Interlaminar Shear Stress Continuity Research Articles

Application of UPV-Instrument in Health Monitoring of Indian Rail Section Using AE Technique

In present work, buckling analysis of laminated composite plates is carried out using recently proposed higher-order zigzag theory (HOZT). Third order variation of in-plane displacement field is taken across the thickness of the plate. For predicting the behavior efficiently for thick plates, quadratic variation of transverse displacement field is assumed for core layer and constant for face layers. The present theory satisfies inter-laminar transverse shear stress continuity condition at interface along with zero value at top and bottom surface of the plate. In present study, nine-noded finite element having eleven degrees of freedom per node is used. Present model is free from requirement of any kind of penalty function or C-1 condition.

Buckling Analysis of Laminated Composite Plates under Thermal Conditions

In present work, buckling analysis of laminated composite plates is carried out using recently proposed higher-order zigzag theory (HOZT). Third order variation of in-plane displacement field is taken across the thickness of the plate. For predicting the behavior efficiently for thick plates, quadratic variation of transverse displacement field is assumed for core layer and constant for face layers. The present theory satisfies inter-laminar transverse shear stress continuity condition at interface along with zero value at top and bottom surface of the plate. In present study, nine-noded finite element having eleven degrees of freedom per node is used. Present model is free from requirement of any kind of penalty function or C-1 condition.

Hygro-thermo-mechanical based bending analysis of symmetric and unsymmetric power-law, exponential and sigmoidal FG sandwich beams

In the present work, an attempt has been made to carry out the bending analysis of sandwich FGM beams under combined hygro-thermo-mechanical loadings. Temperature and moisture-dependent material properties are used during the present study. A comparative study has also been carried out between the beams made up of different homogenization rules. The study has been carried out using recently proposed finite element-based HOZT. The present model satisfies the inter-laminar transverse shear stress continuity condition at interfaces and the zero condition at the top and bottom surfaces of the beam. The data is presented in the form of tables for displacement and stresses and graphs representing stress distribution across the thickness of the beam. For the first time, upward displacement of the sandwich FGM beam has been reported in the present work when subjected to hygro-thermo-mechanical loading. Several new results are also reported in the present work, which will serve as a benchmark for future studies in a similar direction.

Failure mode analysis of laminated composite sandwich plate

Failure mode prediction of laminated composite sandwich plates is presented using improved higher order shear deformation theory (IHSDT) mathematical model and its C0 finite element (FE) implementation in FORTRAN. The proposed 2D IHSDT satisfies the inter-laminar shear stress continuity at each adjacent layer and nil transverse shear stress conditions at top and bottom of the plate are imposed. The parabolic shear stress variation is piecewise across thickness of each layer; hence no need of shear correction factors. The possible modes of failures are transverse matrix cracking, fiber breakage and inter-fiber shear failure of the matrix. The failure mode along with its location for laminated composite sandwich plates are obtained and are found in good agreement with the available 3D elasticity results.

Trigonometric zigzag theory for static analysis of laminated composite and sandwich plates under hygro-thermo-mechanical loading

In the present work, the static response of symmetric and anti-symmetric laminated composite and sandwich plates is investigated for elevated temperature and moisture conditions. Analysis is carried out using recently developed zigzag model which is based on a trigonometric (secant) shear deformation in the plate. The theory incorporates inter-laminar shear stress continuity along with the traction free boundary conditions at the top and bottom surfaces. The finite element method is employed for analysis, using the eight noded isoparametric serendipity element, accounting for the C0 continuity. Numerous examples covering the various features such as effect of thermal and moisture coefficients, material anisotropy, boundary and loading conditions and span to thickness ratio are solved for symmetric as well as anti-symmetric plates. Results in the form of deflection and stresses are presented and validated with the available results in the existing literature. Further, few new results are also provided in this work, to set a benchmark study for the future research.

Influence of openings and additional mass on vibration of laminated sandwich rhombic plates using IHSDT

In this article, investigations on the influence of openings and additional mass on free vibration analysis of laminated composite sandwich skew plates using improved higher order shear deformation theory (IHSDT) have been done. The IHSDT model satisfies the interlaminar shear stress continuity at the layer interfaces and also ensures zero transverse shear stress conditions at the top and bottom of the plate. The piecewise parabolic shear stress variation across the thickness of each layer is considered. No shear correction factors are required. The 2-D C0finite element (FE) model has been developed by authors based on IHSDT. FE model based on IHSDT has been coded in FORTRAN. The problem of C1continuity requirement associated with the IHSDT is overcome using an appropriate C0FE formulation. The free vibration frequencies of laminated composite and sandwich plates obtained using the present 2-D FE model are in good agreement with the 3-D elasticity results. The influence of the side-to-thickness ratio, skew angles, boundary conditions, and mode shapes is taken into consideration for the present study.

