Lamination Schemes Research Articles

Performance analysis of uncoated and coated (TiN-, TiAlN-) carbide drills in drilling graphene-reinforced GF/epoxy nanocomposites: Analytical and experimental study

The present study aims to investigate the performance of conventional uncoated and coated (TiN, TiAlN) solid carbide drill tools in drilling bi-directional graphene-reinforced (2 wt.%) glass fiber (GF)/epoxy polymer nanocomposite laminate with two distinct lamination schemes ([0/90]12S and [0/90/±45]6S). Performance measures included thrust force, torque, tool flank wear, peak acoustic emission, root mean square (RMS) of acoustic energy, and average surface roughness. Moreover, the delamination that occurs beyond the critical value of thrust force (computed analytically) has also been addressed. Optimized drilling parameters were used for experimentation to minimize thrust force and torque simultaneously. Both TiN and TiAlN-coated carbide drills outperformed uncoated carbide drills for fewer holes (around 25 for TiN and about 40 for TiAlN), but their performance deteriorated with more holes due to coating chipping or peeling from the original tool material. The (0/90 ± 45)6S graphene-reinforced layup showed less tool wear, deterioration, and acoustic emission energy compared to the (0/90)12S neat layup. TiAlN-coated drills exhibited the smallest wear on the flank face followed by TiN-coated and uncoated carbide drills. Moreover, the smoothest cut surface throughout the 300 holes drilled, averaging 1.5 µm to 1.8 µm in surface roughness, was observed with the TiAlN-coated drill. Therefore, the TiAlN-coated drill is recommended for drilling a larger number of holes due to its reduced tool wear, smoother cut surfaces, and better form accuracy with minimal delamination.

On the bending, buckling and free vibration analysis of bio-inspired helicoidal laminated composite shear and normal deformable beams

The mechanical behaviours of bio-inspired helicoidal symmetric laminated composite (BIHLC) beams are investigated via the Ritz method. By exploiting the variational formulation, equations of motion along with element stiffness, geometrical stiffness, and mass matrices are derived. The study conducts a thorough examination, covering bending, buckling stability, and free vibration analyses of BIHLC beams with various lamination schemes. The developed model is verified against existing literature on conventional composite laminated and BIHLC beams. The study also examines the mechanical response of BIHLCs, considering boundary conditions, lamination schemes, orthotropy ratios, and aspect ratios. Notably, deflections, critical buckling loads, and fundamental frequencies demonstrate variations dependent on the specific lamination scheme, boundary condition, and aspect ratio. Novel findings, presented for the first time, offer valuable insights for future studies in this area.

Experimental and numerical investigation of the modal parameters for thin laminated composite plates

In the present work, glass fiber-reinforced (GFR) composite specimens were fabricated using the vacuum-bag molding process. The properties related to the vibrational response of the fabricated composite plates, such as natural frequency, modal density, and damping loss factor (DLF), were investigated through both experimental and numerical approaches. The effects of different parameters, including boundary conditions (BCs), fiber orientations, laminate layer numbers, and aspect ratios, were comprehensively studied. It was found that the experimental and numerical results were in close agreement. For each case, finite element analysis was performed to determine the natural frequencies and mode shapes. Regarding the various BCs, the DLF was observed to be highest (0.47) for fully clamped BC and lowest (0.12) for free-free BC, whereas the modal density was highest (0.068) for cantilever BC and lowest (0.037) for fully clamped BC. In terms of different lamination schemes, the DLF was highest (0.42) for a plate with quasi-isotropic fibers and lowest (0.25) for a plate with unidirectional fibers, while the modal density was highest (0.068) for quasi-isotropic fibers and lowest (0.047) for unidirectional fibers. Regarding the plates with different laminate layers, the highest DLF (0.47) was observed for a plate with 16 layers, while the lowest DLF (0.33) was found in a plate with 8 layers. Conversely, the highest modal density (0.067) was observed for a plate with 8 layers, and the lowest (0.057) was noted for a plate with 16 layers. Lastly, considering aspect ratios, the highest DLF (0.48) was observed for an aspect ratio of 0.5, and the lowest (0.26) for an aspect ratio of 1.5. The highest modal density (0.09) was also observed for an aspect ratio of 0.5, while the lowest modal density (0.045) was for an aspect ratio of 1.5.

