A refined asymptotic theory and computational model for multilayered composite plates

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

Thermo-mechanics of undamaged and damaged multilayered composite plates: a sub-laminates finite element approach

This paper presents accurate two-dimensional solutions for bending response of four types of single-layer orthotropic rectangular plates. The plates considered are of the type having two opposite sides simply-supported, and two other sides having combinations of simply-supported, clamped, and free-boundary conditions. Analytical solutions for deflections and stresses of rectangular plates are developed by means of the simple (SFPT) and mixed (MFPT) first-order shear deformable plate theories. The present MFPT not only shows improvement on predicting frequencies, critical buckling loads, deflections and in-plane stresses, but also accounts for variable transverse shear stress distributions through the thickness. This puts into evidence the important role played by MFPT in the modeling of homogeneous plate theories, which in contrast to SFPT does not require the incorporation of a shear-correction factor. For illustrative purposes, sample free vibration, stability, and bending problems for simply supported orthotropic plates are considered and comparisons of the obtained results are made with the exact and higher-order shear deformation theory results given in the literature.

Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: An evaluation of a new displacement model

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.

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.

This paper addresses the problem of multilayered plates with embedded piezoelectric layers by finite element method (FEM). Original ideas in previous papers (Int. J. Numer. Methods Eng. 2002; 195: 191–231, 253–291) have been extended to the static and dynamic analysis of coupled electro‐mechanical problems. Two variational statements, the Principle of Virtual Displacements (PVD) and the Reissner Mixed Variational Theorem (RMVT) are employed to derive classical and mixed finite element matrices, respectively. Transverse stress assumptions are made in the framework of RMVT and the resulting finite elements describe a priori interlaminar continuous transverse shear and normal stresses. The unified formulation (UF) has been referred to in order to derive hierarchical finite elements (FEs) in term of a few fundamental nuclei for a large variety of piezoelectric plate theories. Both modellings that preserve the number of variables independent from the number of layers (equivalent single layer models, ESLM) and layer‐wise models (LWM) in which the same variables are independent in each layer have been treated. The expansion order N assumed for displacement, transverse stress and electrical potential fields in the plate thickness direction z as well as the number of the element nodes Nn have been taken as free parameters of the considered formulations. By varying N, Nn, variable treatment (LW or ESL) as well as variational statements (PVD and RMVT), a large number of FEs have been presented. Compliances and/or stiffness are accumulated from layer to multilayered level according to the corresponding variable treatment.The numerical evaluations and assessment for the presented plate elements have been provided. The superiority of RMVT applications with respect to classical ones based on PVD has been confirmed for piezolectric plates. The proposed RMVT elements, in fact, are able to give a quasi‐three‐dimensional description of stress/strain mechanical and electrical fields in multilayered thick and thin piezolectric plates. Copyright © 2006 John Wiley & Sons, Ltd.

The formulation of a geometrically nonlinear theory of anisotropic multilayered plates of general layups featuring interlayer slips is discussed. The theory rests on a displacement field, which accounts for an arbitrary distribution of the tangential displacements through the laminate thickness, fulfills a priori the static continuity conditions of tangential stresses at the layer interfaces, and allows for jumps in the tangential displacements so as to provide the possibility of incorporating effects of interfacial imperfection. For the interlayer displacement jump, a linear shear slip law is postulated. No a priori assumption is made on the type and order of the expansion in the thicknesswise direction of the tangential displacements. The pertinent equations of motion and consistent boundary conditions are derived by means of the dynamic version of the principle of virtual work. These are given in terms of force and moment stress resultants and in terms of generalized displacements. The generalization achieved by the proposed approach is shown by deriving, as particular cases, the recently proposed first-order and third-order models for laminated plates featuring interlayer slips

Two-scale analytical solutions of multilayered composite rectangular plates with in-plane small periodic structure

Three-dimensional asymptotic finite element method for anisotropic inhomogeneous and laminated plates

This review article is devoted to the use of the Reissner Mixed Variational Theorem (RMVT) forward two-dimensional modeling of flat and curved, multilayer structures. A thorough review of the literature involving the use in the modeling of multilayered plates and shells using RMVT is also presented. In the first part, the paper overviews relevant key points that should be taken into account for an accurate description of strain and stress fields in multilayered plate and shell analysis. It is then shown that RMVT has been originated in view of the fulfillment of such key points, herein referred to as C0-Requirements (zig-zag form of the displacement fields in the thickness direction and continuity of transverse normal and shear stresses at each layer interface). Classical variational statements are used to introduce Reissner’s Theorem. In the second part, the paper presents various ways in which RMVT can be used to develop plate and shell theories in a systematic manner. The so called layer-wise and equivalent single layer variable description are considered. Both strong and weak (finite element) forms of governing equations have been derived. A Weak Form of Hooke’s Law (WFHL), is also discussed as an idea to eliminate transverse stress variables leading to standard classical models with only displacement unknowns. Two appendices display details of governing equations related to multilayered doubly curved shells and to finite element matrices of multilayered plates. A third part reviews the works that have appeared in literature which make use of RMVT. Mainly papers on multilayered plate and shell modelings have been addressed. The final part of the paper is devoted to giving an overview with selected results of numerical performance that can be acquired by RMVT applications; extensive comparison to elasticity solutions and to other significant analyses, based on classical and refined approaches, are given. It is concluded that Reissner’s Mixed Theorem should be considered as a natural tool for multilayered structure analyses; it plays a similar role to that of the Principle of Virtual Displacement in the analysis of isotropic single-layer structures. This review article includes 119 references.

Hygrothermal effects on the bending of angle-ply composite plates using a sinusoidal theory

Efficient linear transverse normal stress analysis of layered composite plates

Auxetic materials are solids that exhibit negative Poisson's ratio. Due to its uniqueness, it is expected that auxetic solids and structures manifest certain mechanical responses that are distinct from conventional materials. So far classical plate theory (CPT) has been used to investigate the behavior of thin auxetic plates and, for thick auxetic plates, the first-order shear deformation theory (FSDT) has been recently employed. The third-order shear deformation theory (TSDT) is adopted herein as it employs a realistic transverse shear stress and strain distribution across the plate cross section, and therefore removes the need for a correction factor. The results obtained herein reveal that as a plate material's Poisson's ratio becomes more negative, the plate deflection characteristic mimics that of (a) reduced plate thickness, (b) reduced plate aspect ratio, and (c) reduced load waviness. The results of this investigation support (i) the use of auxetic materials in applications where there is a need to reduce the extent of transverse shear deformation, and (ii) the use of the simpler CPT instead of any shear deformation plate theory if the Poisson's ratio of the plate material is sufficiently negative.

A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations