Higher Order Zigzag Theory Research Articles

Comprehensive transverse shear stress analysis for FG-GRC sandwich plates based on a refined higher-order zigzag theory

Comprehensive transverse shear stress analysis for FG-GRC sandwich plates based on a refined higher-order zigzag theory

Free vibration analysis of laminated composite and sandwich shells using wavelet finite element method

The present work carries out free vibration analysis of laminated composite shells and panels using wavelet finite element method (WFEM). Two different wavelets, namely, Haar and B-spline wavelet on the interval (BSWI) are employed. The analysis is carried out using higher-order zigzag theory (HOZT), and the WFEM is set up according to Hamilton’s principle. The two-dimensional scaling functions are employed to substitute the interpolation functions as used in the FEM. Owing to the capability of the WFEM to work efficiently with lesser degrees of freedom compared to the traditional FEM, the proposed methodology is validated with the results available.

Stability and dynamic analyses of hybrid laminates using refined higher-order zigzag theory

This article presents a comparative study on the stability and dynamic response of hybrid laminated composite plates over monolithically produced laminated composite plates. A Refined Higher-order Zigzag Theory (RHZT) is formulated and implemented using finite element method for the analysis of hybrid laminates. This formulation considers both the interlaminar shear stress continuity and shear-free boundary conditions at surfaces of the plates. The numerical implementation employs C 0 continuous eight-noded isoparametric plate elements considering geometric nonlinearity. The element stiffness matrix is formulated to consider both the linear and nonlinear terms of the strain-displacement equations. Derivation of the consistent mass matrix for a plate element is presented following the approximation of total kinetic energy and utilising Hamilton’s principle. Numerical examples are provided to demonstrate buckling and free vibration analyses (as eigenvalue problems). The results are numerically verified and validated using data from published literature. Finally, parametric studies are presented to demonstrate the effectiveness of fibre hybridisation approach on the buckling and free vibration behaviour of laminated composites.

Free vibration analysis of bio-inspired double- and cross-helicoidal laminated composite plates

Nature-built structures effectively sustain higher loads without failing, even though they are made of weak organic materials. The laminated construction mode in various fish scales provides them toughness and flexibility. The present manuscript aims to carry out the free vibration analysis of double- and cross-helicoidal laminated composite plates inspired by the scales of fish. The study has been carried out using the recently proposed finite element-based higher-order zigzag theory. The influence of aspect ratio, side-to-thickness ratio, skew angle, and end conditions on the free vibration behavior of double- and cross-helicoidal plates is depicted. The mode shapes of the plates are studied in detail. The free vibration behavior of skew plates is also studied for the first time. An improved performance of the helicoidal plate compared to the conventional lamination scheme has been obtained.

Linear static, geometric nonlinear static and buckling analyses of sandwich composite beams based on higher-order refined zigzag theory

This study aims at developing finite element formulations based on higher-order refined zigzag theory (HRZT) to analyze sandwich composite beams under linear static bending, geometric nonlinearity and buckling. In HRZT, the higher-order terms associated with average shear strain and rotation due to zigzag are added based on refined zigzag theory (RZT). In linear static bending analysis, both C0 and C1 elements are developed. For the C0 element, an extra node is used in order to eliminate shear locking. For geometric nonlinear static analysis, the two-node C0 element is developed to solve the bending response with lateral loading and buckling response. The numerical results are compared with those calculated by 2D exact solutions, analytical solutions of HRZT and 2D models using commercial software. Various beam theories such as first-order shear deformation theory (FSDT), higher-order shear deformation theory (HSDT), RZT, and other types of higher-order zigzag theory are also introduced for comparisons. Through comprehensive comparisons with existing works on FEM or zigzag theories, the HRZT beam elements developed in this study exhibit superior accuracy and are free from shear locking in linear static analysis. Furthermore, the study also demonstrates that these elements achieve high accuracy in geometric nonlinear analysis and buckling analysis.