3D electro-elastic static analysis of advanced plates and shells

The proposed three-dimensional (3D) coupled electro-elastic shell model allows the static analysis of smart structures embedding classical piezoelectric and functionally graded piezoelectric layers. Plates, cylindrical and spherical panels are investigated in both sensor and actuator configurations. The primary variables of the coupled model are displacement components and the electric potential. Therefore, displacements, stresses, strains, electric potential and electric displacements are calculated for smart structures used as sensors (applied mechanical load) and smart structures used as actuators (applied electric potential). In the case of spherical shells, 3D equilibrium equations are coupled with the 3D divergence electric displacement equation. The obtained coupled system is also valid for cylindrical shells and plates thanks to the use of a mixed curvilinear orthogonal reference system. The partial differential governing equations are solved using the Navier harmonic form and the exponential matrix method for simply supported structures. Preliminary assessments are proposed to validate the model and further benchmarks are analyzed to discuss the effects connected with the thickness ratio, the lamination scheme, the load conditions, the geometry of the structures and the employed materials. The main innovation point of the proposed model is the possibility to analyze several geometries including different materials and applied loads by means of a unique and general formulation where partial differential equations are solved in closed form. The use of functionally graded piezoelectric materials allows to eliminate all stress component discontinuities at each layer interface.

Bone healing under different lay-up configuration of carbon fiber-reinforced PEEK composite plates.

Secondary healing of fractured bones requires an application of an appropriate fixator. In general, steel or titanium devices are used mostly. However, in recent years, composite structures arise as an attractive alternative due to high strength to weight ratio and other advantages like, for example, radiolucency. According to Food and Drug Administration (FDA), the only unidirectionally reinforced composite allowed to be implanted in human bodies is carbon fiber (CF)-reinforced poly-ether-ether-ketone (PEEK). In this work, the healing process of long bone assembled with CF/PEEK plates with cross- and angle-ply lay-up configurations is studied in the framework of finite element method. The healing is simulated by making use of the mechanoregulation model basing on the Prendergast theory. Cells transformation is determined by the octahedral shear strain and interstitial fluid velocity. The process runs iteratively assuming single load cycle each day. The fracture is subjected to axial and transverse forces. In the computations, the Abaqus program is used. It is shown that the angle-ply lamination scheme of CF/PEEK composite seems to provide better conditions for the transformation of the soft callus into the bone tissue.

Seismic performance of various types of cold-formed steel composite shear walls with CFRP-toughened screw connections

The cracking of screw connections at the corners of wallboards is a typical failure mode for cold-formed steel (CFS) shear walls, resulting in premature performance degradation of CFS structures. A toughening method with carbon fiber reinforced polymer (CFRP) sheets at screw connection locations is proposed for strengthening the CFS shear walls. Totally 6 full-scale CFS shear walls with or without CFRP-toughened connections were tested, and the parameters of the lamination scheme, wallboard type and screw distance were investigated. A numerical model is developed for simulating the seismic behaviour of the tested specimens, and a theoretical model for predicting their shear strength is proposed. Results showed that the shear strength and lateral stiffness of the CFS walls with CFRP-toughened screw connections increased by more than 30 %, and the continuous lamination scheme provided greater strength. The fastener-based numerical model could effectively be used for predicting the hysteretic performance of toughened CFS shear walls well; both the pinch behaviour and ultimate strength are predicted well, and it can be used as an effective tool for the seismic design of toughened CFS shear walls with a theoretical model.