Ultimate Strength Analysis of Laminated Composite Sandwich Plates

The ultimate strength analysis of laminated composite sandwich plates is presented via ultimate failure load prediction along with modes of failure for laminated composite sandwich plates using mathematical model based on improved higher order shear deformation theory (IHSDT). The proposed IHSDT mathematical model satisfies the inter-laminar shear stress continuity at each layer interface and also ensures zero transverse shear stress conditions at the plate top and bottom. The piecewise parabolic shear stress variation across the thickness of each layer is considered. No shear correction factors are required. The suitable C0 FE formulation of IHSDT model is developed by authors.

Hygrothermal analysis of laminated composites using C0 FE model based on higher order zigzag theory

A C0 FE model developed based on an efficient higher order zigzag theory is used for hygrothermal analysis of laminated composite plates. The C0 FE model satisfies the inter-laminar shear stress continuity at the interfaces and zero transverse shear stress conditions at plate top and bottom. In this model the first derivatives of transverse displacement have been treated as independent variables to circumvent the problem of C1 continuity associated with the above plate theory. In the present theory the above mentioned C0 continuity of the present element is compensated in the stiffness matrix formulation by using penalty parameter approach. In order to avoid stress oscillations observed in the displacement based finite element, the stress field derived from temperature/moisture fields (initial strains) must be consistent with total strain field. Special steps are introduced by field consistent approach (e.g., sampling at gauss points) to compensate this problem. A nine noded C0 continuous isoparametric element is used in the proposed FE model. Comparison of present numerical results with other existing solutions shows that the proposed FE model is efficient, accurate and free of locking.

Improved zigzag theories for laminated composite and sandwich plates with interlaminar shear stress continuity

In this present work, improved zigzag theories are developed for the flexural analysis of laminated plates using algebraic, hyperbolic, inverse trigonometric and trigonometric shear strain functions. The governing differential equations and boundary conditions of the structural system are obtained through the principle of virtual work. A generalized Navier closed form solution technique is applied for the flexural analysis of laminated plates. The present theories fulfill the transverse shear stress continuity and in-plane displacement continuity at each layer interfaces. Moreover, the present theories exhibit a constant variation of transverse displacement and parabolic variation of transverse shear stresses across the plate thickness. The tangential stress free boundary conditions are satisfied on the external surfaces of the panel; hence the necessity of artificial shear correction factor is ignored. The present theories consist of 5 unknowns as in the case of FSDT. Several numerical examples are carried out for a broad range of lamination sequence and geometric parameters. To reveal the potency and performance of the present models, numerical comparisons are made with the 3D elasticity solution and other numerical methods and it is observed that the present models perform very well for the static behavior of laminated plates.

Calculation of interlaminar shear stresses in laminated shallow shell panel using refined higher order shear deformation theory

In general, calculation of inter-laminar shear stresses in laminated shells using 2D finite element models involves cumbersome post processing techniques. This paper presents a simple and efficient method for accurate evaluation of transverse shear stresses in laminated composite shallow shells by using a displacement based C0 2D FE model derived from refined higher order shear deformation theory (RHSDT) and a least square error (LSE) method. The theory satisfies the inter-laminar shear stress continuity conditions at the layer interfaces and zero transverse shear stress conditions at the top and bottom of the plate. The effect of three curvature terms in the strain components of composite shells is also considered by following the Sander’s approximations. In order to overcome the problem of C1 continuity of transverse displacement encountered at the time of FE implementation of the present shell theory (RHSDT), the first derivatives of transverse displacement have been replaced by a independent C0 variables. The LSE method is applied at the post-processing stage, after in-plane stresses are calculated by using the present FE model based on RHSDT. Thus the proposed method is quite simple and efficient compared to the usual method of integrating the 3D equilibrium equations for calculation of transverse stresses in laminated composite shells. Accuracy of the method is demonstrated in the numerical examples through comparison of the present results with those obtained from different models based on refined higher order shear deformation theory (RHSDT), higher order shear deformation theory (HSDT), exact analytical and 3D elasticity solutions.

Efficient Failure Analysis of Laminated Composites and Sandwich Cylindrical Shells Based on Higher-Order Zigzag Theory

AbstractAn efficient failure analysis of laminated composite and sandwich cylindrical shell is done for the first time using an efficient C0 finite-element (FE) model based on higher-order zigzag theory (HOZT). The FE implementation based on HOZT to study the failure of composite and sandwich shells incorporating all three radii of curvature is presented. The proposed two-dimensional (2D) FE model satisfies the interlaminar shear stress continuity at the layer interfaces and also ensures zero transverse shear stress conditions at the shell top and bottom. The problem of C1 continuity associated with the HOZT is circumvented by using an appropriate C0 FE formulation. The piecewise parabolic shear stress variation across thickness of each layer is considered and hence, shear deformation is accurately modeled for composites and sandwich shells. The failure load results for laminated composite and sandwich shells obtained by using the present 2D FE model are quite close to the 3D elasticity results. Many new ...

