Transverse Loading Conditions Research Articles

Investigation of the transverse compressive and buckling strength of aluminium grid reinforced hybrid GFRP composite

This work is concerned with the effect of addition of aluminium grid in Glass Fibre Reinforced Polymer Matrix Composite (GFRP) on the transverse compressive and buckling (axial) compressive strength of the composite. The 5-layered cylindrical composite consisting of alternate layers of bidirectional E-glass fibres and aluminium grid in an epoxy matrix, were fabricated using hand lay-up technique and subjected to transverse compressive and axial compressive (buckling) loads. Non-linear stress – strain response was achieved in transverse and axial loading conditions due to the yielding of the aluminium fibres. Fractography studies revealed that the brittle failure of the glass fibres and the yielding of aluminium fibres resulted in fibre rotation and shear distortion that helped to dissipate the crack propagation energy thereby increasing the strain to failure. This method may be effectively used to arrest the crack propagation that might develop as leakage cracks in composite pipes, enabling the hybrid composite to be used for underground pipelines in chemical and offshore platform applications

Dynamic properties and damping predictions for laminated plates: High order theories – Timoshenko beam

The main aim of this study is to predict the elastic and damping properties of composite laminated plates. This problem has an exact elasticity solution for simple uniform bending and transverse loading conditions. This paper presents a new stress analysis method for the accurate determination of the detailed stress distributions in laminated plates subjected to cylindrical bending. Some approximate methods for the stress state predictions for laminated plates are presented here. The present method is adaptive and does not rely on strong assumptions about the model of the plate. The theoretical model described here incorporates deformations of each sheet of the lamina, which account for the effects of transverse shear deformation, transverse normal strain-stress and nonlinear variation of displacements with respect to the thickness coordinate. Predictions of the dynamic and damping values of laminated plates for various geometrical, mechanical and fastening properties are presented. Comparison with the Timoshenko beam theory is systematically made for analytical and approximation variants.

Analytical predictions of delamination threshold load of laminated composite plates subject to flexural loading

An analytical approach is proposed to determine delamination threshold loads of fiber-reinforced laminated composite plates with arbitrary stacking sequences under transverse loading conditions. Following the concept of cohesive zone modeling, a laminated plate is considered as an assembly of two sub-laminates connected by a virtual elastic-brittle layer with infinitesimal thickness. The problem is formulated and solved by the Rayleigh-Ritz method based on first-order shear deformation theory. The problem of quasi-static face-on (transverse) indentation test is analyzed as an example. The results, including elastic stiffness of flexural response, traction distributions over the potential crack interface, and threshold loads and initiating locations of delamination, are found to be in very good agreement with finite element simulations using cohesive elements. The modeling strategy, therefore, is useful for aerospace structural engineers at the preliminary design stage of laminated composite aerospace structures.

Vibration, buckling and bending behavior of functionally graded multi-walled carbon nanotube reinforced polymer composite plates using the layer-wise formulation

Polymer matrix nanocomposites reinforced with uniformly dispersed and randomly oriented multi-walled carbon nanotubes (MWCNTs) are identified as excellent candidates for functionally graded structural members. This paper presents static and dynamic behavior of functionally graded polymer composite plates reinforced by randomly oriented multi-walled carbon nanotubes using novel layer-wise formulation concept. The weight fraction of MWCNTs in functional graded plate is represented by layer-wise variation along the thickness and MWCNTs are considered as uniformly dispersed in each layer. The effective elastic modulus of nanocomposite plate is predicted with modified Halpin-Tsai model, while the Poisson’s ratio and density are determined by rule of mixtures. System of governing equations are derived based on generalized higher order shear deformation (HSDT) plate theory and Navier technique is employed to obtain the solution for free-vibration, buckling and static bending problems of simply supported plates under axial and transverse loading conditions at various aspect-ratios. In order to understand the effect of important reinforcement and plate parameters on the natural frequencies, critical buckling loads and bending deflections, different parametric studies are conducted. Results reveal that different types of weight distributions have significant influence on structural characteristics.

Numerical investigation of fiber random distribution on the mechanical properties of yarn in-plain woven carbon fiber-reinforced composite based on a new perturbation algorithm

Interior fibers in yarns of plain woven carbon fiber-reinforced composite are distributed randomly, which further influences the mechanical properties of yarns. To explore the stochastic nature of fibers’ distribution in yarn and its effect on the properties of yarn, this study proposes a new perturbation algorithm named Sequential Random Perturbation algorithm to reconstruct the microstructure of randomly distributed fibers, based on which representative volume element micromechanical models consisting of three phases to accurately predict the mechanical properties of yarn are established. The algorithm is based on successive smart perturbations of fibers to gain microstructures of arbitrary volume fraction, and statistical study shows that the algorithm is in good agreement with experimental results. Finally, representative volume element models are simulated to predict the whole mechanical properties of composite yarns to reflect the failure mechanisms and microstructure–property relations. The randomness of fiber distribution has some degree of influence on mechanical properties of yarn, especially strength responses. The failures under axial tension and compression are dominated by fiber breakage, while under transverse and shear loading conditions, the failures are mostly decided by interface debonding and matrix damage.