Free and Forced Vibration Analysis of Carbon/Glass Hybrid Composite Laminated Plates Under Arbitrary Boundary Conditions

This paper presents the theoretical investigations on the free and forced vibration behaviours of carbon/glass hybrid composite laminated plates with arbitrary boundary conditions. The unknown allowable displacement functions of the physical middle surface are expressed in terms of standard cosine Fourier series and sinusoidal auxiliary functions to ensure the continuity of the displacement functions and their derivatives at the structural boundaries. Arbitrary boundary conditions are achieved through the introduction of an artificial spring technique. The first shear deformation theory and Lagrange equations are utilized to derive the energy expression, and the eigenvalue equations associated with free and forced vibration are obtained by Rayleigh-Ritz variational operations. Subsequently, these equations are then solved to determine the natural frequency, mode of vibration, and the steady-state displacement response under forced excitation. The new results are compared with those from references and finite element methods to verify the convergence, accuracy and efficiency of the analytical method. The effects of hybrid ratios, stacking sequences, lamination schemes, fibre orientation, boundary conditions and excitation force on the free and forced vibration behaviours of the carbon/glass hybrid composite laminated plates are analyzed in detail.

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.

Free vibration analysis of laminated anisotropic doubly-curved shell structures reinforced with three-phase polymer/CNT/fiber material

The present work investigates the vibrational response of laminated anisotropic doubly-curved shell structures reinforced with Carbon Nanotubes (CNTs) short fibers. The fundamental equations are derived from a curvilinear reference system of principal coordinates, employing the Equivalent Single Layer (ESL) methodology. Furthermore, a general variation in laminate thickness is considered. The unknown field variable is described using higher order theories through the unified formulation, taking into account a general interpolation of the unknown variables with Lagrange polynomials across the physical domain. The Hamiltonian Principle is adopted for the derivation of the dynamic equilibrium equations, which arediscretized numerically by using the Generalized Differential Quadrature (GDQ) method. In addition, an efficient isogeometric NURBS-based mapping is adopted for the distortion of the physical domain. The boundary conditions of the differential problem are modelled through a general distribution of linear elastic springs along the lateral surfaces of the three-dimensional doubly-curved solid. The theory is then applied to study the vibrational modes of structures with different curvatures and lamination schemes, taking into account a general distribution of CNTs along the thickness direction. The homogenized properties of CNTs layers are obtained from the Mori-Tanaka procedure, which accounts for the agglomeration effects of the dispersed nanofibers within the matrix. Unlike previous studies focusing on doubly-curved shells reinforced with composite materials and CNTs, the present formulation enables to derive the vibration characteristics of structures made of generally anisotropic materials with general orientations. Furthermore, the calibration of the parameters for the linear elastic springs’ distribution leads to general external constraints within a single element, thus reducing the computational cost of the problem.

Transient analysis of bio-inspired shear and normal deformable laminated composite plates using a higher-order finite element model

A study based on the transient responses of bio-inspired helicoidal laminated composite plates is performed by using a higher-order finite element model (HOFEM) consisting of the thickness stretching effect. The obtained results show good agreement with those available in the open literature. The shear locking phenomena is not inspected by employing the developed HOFEM for the helicoidal lamination schemes. The effects of path of the concentrated moving load, lamination scheme, boundary condition, speed, aspect and orthotropy ratios on the transient responses are investigated. Dynamic dimensionless center deflections and dynamic amplification factors are affected by considering not only the lamination scheme but also the path of the load, boundary condition, orthotropy and aspect ratios.

Free vibration analysis of composite beams and laminated reinforced panels by refined dynamic stiffness method and CUF-based component-wise theory

This paper presents a comprehensive analysis of the free vibration behavior of composite beams and laminated reinforced panels. Employing high-order theories with displacement variables only, the investigation combines dynamic stiffness method (DSM) and the Carrera unified formulation (CUF). The 3D displacement field can be expanded in the framework of CUF as any order of generic unknown variables over the cross-section, in the case of beam theories. Specifically, Lagrange expansions (LE) of cross-sectional displacement variables are considered, enabling the refinement modeling of complex cross-sections with different layers (layer-wise) and components (component-wise). The governing differential equations and natural boundary conditions are derived using the principle of virtual displacements. Subsequently, an exact dynamic stiffness matrix is developed by establishing a relationship between the amplitudes of harmonically varying loads and the corresponding responses. The Wittrick–Williams algorithm is employed to solve the transcendental eigenvalue problem resulting from this approach. The Lagrange-based CUF(LE)-DSM outperforms other polynomials (such as Taylor)-based CUF in analyzing composite structures, enabling detailed analysis with various geometries, lamination schemes and boundary conditions. It delivers accurate results in reinforced panel analysis, requiring only 13% of the DOFs compared to 3D FE models, thereby reducing computational costs significantly, as confirmed by comparative studies and validations.

