi-pin joints. An analytical method is proposed in this paper to calculate stress distribution of these joints under tensile load. Stress functions in this method are created considering the pin load and bypass load, according to a geometry division of the whole plate. Superposition relationships are built for each section type with an influence coefficient of bypass load. Stress components could be obtained by calculation of stress functions when material properties, geometry dimension and load are known. Experiments and finite element method are employed to verify the validation of proposed method. Results show that pin position affects stress state, and mainly embodies in σx. The first pin always gets the highest stress level, while for the other pins the stress is quite similar. Increase pin number will decrease stress level but the effect is relatively small for the first pin.

Equivalent model of thin-walled orthotropic composite plates with straight segments using variational asymptotic method

Accurate and effective prediction of the static and dynamic behavior of thin-walled orthotropic composite plates (TW-OCP) is necessary in the preliminary design. Considering that the thickness of each segment of TW-OCP is relatively thin, the constitutive modeling of unit cell is carried out to obtain the constitutive relations by using variational asymptotic method, which can be used as effective properties of the two-dimensional equivalent plate model (2D-EPM). Furthermore, constraints are applied at the intersections of each segment to ensure the continuity of displacement and slope. Finally, the effects of different structural parameters on the equivalent stiffness and anisotropy are discussed, such as the layup configuration of the panel, the inclination angle and thickness of stiffeners, and the period length of unit cell. The results show that compared with the results from three-dimensional finite element model (3D-FEM), the 2D-EPM not only has high accuracy, but also greatly reduces the degree of freedom, which has a high computational efficiency. Geometric shape (mainly determined by the inclination angle of longitudinal stiffeners) is one of the main factors that determine the anisotropy and equivalent stiffness of TW-OCP. The established equivalent model provides a simple, quick, and comprehensive way for the design and optimization of TW-OCP.