Mode I transverse intralaminar fracture in glass fiber-reinforced polymers with ductile matrices

The fracture toughness of laminated composite materials is a very important property for damage-tolerant design, but remains poorly understood under transverse mechanical loading conditions. In this study, the transverse intralaminar fracture in unidirectional laminates with ductile polymer matrices is investigated. The presence of a ductile matrix calls for the use of concepts of nonlinear fracture mechanics for the accurate determination of the resistance of the composite to crack propagation. Unidirectional glass fiber-reinforced polymers with a polyurethane (PU) matrix are studied and compared to a benchmark epoxy (EP). The fracture toughness of these composites was evaluated through the determination of R-curves using the J-integral method, whereas the underlying fracture mechanisms were investigated through in situ testing in a scanning electron microscope. The results suggest stronger adhesion of the polyurethane matrix onto the glass fibers as compared to the epoxy-based polymer. This enables full exploitation of the ductile behavior of the PU matrix, ultimately endowing the laminate with outstanding fracture toughness. The investigated PU matrix has thus the potential to generate laminated composite parts with significantly higher damage tolerance than its epoxy counterpart.

Bending and buckling analysis of corrugated composite sandwich plates

In this paper, bending and buckling behavior under uniaxial load of corrugated soft-core sandwich plates with laminated composite face sheets are explored. To this aim, analyses via three-dimensional finite element method are performed using ANSYS 12.0. The core is assumed as a soft isotropic material completely bonded to two stiff laminated composite face sheets. In particular, linear uniaxial critical buckling loads of sandwich plates with sinusoidal and trapezoidal corrugation are analyzed. The through-thickness displacement, normal and shear stresses at the important points of the sandwich plates under uniform transverse loading conditions are obtained. A series of numerical solutions are performed to study the contribution of corrugation shape, face sheet lay-up architecture, boundary conditions and length/thickness ratio of the plate on the bending behavior and linear uniaxial buckling loads of the sandwich plates. For the sake of verification, the linear uniaxial critical buckling loads of the corrugated sandwich plates are then compared with those of flat sandwich plates previously reported in the literatures. It has been shown that the linear uniaxial buckling capacity of sandwich plates is considerably improved by introducing corrugation on both face sheets. The improvement was found to be more significant in the case of trapezoidal corrugation than that of sinusoidal one. Moreover, comparing with corrugated sandwich plates, the contribution of the lay-up architecture to linear uniaxial critical buckling load was negligible in the case of plates with constant thickness.

Virtual Design, Modelling and Analysis of Functionally graded materials by Fused Deposition Modeling

Functionally graded material answers the need of material incompatibility in the area of additive manufacturing. In this work virtual design, modelling and analysis of functionally graded material (FGM) is achieved. Based upon the relationship of material properties with process parameters of fused deposition modelling (FDM) process, tailor made properties are assigned to components in different regions. FGM is proposed and is subjected to transverse loading conditions. This is accomplished by actual CAD modelling and analysis using ANSYS 14. Encouraging results in direction of FGM fabrication are obtained at the end of this research. It is observed that the proposed FGM exhibits around 51% reduction in deformation for transverse loading conditions as compared to the component obtained at default Modeller settings. This work can very easily be extended in the direction of each mechanical property to customize materials for specific applications.

Stress concentration and deflection in isotropic and orthotropic plates with opening. Finite element study

In this paper, stress concentration factors (SCFs), in-plane displacements and transverse deflection in orthotropic as well as in isotropic plates with central circular cutouts were studied. This study was made by using a quadrilateral finite element with thirty-two degrees of freedom. The element is a combination of a linear isoparametric membrane element and a high precision rectangular Hermitian element. The main objective of this study is to demonstrate the accuracy of the present element for analyzing the effect of (d/b) ratio (where (d) is hole diameter and (b) is plate width) upon (SCFs), in-plane displacements and transverse deflection in isotropic and orthotropic plates under different in-plane and transverse static loading conditions. Also, in order to understand the effect of the support conditions on the transverse deflection, different plates with various (d/b) ratios are studied. The variations of in-plane displacements, stress concentration factor and transverse deflection with respect to (d/b) ratio are presented in graphical form and discussed. The numerical results obtained by the present element are compared favorably with the analytic solutions, which demonstrate the accuracy of the present element.