Equivalent layer-wise theory for the hygro-thermo-magneto-electro-elastic analysis of laminated curved shells

The paper presents a multifield formulation involving five different physical problems under the equilibrium thermodynamic conditions for laminated doubly-curved shell structures. More specifically, the study focuses on the coupling between the mechanical elasticity and the thermo-hygrometric problem, while also considering the magneto-electricity of the solid. The configuration variables are described with a generalized formulation based on the Equivalent Layer Wise (ELW) approach, taking into account higher order polynomial interpolations along the thickness direction. The fundamental relations are derived from the Master Balance principle and solved using the Navier's method. Furthermore, the three-dimensional response of the doubly-curved shell solid in terms of primary and secondary variables is recovered from the two-dimensional solution with a methodology based on the three-dimensional multifield balance equations and the Generalized Differential Quadrature (GDQ) numerical technique. Some examples are then presented in which panels of different curvatures and lamination schemes are investigated. The results are compared with success to those coming from three-dimensional numerical models developed with a commercial software. It is shown that the present analytical solution is a valid tool for modelling multifield problems for the evaluation of the response of doubly-curved shells under generalized external actions and pre-determined values of the configuration variables.

Thermo-Mechanical analysis of laminated Doubly-Curved Shells: Higher order Equivalent Layer-Wise formulation

The paper presents a refined two-dimensional formulation for the thermo-mechanical analysis of laminated doubly-curved shell structures under thermodynamic equilibrium conditions. Both the kinematic configuration variables and the temperature variation with respect to the natural equilibrium state are described with a generalized formulation, following the Equivalent Layer-Wise (ELW) approach employing higher order polynomials, along with some proper zigzag functions. The governing equations are derived from the stationary configuration of the Helmholtz free energy of the system, and a semi-analytical solution is found. In the post-processing phase, the Fourier-based Generalized Differential Quadrature (F-GDQ) is applied to recover the actual three-dimensional response of the doubly-curved shell solid, and very accurate results are obtained for the quantities of both mechanical and heat conduction problems. In addition, the integrals occurring in the theory are performed numerically with the Taylor-based Generalized Integral Quadrature (GTIQ), showing a high level of accuracy with a reduced number of sample points. The model is validated in some case studies, where the accuracy of the model is shown, and the numerical predictions are successfully compared with those ones from refined three-dimensional numerical simulations. After that, an extensive set of parametric investigations is reported, pointing out the effects of the panel curvature, lamination schemes and different levels of coupling on the thermo-mechanical structural behavior of the investigated panels.

Comprehensive analysis of bio-inspired laminated composites plates using a quasi-3D theory and higher order FE models

A comprehensive study is carried out by employing various finite element models (FEMs) for the bending, buckling stability and free vibration analyses of bio-inspired helicoidal composite plates with various lamination schemes. A higher order quasi-3D kinematic plate theory is developed to include a shear deformation effect. The variational formulation of the problem is exploited to derive the equations of motion, element stiffness, geometrical stiffness, and mass matrices based on a non-conforming rectangular element. Three different finite elements models are derived based on non-conforming elements with different number of nodes and degree of freedom. The developed finite element model has been validated with those found in the open literature. The effects of boundary condition, lamination scheme, orthotropy ratio and aspect ratio on the mechanical response of the bio-inspired helicoidal composite plates are examined. Notably, for the lamination schemes investigated in this study, no shear locking phenomenon was observed in the analyses conducted using these FEMs. Dimensionless centre deflections, critical buckling loads and fundamental frequencies of bio-inspired helicoidal composite plates vary depending on the type of lamination scheme, boundary condition and aspect ratio. The new orientation schemes can replace the traditional ones to overcome the shear singularity and overcome the delamination defects.