Stability and mode shape analysis of doubly- and cross-helicoidal laminated sandwich plates inspired from dactyl’s club

The present work intends to use higher-order zigzag theory to analyze double- and cross-helicoidal laminated sandwich plates under buckling conditions. Geometry and boundary effects on buckling and mode shapes are examined. The behavior of helicoidal sandwich plates is compared with the cross-ply and quasi-isotropic lamination schemes. In the case of plates with free edges, the bio-inspired laminated sandwich plates outperform the more traditional cross-ply and quasi-isotropic laminated schemes. Numerous more findings are provided as well, all of which may be used as a standard by which to measure the success of comparable future research efforts.

First-Ply Failure Analysis of Helicoidal/Bouligand Bio-Inspired Laminated Composite Plates

Among the first, the present paper focuses on studying the first-ply failure load for bio-inspired helicoidal laminated composite plates. Five different layup schemes, namely, helicoidal recursive, helicoidal semicircular, helicoidal exponential, Fibonacci helicoidal, and linear helicoidal, were studied. The performance of the five helicoidal layups was compared with the commonly used cross-ply and quasi-isotropic lamination schemes. Maximum stress, maximum strain, Tsai–Hill, Tsai-Wu, and Hoffman failure theories were employed in the framework of the recently proposed finite-element-based higher-order zigzag theory to determine the first-ply failure load. It was observed that the maximum strain theory predicted the lowest value of the first-ply failure load, whereas Tsai–Wu predicted the highest one. For some cases, Tsai–Hill and Tsai–Wu theories were not able to predict the first-ply failure load. For plates having free edges, the bio-inspired plates exhibited the first-ply failure load compared to the conventional layup sequences.

First-Ply Failure Analysis of Bioinspired Double and Cross-Helicoidal Laminated Sandwich Plates

Inspired from the helicoidal schemes available from biological creatures, the present paper aims to predict the first-ply load for laminated composite and sandwich plates inspired from biological creatures. The laminated composite and sandwich plates are assumed to be made up of double- and cross-helicoidal lamination schemes. The first-ply failure load is determined using the recently proposed higher-order zigzag theory. Five different failure criteria (namely, maximum stress, maximum strain, Tsai–Hill, Tsai–Wu, and Hoffman’s theory) are used to predict the first-ply failure load. The performance of the helicoidal plate is compared with the cross-ply and quasi-isotropic lamination schemes. The influences of the end conditions, the ratio of the thickness of the core to the face layers, and the thickness-to-side ratio on the first-ply failure load are carried out. It has been observed that for helicoidal plates, a higher value of the first-ply failure load is observed as compared to quasi-isotropic and cross-ply laminates, especially for plates having free edges. The maximum strain theory should not be used for predicting the failure load for helicoidal laminated plates because it undermines the strength of the plate.

Free vibration analysis of bio-inspired helicoid laminated composite plates

Helicoidal schemes possessed by biological creatures possess high strength and stiffness. The adoption of the layup configurations possessed by these biological creatures is not fully explored. The present article aims to carry out the free vibration analysis of biological-inspired laminated composite (B-ILC) plates having helicoidal layup. The analysis is carried out using higher-order zigzag theory (HOZT) as due to the presence of several layers, the HOZT can predict the behavior accurately compared to the shear deformation theory. Based on Hamilton’s principle, the governing equations are worked out and analyzed using the finite element method. The influence of boundary conditions, geometric properties, number of layers, the skew angle of the plate, and material properties on the free vibration behavior are studied in detail.

Buckling and free vibration analysis of bio-inspired laminated sandwich plates with helicoidal/Bouligand face sheets containing softcore

Helicoidal laminates inspired by mantis shrimp crustacean can sustain higher loads compared to conventional laminated structures. However, there is still a lack of bending studies on the plates inspired by these helicoidal structures. The buckling and free vibration studies have been undertaken in the present work on the laminated composite and sandwich plates inspired by the helicoidal structures of the biological characters. Investigations are carried out using higher-order zigzag theory. For sandwich plates, the top and bottom face sheets are assumed to be made up of helicoidal layup schemes. Different kinds of helicoidal schemes, namely, recursive, exponential, semicircular, Fibonacci, and linear helicoidal are considered during the analysis. The buckling and free vibration behavior of helicoidal-based laminated sandwich plates are compared with the conventional laminated sandwich plates such as uniform distribution and cross-ply configurations. The influence of the number of layers, helicoidal schemes, geometric properties, and end conditions on the buckling and free vibration analysis of bio-inspired helicoidal laminated composite and sandwich plates is carried out in detail.