Static and Dynamic Control of Smart Composite Laminates

An efficient continuous two-dimensional finite-element model has been presented in this paper for the control of laminated composite and sandwich plates embedded/surface-bonded with piezoelectric layers and subjected to mechanical loading as well as electric potential. The problem of modeling of smart laminates involves the coupling between mechanical and electrical fields. The structural component is modeled by an efficient equivalent single-layer plate theory, which ensures interlaminar shear-stress continuity and zero transverse shear-stress conditions at the top and bottom of the plate surfaces. Moreover, this theory contains unknowns defined at the reference plane (i.e., midplane) only. The electric field is modeled using layerwise theory, which contains the unknowns at each layer interfaces. The proposed combine model, which may be called a refined hybrid plate model, is implemented to analyze the coupled problem of piezoelectricity in laminated composites and sandwich plates.

Accurate dynamic response of laminated composites and sandwich shells using higher order zigzag theory

Forced vibration response of laminated composite and sandwich shell is studied by using a 2D FE (finite element) model based on higher order zigzag theory (HOZT). This is the first finite element implementation of the HOZT to solve the forced vibration problem of shells incorporating all three radii of curvatures including the effect of cross curvature in the formulation using Sanders' approximations. The proposed finite element model satisfies the inter-laminar shear stress continuity at each layer interface in addition to higher order theory features, hence most suitable to model sandwich shells along with composite shells. The C0 finite element formulation has been done to overcome the problem of C1 continuity associated with the HOZT. The present model can also analyze shells with cross curvature like hypar shells besides normal curvature shells like cylindrical, spherical shells etc. The numerical studies show that the present 2D FE model is more accurate than existing FE models based on first and higher order theories for predicting results close to those obtained by 3D elasticity solutions for laminated composite and sandwich shallow shells. Many new results are presented by varying different parameters which should be useful for future research.

Static, Vibration and Buckling Analysis of Skew Composite and Sandwich Plates Under Thermo Mechanical Loading

Static, vibration and buckling behavior of laminated composite and sandwich skew plates is studied using an efficient C<sup>0</sup> FE model developed based on refined higher order zigzag theory. The C<sup>0</sup> FE model satisfies the interlaminar shear stress continuity at the interfaces and zero transverse shear stress conditions at plate top and bottom. In this model, the first derivatives of transverse displacement have been treated as independent variables to overcome the problem of C<sup>1</sup> continuity associated with the plate theory. The C<sup>0</sup> continuity of the present element is compensated in the stiffness matrix formulation by adding a suitable term. In order to avoid stress oscillations observed in the displacement based finite element, the stress field derived from temperature is made consistent with the total strain field by using field consistent approach. Numerical results are presented for different static, vibration and buckling problems by applying the FE model under thermo mechanical loading, where a nine noded C<sup>0</sup> continuous isoparametric element is used. It is observed that there are very few results available in the literature on laminated composite and sandwich skew plates based on refined theories. As such many new results are also generated for future reference

Vibration of laminated composites and sandwich shells based on higher order zigzag theory

Free vibration response of laminated composite and sandwich shell is studied by using an efficient 2D FE (finite element) model based on higher order zigzag theory (HOZT). This is the first finite element implementation of the HOZT to solve the vibration problem of shells incorporating all three radii of curvatures including the effect of cross curvature in the formulation using Sanders’ approximations. The proposed finite element model satisfies the inter-laminar shear stress continuity at the interfaces in addition to higher order theory features, hence most suitable to model sandwich shells along with composite shells. The C0 finite element formulation has been done efficiently to overcome the problem of C1 continuity associated with the HOZT. The present model can also analyze shells with cross curvature like hypar shells, etc., besides normal curvature shells like cylindrical, and spherical shells. The numerical studies show that the present 2D FE model is more accurate than existing FE models based on first and higher order theories for predicting results close to those obtained by 3D elasticity solutions for laminated composite and sandwich shallow shells. Many new results are presented by varying different parameters which should be useful for future research.

