C0 triangular elements based on the Refined Zigzag Theory for multilayer composite and sandwich plates

C0 beam elements based on the Refined Zigzag Theory for multilayered composite and sandwich laminates

Advanced and refined variable-kinematics plate theories built with a hierarchical approach in an extended framework of Carrera's unified formulation (CUF) are combined with Ritz and Galerkin methods to deal with a thermo-mechanical buckling analysis of anisotropic multilayered composite and sandwich plates. Buckling interaction curves and stability envelopes for different thermal and mechanical loading combinations are presented. The influence of the kinematics description and the expansion orders upon the results accuracy is evaluated. The effect of the transverse normal deformation on critical temperature parameters is thoroughly investigated. Convergence and results accuracy are discussed.

A refined zigzag theory is presented for laminated-composite and sandwich plates that includes the kinematics of first-order shear-deformation theory as its baseline. The theory is variationally consistent and is derived from the virtual work principle. Novel piecewise-linear zigzag functions that provide a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories are used. The formulation does not enforce full continuity of the transverse shear stresses across the plate's thickness, yet is robust. Transverse-shear correction factors are not required to yield accurate results. The theory is devoid of the shortcomings inherent in the previous zigzag theories including shear-force inconsistency and difficulties in simulating clamped boundary conditions, which have greatly limited the accuracy of these theories. This new theory requires only C0-continuous kinematic approximations and is perfectly suited for developing computationally efficient finite elements. The theory should be useful for obtaining relatively efficient, accurate estimates of structural response needed to design high-performance load-bearing aerospace structures

A new first-order shear deformation theory (FSDT) has been developed and verified for laminated plates and sandwich plates. Based on the definition of Reissener–Mindlin’s plate theory, the average transverse shear strains, which are constant through the thickness, are improved to vary through the thickness. It is assumed that the displacement and in-plane strain fields of FSDT can approximate, in an average sense, those of three-dimensional theory. Relationship between FSDT and three-dimensional theory has been systematically established in the averaged least-square sense. This relationship provides the closed-form recovering relations for three-dimensional variables expressed in terms of FSDT variables as well as the improved transverse shear strains. This paper makes two main contributions. First an enhanced first-order shear deformation theory (EFSDT) has been developed using an available higher-order plate theory. Second, it is shown that the displacement fields of any higher-order plate theories can be recovered by EFSDT variables. The present approach is applied to an efficient higher-order plate theory. Comparisons of deflection and stresses of the laminated plates and sandwich plates using present theory are made with the original FSDT and three-dimensional exact solutions.

Acoustic Emission (AE) technique is non-destructive Structural Health Monitoring (SHM) technique which has the potential to detect internal damages in real time. Literature reveals that researchers have used three-dimensional (3d) Finite Element Method (FEM) to predict AE waveforms in isotropic and single-layer anisotropic plates. However, the study to predict acoustic emission waveforms using FEM in layered composites and sandwich plates is limited in literature. Modelling of such layered plates is challenging as material properties may vary from one layer to another across the plate thickness. In this study, an effort has been made for two-dimensional finite element modelling for predicting AE waveforms in layered composites and sandwich plates using a generalised refined plate theory modelling. Numerical examples are first solved for isotropic and anisotropic plates and validated with the results obtained from 3d FEM. New results are presented for multilayered composites and sandwich plates.

Modern composite armor plate is generally composed of faceplate with high hardness and backplate with good toughness. 45 steel/60Si2CrA multilayer composite casting blank with 11 layers, containing 60Si2CrA steel as faceplate and 45 steel as backplate, was fabricated by composite casting. The deformation and heat treatment process of 45steel/60Si2CrA multilayer composite plate were studied. The results show that the interfaces between faceplate and backplate have good combination and the thickness of each layer is basic uniform by reasonable deformation distribution. Yield and tensile strength of the composite plate reaches 956MPa and 1018MPa, the hardness of 45 steel layer and 60Si2CrA layer is 448HV and 536HV respectively after the heat treatment of 860°C water quenching+ high temperature tempering. The mechanical properties meet the qualification of armor plate. The bulletproof test displays that 45 steel/60Si2CrA multilayer composite armor plate can prevent the breakthrough of DAP51B type bullet with the velocity of 500m/s.