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.

On machine learning assisted data-driven bridging of FSDT and HOZT for high-fidelity uncertainty quantification of laminated composite and sandwich plates

First-order shear deformation theory (FSDT) is less accurate compared to higher-order theories like higher-order zigzag theory (HOZT). In case of large-scale simulation-based analyses like uncertainty quantification and optimization using FSDT, such errors propagate and accumulate over multiple realizations, leading to significantly erroneous results. Consideration of higher-order theories results in significantly increased computational expenses, even though these theories are more accurate. The aspect of computational efficiency becomes more critical when thousands of realizations are necessary for the analyses. Here we propose to exploit Gaussian process-based machine learning for creating a computational bridging between FSDT and HOZT, wherein the accuracy of HOZT can be achieved while having the low computational expenses of FSDT. The machine learning augmented FSDT algorithm is referred to here as modified FSDT (mFSDT), based on which extensive deterministic results and Monte Carlo simulation-assisted probabilistic results are presented for the free vibration analysis of shear deformation sensitive structures like laminated composite and sandwich plates considering various configurations. The proposed algorithm of bridging different laminate theories is generic in nature and it can be utilized further in a range of other static and dynamic analyses concerning composite plates and shells for accurate, yet efficient results.

Vibrational study of FG skew sandwich plates having geometric distortions

An innovative composite material called functionally graded material (FGM) has gained a lot of interest in various engineering applications. This work aims to carry out vibrational study of FG skew sandwich plates having geometric distortions. It is performed using Higher Order Zigzag Theory and dimensionless frequencies are obtained. Using this theory fulfil the criteria of continuous transverse shear stress at inter-laminar junctions and zero at the top and bottom surface of the plate. It thus eliminates the necessity of factor for shear correction. The material properties follow the power law variation. The frequencies are obtained using code for the proposed FE model and are confirmed with those from the previous studies. New findings are put forth which can be used as reference for future studies in similar field.

Bending and free vibration analysis of symmetric and unsymmetric functionally graded CNT reinforced sandwich beams containing softcore

In the present work, bending and free vibration analyses of functionally graded carbon nanotube-reinforced (FG-CNTR) sandwich beams are carried out using finite element-based higher-order zigzag theory. Face sheets are assumed to be made up of FG-CNTR composite, and the core is assumed to be made up of balsa wood (softcore). The present formulation also takes into account transverse normal stresses. The computational model incorporates transverse shear stress and transverse normal stress continuity condition at interfaces. Zero transverse shear stress condition at the bottom and top surfaces of the beam is also satisfied. The principle of minimum potential energy is employed for carrying out bending analysis, while Hamilton’s principle is adopted for free vibration analysis. The investigation is carried out for different gradation laws which govern the distribution of CNTs across the thickness of face sheets. The influence of the core’s thickness on stresses and displacements is also critically analyzed in the present work. It has been observed that the thickness of the core and CNT gradation law significantly affect the mechanical behavior of the sandwich FG-CNTRC beam.

Free vibration and modal stress analysis of FG-CNTRC beams under hygrothermal conditions using zigzag theory

The present study aims to carry out free vibration analysis of functionally graded single-walled carbon nanotube-reinforced composite (FG-CNTRC) beams under hygro-thermal conditions. The study is carried out using the recently proposed C-0 finite element-based higher-order zigzag theory. The study is carried out on five different CNTRC graded beams. Temperature and moisture-dependent material properties are used. Constant temperature or moisture distribution across the thickness of the beam is taken. Hamilton's principle has been used for defining the governing differential equations. Modal stresses are also studied for the first six mode shapes. Stresses at the higher mode of vibration are found to be more affected by temperature or moisture concentration as compared to the stresses observed for the fundamental mode of vibration. It is observed that the nature of stress distribution across the beam is widely affected by the gradation law along with moisture or temperature values to which the beam is subjected. FG-O beam is found to be least sensitive under thermal conditions whereas FG-X beam is found to be the most.