On the Importance of the Recovery Procedure in the Semi-Analytical Solution for the Static Analysis of Curved Laminated Panels: Comparison with 3D Finite Elements.

The manuscript presents an efficient semi-analytical solution with three-dimensional capabilities for the evaluation of the static response of laminated curved structures subjected to general external loads. A two-dimensional model is presented based on the Equivalent Single Layer (ESL) approach, where the displacement field components are described with a generalized formulation based on a higher-order expansion along the thickness direction. The fundamental equations are derived from the Hamiltonian principle, and the solution is found by means of Navier's approach. Then, an efficient recovery procedure, derived from the three-dimensional elasticity equations and based on the Generalized Differential Quadrature (GDQ) method, is adopted for the derivation of the three-dimensional solution. Some examples of investigation are presented, where the numerical predictions of refined three-dimensional Finite-Element-based models are matched with a high level of accuracy. The model is validated for both straight and curved panels, taking into account different lamination schemes and load shapes. Furthermore, it is shown that the numerical solution to the elasticity problem in the recovery procedure is determining and accurately predicting the three-dimensional static response of the doubly-curved shell solid.

Nonlinear periodic response of viscoelastic laminated composite plates using shooting technique

The nonlinear periodic response of viscoelastic laminated composite plates subjected to harmonic excitation is carried out in time domain using the generalized Maxwell model in the form of a Boltzmann integral. The integral form of the viscoelastic constitutive relation is converted to the incremental form for the finite element formulation based on the Reissner–Mindlin plate theory incorporating von Karman geometric nonlinearity. The recursive relations are developed to compute the current time-step solution using only the previous time-step solution. The periodic response is obtained using shooting technique coupled with Newmark’s time integration and arc length continuation method. The implementation of the shooting technique for the Boltzmann Integral based viscoelasticity done for the first time in this study involves derivation of a number of additional recursive relations and initial conditions at the beginning of each shooting cycle. The nonlinear periodic vibration characteristics such as frequency response, damping factor, steady-state response history, phase plane plots, and frequency spectra are presented for viscoelastic plates with different boundary conditions and lamination schemes. Further, the influence of relaxation time and number of Maxwell elements on the frequency response characteristics are investigated. It is seen that the shooting technique is capable of predicting periodic responses of viscoelastic dynamical systems directly from the second-order equations of motion and is more efficient than the direct time integration method. The nonlinear response of viscoelastic plates predicted using the equivalent elastic model with Rayleigh proportional damping (having same linear frequency response) is found to be significantly different from the one predicted using viscoelastic constitutive model.

Analitičko ispitivanje poroznih laminiranih ploča od funkcionalno gradiranih kompozita ojačanih ugljeničnim nanocevima (FG-CNTRC) na izvijanje i slobodne vibracije

Introduction/purpose: The aim of this study is to examine the buckling and free vibration behavior of laminated composite plates reinforced with carbon nanotubes when various sources of uncertainty are taken into account with 1 the main focus being the existence of porosity. Methods: A porous laminated plate model is developed using a high order shear deformation theory. Different configurations of functionally graded aligned single-walled carbon nanotubes throughout the thickness of each layer are being investigated. The effective properties of materials are evaluated through the extended rule of mixture while considering an upper bound for the effect of porosity. The governing equations are derived and solved using the virtual work principle and Navier's approach. The validity of the current formulation is confirmed by comparing the results with the existing data from literature sources. The impact of numerous parameters such as porosity, carbon nanotube volume fraction, reinforcement distribution types, lamination scheme, and the number of layers on the buckling and free vibration responses is investigated in detail. Results: A key finding of this study is the significant reduction in buckling resistance of laminated FG-CNTRC plates due to porosity, contrasting with the minor impact on the free vibration response. Conclusion: The results of this paper emphasize the critical role of porosity in structural integrity and provide novel insights into the behaviour of advanced composite materials.