An enhanced inverse finite element method for displacement and stress monitoring of multilayered composite and sandwich structures

To improve the vibrational acoustic properties of traditional composite sandwich plates featuring honeycomb structures, an analysis is performed on the vibrational acoustic response of star-shaped honeycomb sandwich plates with a negative Poisson’s ratio (NPR), utilizing the first-order shear deformation theory (FSDT). The sandwich plate consists of aluminum plates as its top and bottom layers, sandwiching NPR honeycomb structure. Utilizing Hamilton’s principle, the dynamic equation for the sandwich plate is derived under the condition of four-sided simply supported boundaries. Subsequently, the eigenvalue of the modal function matrix is computed to determine the natural frequency utilizing the coupled Navier method. The radiation sound pressure level of the sandwich plate’s radiation in the far field is determined by employing Rayleigh integral theory. The accuracy and effectiveness of the proposed model are validated by contrasting its calculation outcomes with those obtained from COMSOL simulation software. Additionally, the influence of geometric parameters of cellular cells on vibrational acoustic response is thoroughly examined. The outcomes indicate that the relative error of the maximum amplitude of the radiation sound pressure level (SPL) between theoretical and simulation results is 2.3%. Under identical conditions, when the cellular wall thickness is increased to 3 mm, the amplitude of the SPL decreases by approximately 12.24%, with a maximum trough drop of approximately 9.86%. As the cellular side length decreases, and the thickness of the sandwich layer increases, the radiation sound pressure level under point excitation decreases. Consequently, the resonance peak shifts toward lower frequencies, and the trough migrates toward a lower radiation sound pressure level. Variations in cellular structure parameters notably influence the movement trend and amplitude of the sound pressure level in a sandwich plate. The random porous metal material is filled into the star-shaped sandwich plate to examine how this random porous material affects the acoustic radiation properties of the structure. The inclusion of random porous material demonstrates a good noise reduction effect.

Global buckling and wrinkling of variable angle tow composite sandwich plates by a modified extended high-order sandwich plate theory

An attempt has been made to study the effect of cross‐sectional warping in the symmetrically laminated anisotropic composite sandwich plates for transient loads. A higher‐order shear deformation theory (HOST) is used in conjunction with the simple displacement based C° finite element method (FEM). As is well‐known, the classical first‐order theories hitherto considered were inadequate to describe the propagation of waves in the highly orthotropic sandwich laminates. The present theory, which is more accurate than the Reissner‐Mindlin theory, is applied herein, for the evaluation of plate response to different types of dynamic loads. An explicit central difference scheme is employed for the integration of dynamic equations of equilibrium with a diagonalized mass matrix obtained by a special procedure applicable to quadrilateral isoparametric elements. The numerical results of the present investigation have been compared with the first‐order shear deformation theory (FOST) and the differences between HOST and FOST are examined. The results presented here should be useful in obtaining better correlation between theory and experiment, and to numerical analysts in verifying their results.

This work presents a survey of five theories to assess the uncertainty of projectile impact induced damage on multi-layered carbon-epoxy composite plates. Because the types of uncertainty dealt with in this application are multiple (variability, ambiguity, and conflict) and because the data sets collected are sparse, characterizing the amount of delamination damage with probability theory alone is possible but incomplete. This motivates the exploration of methods contained within a broad Generalized Information Theory (GIT) that rely on less restrictive assumptions than probability theory. Probability, fuzzy sets, possibility, and imprecise probability (probability boxes (p-boxes) and Dempster-Shafer) are used to assess the uncertainty in composite plate damage. Furthermore, this work highlights the usefulness of each theory. The purpose of the study is not to compare directly the different GIT methods but to show that they can be deployed on a practical application and to compare the assumptions upon which these theories are based. The data sets consist of experimental measurements and finite element predictions of the amount of delamination and fiber splitting damage as multilayered composite plates are impacted by a projectile at various velocities. The physical experiments consist of using a gas gun to impact suspended plates with a projectile accelerated to prescribed velocities, then, taking ultrasound images of the resulting delamination. The nonlinear, multiple length-scale numerical simulations couple local crack propagation implemented through cohesive zone modeling to global stress-displacement finite element analysis. The assessment of damage uncertainty is performed in three steps by, first, considering the test data only; then, considering the simulation data only; finally, performing an assessment of total uncertainty where test and simulation data sets are combined. This study leads to practical recommendations for reducing the uncertainty and improving the prediction accuracy of the damage modeling and finite element simulation.

Thermal buckling of various types of FGM sandwich plates

Free vibration analysis of a laminated composite sandwich plate with compressible core placed at the bottom of a tank filled with fluid

The paper deals with the fully coupled response characteristics of a multilayered composite plate with piezoelectric layers. The response quantities of the plate are coupled by the mechanical field and the electric field. Based on the three-dimensional linear piezoelectricity and the first-order shear deformation theory, the fundamental unknowns, such as the displacements and the electric potential, are assumed to be expandable through the plate thickness coordinate. The governing equations of motion of the plate are presented in terms of the unknown displacement and electrical potential coefficients. When the boundary conditions and electromechanical inputs are specified, the double Fourier series is used to obtain the response of the simply supported multilayered plates. Numerical results for the static and dynamic response of the laminated composite plates with different lamination schemes and having a PIC-151 piezoelectric material layer are obtained. The effects of the plate thinness ratio, plate aspect ratio, lamination scheme, fiber orientations, and piezoelectric coupling on the static and dynamic response are presented.

Sound transmission characteristics of a composite sandwich plate using multi-layer first-order zigzag theory