Analysis of carbon nanotube reinforced composite plate using finite element method with higher order zigzag theory

ABSTRACT Static investigation of slim to tolerably thick composite plate built up by single-walled cabon nanotubes (CNT) is examined utilising the limited component technique dependent on higher order zigzag theory. The efficient material properties of nanocomposite plate have been dictated by the rule of mixture. It is seen that there are no outcomes accessible in the open writing on static investigation of nanocomposite plate dependent on refined theories. Point-by-point parametric investigations have been conveyed to uncover the impacts of the volume parts of the CNT, the edge to thickness proportions and different edge conditions on the bending behaviour of plate. To approve the current examination, some mathematical outcomes were compared with those accessible in the open literature, thus numerous outcomes have been created for future reference.

Free vibration analysis of laminated composite hybrid and GFRP shells based on higher order zigzag theory with experimental validation

Free vibration response behavior of laminated composite hybrid and Glass Fiber Reinforced Plastic (GFRP) shells is analyzed using a modified higher order zigzag theory (HOZT). The laminated shell model is developed by considering the thickness co-ordinate to radius of curvature ratio (z/R) as well as zero shear conditions at free surfaces of the shell. The C0 finite element formulations with nine-noded quadrilateral isoparametric shell element having seven degrees of freedom per node are adopted to compute the natural frequency of the shells. The hybrid laminate is modeled by placing carbon fibers in the outermost layers and glass fibers in the rest to improve the flexural behavior of the shell. Experimental studies are performed to find out the mechanical properties of hybrid and GFRP laminates such as Young modulus, shear modulus and poison's ratio. The experimental procedure of free vibration is carried out by Bruel & Kjaer (B&K) modal analysis instruments along with RT Pro modal analysis software and the results are compared with the theoretical findings. Moreover the present theoretical results have been examined by comparing with 2D solutions as well as 3D elasticity solutions available in the published literature to verify the accuracy of the present HOZT. An extensive parametric study on laminated composite hybrid and GFRP shells with various laminations is undertaken to investigate the effect of reinforcement scheme on the free vibration behavior of such laminated shells.

Superharmonic vibrations of sandwich beams with fibre composite core layer based on the multiple scale method

This paper deals with the secondary vibration problem in the superharmonic case near the harmonic excitation of 1/3w1, arising from the vibration nonlinearity that characterizes the slender and less damping laminated beam with composite material core. For this aim the multiple scale method in conjunction with the higher order zigzag theories are used to obtain the resonance responses. In the present work the nonlinear forced vibration problem of sandwich beams under harmonic excitation is solved by the multiples scales method, based by the introduction of an artificial parameter with higher order expansions, to control the nonlinear analytical solutions. The application of this method demonstrates the sensitivity of the sandwich beams with viscoelastic composite layer to the secondary superharmonic vibrations. Following, parametric study is conducted to demonstrate the vulnerability of the laminated structures to the superharmonic vibrations and to reduce as far as possible the amplitude vibrations achieved by more appropriated structural design. The results reveal the effect of the slenderness of the sandwich beams on the hardening changes. In the other hand the results demonstrate the importance of fibre orientation angle to reduce as far as possible the amplitude responses of the sandwich structures in superharmonic vibration case.

Bending analysis of laminated sandwich plates under hygrothermal loadings

Abstract In present work, hygrothermal based analysis of laminated composite and sandwich plates is carried out by using recently proposed finite element based higher-order zigzag theory. Present formulation satisfies transverse shear stress continuity condition at top and bottom surface of the plate. Also, the model satisfies transverse shear stress free condition at the bottom and top surface of the plate. A nine-noded C-0 Lagrangian finite element having eleven degrees of freedom per node is used during study. Proposed model is free from any kind of inclusion of penalty function. Effectiveness of the present model is carried out by comparing the present results with those available in the literature.