Evaluation of Various Laminated Plate Theories Accounting for Interlaminar Transverse Shear Stress Continuity

Based on a unified form of the plate kinematics in terms of the transverse shear functions and the Heaviside step function, the analytical solutions of laminated plates corresponding to a number of higher-order shear deformation plate theories are solved in this paper. The accuracy assessment of these higher-order laminated plate theories is conducted by comparing the resulting analytical solutions with the elasticity solutions and finite element results. The accuracy study shows that the interlaminar shear stress continuity condition is very important for the accurate prediction of the transverse shear stresses across the laminated plate thickness. The comparison study also indicates that the new laminated plate theory accounting for the interlaminar transverse shear stress continuity proposed by the authors yields both very accurate displacements and accurate stresses. This new higher-order laminated plate theory can be efficiently used in the finite element analysis of laminated composite plates since it uses the same five field variables as those used in the first-order shear deformation plate theory.

Finite element analysis of laminated composite and sandwich shells using higher order zigzag theory

Static analysis of laminated composite and sandwich shell is presented by developing a C0 finite element (FE) formulation based on higher order zigzag theory (HOZT) using Sander’s approximations. The proposed model satisfies the inter-laminar shear stress continuity at the interfaces; and zero transverse shear stress conditions at shell top and bottom. This is the first finite element implementation of the HOZT to solve the problem of shells incorporating cross curvature effects in shells. The present HOZT predicts transverse shear stresses more accurately than FE results previously published in literature. Numerical results show that the present 2D model is very efficient in predicting the static response of laminated composite and sandwich shallow shell very close to 3D elasticity solutions.

An optimal versatile partial hybrid stress solid-shell element for the analysis of multilayer composites

SUMMARY In the present contribution we propose an optimal low-order versatile partial hybrid stress solid-shell element that can be readily employed for a wide range of geometrically linear elastic structural analyses, that is, from shell-like isotropic structures to multilayer anisotropic composites. This solid-shell element has eight nodes with only displacement degrees of freedom and only a few internal parameters that provide the locking-free behavior and accurate interlaminar shear stress resolution through the element thickness. These elements can be stacked on top of each other to model multilayer composite structures, fulfilling the interlaminar shear stress continuity at the interlayer surfaces and zero traction conditions on the top and bottom surfaces of composite laminates. The element formulation is based on the modified form of the well-known Fraeijs de Veubeke–Hu–Washizu multifield variational principle with enhanced assumed strains formulation and assumed natural strains formulation to alleviate the different types of locking phenomena in solid-shell elements. The distinct feature of the present formulation is its ability to accurately calculate the interlaminar shear stress field in multilayer structures, which is achieved by the introduction of the assumed interlaminar shear stress field in a standard enhanced assumed strains formulation based on the Fraeijs de Veubeke–Hu–Washizu principle. The numerical testing of the present formulation, employing a variety of popular numerical benchmark examples related to element patch test, convergence, mesh distortion, shell and laminated composite analyses, proves its accuracy for a wide range of structural analyses.Copyright © 2012 John Wiley & Sons, Ltd.

An efficient FE model and Least Square Error method for accurate calculation of transverse shear stresses in composites and sandwich laminates

Accurate evaluation of transverse stresses in laminated composites and sandwich plates using 2D FE models involves cumbersome post-processing techniques. In this paper a simple and efficient method has been proposed for accurate evaluation of through-the-thickness distribution of transverse stresses in composites and sandwich laminates by using a displacement based C0 FE model (2D) derived from Refined Higher Order Shear Deformation Theory (RHSDT) and a Least Square Error (LSE) method. The C0 FE model satisfies the inter-laminar shear stress continuity conditions at the layer interfaces and zero transverse shear stress conditions at the top and bottom of the plate. In this model the first derivatives of transverse displacement have been treated as independent variables to circumvent the problem of C1 continuity associated with the above plate theory (RHSDT). The LSE method is applied to the 3D equilibrium equations of the plate problem at the post-processing stage, after in-plane stresses are calculated by using the above FE model based on RHSDT. Thus the proposed method is quite simple and elegant compared to the usual method of integrating the 3D equilibrium equations at the post-processing stage for calculation of transverse stresses in a composite laminate. In the proposed method, the first two equations of equilibrium are utilized to compute the transverse shear stress variation through the thickness of a laminated plate whereas the third equation of equilibrium gives the normal stress variation. Accuracy of the proposed method is demonstrated in the numerical examples through comparison of the present results with those obtained from different models based on higher order shear deformation theory (HSDT) and 3D elasticity solutions.

An efficient C0 FE model for the analysis of composites and sandwich laminates with general layup

A C0 continuous finite element model is developed to model the refined higher order shear deformation theory. The proposed element is an upgraded version of an element based on higher order shear deformation theory. The C0 continuity of the present element is compensated in the stiffness matrix calculations. The computational efficiency is achieved by the C0 continuous finite element model by satisfying the inter-laminar shear stress continuity at the interfaces and zero transverse shear stress conditions at plate top and bottom. The performance of the upgraded element is illustrated with many numerical examples.