Parametric design and modeling method of carbon fiber reinforcement plastic-laminated components applicable for multi-material vehicle body development

Abstract Combined application of steel, aluminum, and carbon fiber reinforcement plastic (CFRP) is the main direction of future lightweight body development. However, the anisotropy and additional lamination design variables of CFRP parts pose significant challenges for the development of multi-material bodies. This study establishes a parametric design method for the variable-thickness lamination scheme based on non-uniform rational B-splines, it can be coupled with existing parametric design methods for structural shapes to formulate a complete parametric design and modeling of CFRP components. On this basis, a homogenized intermediate material property is derived from classic laminate theory by introducing lamination assumptions, it enables a stepwise multi-material body optimization method to solve the challenge that components’ material design variables switching between CFRP and alloy will introduce/eliminate lamination design variables iteratively, posing a great optimization convergence difficulty. The proposed parametric modeling method for CFRP components was validated by experimental tests of a fabricated roof beam, and the proposed optimization method was applied to a vehicle body, achieving 15.9%, 23.9%, 18.6%, and 12.2% increase in bending and torsional stiffness and modal frequencies; 20.2%, 9.3%, and 12.7% reduction of weight and peak acceleration in frontal and side collisions. This study enables the forward design of multi-material bodies compatible with CFRP parts.

Higher order theories for the modal analysis of anisotropic doubly-curved shells with a three-dimensional variation of the material properties

The manuscript investigates the dynamic properties of doubly-curved shell structures laminated with innovative materials employing the Generalized Differential Quadrature (GDQ) method. A higher order generalized expression of the displacement field variable is assumed following the Equivalent Single Layer (ESL) approach. The geometrical description of the structures follows the differential geometry basics, whereas arbitrarily-shaped domains are distorted by means of generalized isogeometric blending functions. A three-dimensional generally anisotropic elastic constitutive behaviour is assumed within each layer of laminates, and a smooth variation of the material properties is implemented. In particular, a two-dimensional distribution alongside the physical domain is considered, whereas a through-the-thickness dispersion of the material properties is associated to each layer, taking into account both polynomial and non-polynomial analytical expressions. The fundamental equations are derived from the Hamiltonian principle, and they are solved directly in strong form via the GDQ method taking into account a non-uniform discrete computational grid. After some preliminary validating examples, some parametric investigations are performed systematically, showing the influence of the variation of the material properties on the modal response of the structures characterized by different lamination schemes, curvatures and boundary conditions. The proposed model allows for the dynamic analysis of the structures of different curvatures characterized by very complicated dispersions of the material properties following a simple and accurate methodology.

Thermal Stress Analysis of Composite Laminates using Trigonometric Shear Deformation Theory and Finite Element Method

Laminated composite materials offer a versatile design approach for achieving the desired levels of stiffness and strength by selecting specific lamination schemes. The Trigonometric Shear Deformation Theory (TrSDT) effectively addresses the appropriate distribution of transverse shear strains throughout the plate thickness while maintaining stress-free boundary conditions on the plate's top surfaces. Consequently, there is no need for a shear correction factor. In this research paper, we use the Trigonometric Shear Deformation Theory (TrSDT) that takes into account the influence of transverse shear deformation. The in-plane displacement field incorporates a sinusoidal function with respect to the thickness coordinate to accommodate the effects of shear deformation. Theories that involve trigonometric functions based on the thickness coordinate in the displacement fields are collectively referred to as Trigonometric Shear Deformation Theories (TrSDTs). In the present study, we conduct a thermal stress analysis of Laminated Composite Plates using the TrSDT. This theory eliminates the need for shear correction factors and provides a more accurate distribution of interlaminar stresses compared to other methods like CPT and FOST. We assess deflection and stress at various locations and for different aspect ratios under thermal loads using TrSDT. Stress evaluations are carried out analytically, and the results are validated by comparing them with existing findings from the literature. To further verify our findings, we model a composite laminate under thermal loads using the commercial Finite Element Method tool ABAQUS, and our results are validated against those obtained with the TrSDT for plates with simply supported boundary conditions.