Blast dynamics of beam-columns via analytical approach

Problems involving forced transverse vibrations of beam-columns have many applications in different fields of engineering. This paper presents an analytical procedure allowing the prediction of the blast dynamic response of a beam-column to a combined action of axial and transverse loads. The solution is based on the continuous formulation and the Euler–Bernoulli beam theory. The response of the beam-column in the quasi-static, dynamic and impulsive regimes is analysed using the developed analytical model. The analysis shows that the number of modes of vibration needed to produce an accurate estimate of the beam-column behaviour may vary depending on the loading regime. Various types of spatial load distributions and time histories of transverse loads commonly used in engineering practice for modelling of extreme loads are discussed. The significance of the axial force and the shape of the transverse load time history for the beam-column response is shown using the response spectrum and pressure–impulse diagram methods. The initial imperfections in the beam-column geometry and applied loads are introduced into the analysis and their effects are also examined. The results obtained by the analytical model are compared to the results of a nonlinear finite element analysis performed in ABAQUS. Certain discrepancies between the beam-column response yielded by the analytical solution and the finite element model were observed at high levels of axial force and quasi-static transverse loading conditions.

Linear Analysis and Non-linear Analysis with Co-Rotational Formulation for a Cantilevered Beam under Static/Dynamic Tip Loads

Abstract In this paper, the behaviour of a cantilevered beam was predicted to examine the difference between linear and non-linear static, dynamic analysis for a structure by using CR nonlinear formulation. Then, external transverse static and dynamic loads were applied at the free tip of the beam. Classical theories were used for the present linear analysis and co-rotational dynamic FEM program was used for the present nonlinear analysis. In the static analysis, effects of the load for the beam deflection were observed in both linear and nonlinear analysis. Then, normalized displacement at the tip of the beam was predicted for different frequency ratio and a significant difference was obtained in the vicinity of the resonant frequency. In addition, effects of frequency and time for the beam deflection were investigated to find the frequency delay. Keywords :linear analysis, nonlinear analysis, two-dimensional beam, natural frequency, harmonic excitation, co-rotational dynamic FEM, static analysis, frequency delay

Influence surfaces by boundary element/least square methods coupling

This work presents a new application for calculating the influence surfaces of transverse displacements, directional derivatives and bending moments for generic bridge decks. A plate bending boundary element method formulation is coupled with the application of a continuous field surface derived by the least square procedure. This original BE formulation permits calculating influence surfaces of plates with polygonal, curved or circular geometry, and several transverse load conditions. The proposal allows future analysis of building floors and single and continuous bridge trusses connected to longitudinal and transversal girders. Numerical examples are presented to demonstrate the potential of the present formulation and the results are compared with analytical values and with usual vehicular loads.

Análise Numérica do Comportamento Mecânico de Placas Finas Perfuradas de Materiais Compósitos sob Flexão

Este trabalho busca analisar numericamente o comportamento mecânico de placas de dois materiais compósitos submetidas à flexão causada por um carregamento estático transversal uniforme, comparando com o comportamento de uma placa de material isotrópico. Todas as placas estudadas possuem uma perfuração elíptica centralizada. De acordo com o método Constructal Design, esse furo elíptico pode variar em função do parâmetro <em>H</em><sub>0</sub>/<em>L</em><sub>0</sub> (relação entre os semi-eixos da elipse), entretanto a relação entre o volume da perfuração e o volume da placa (<em>φ</em>) é mantida constante. Dessa maneira é possível avaliar a influência da geometria do furo no comportamento mecânico das placas, tendo como objetivo minimizar a deflexão sofrida pela placa. Além disso, foram consideradas ainda três condições de vinculação para as placas: apoiada nos quatro lados, engastada nos quatro lados e apoiada em dois lados e engastada nos outros dois. Um modelo computacional desenvolvido no software ANSYS, que é baseado no Método dos Elementos Finitos (MEF), foi empregado para simular numericamente a flexão nas placas. Os resultados mostraram que a geometria do furo pode influenciar de maneira significativa na performance das placas como componentes estruturais. Melhorias de até aproximadamente 115% foram obtidas para a deflexão máxima da placa.

On the effect of the backup plate stiffness on the brittle failure of a ceramic armor

The present investigation enquires the role of the backup plate mechanical properties in the brittle failure of a ceramic tile. It provides a full-field solution for the elastostatic problem of an infinite Kirchhoff plate containing a semi-infinite rectilinear crack (the tile) resting on a two-parameter elastic foundation (the backup plate) and subjected to general transverse loading condition. The backup plate is modeled as a weakly non-local (Pasternak type) foundation, which reduces to the familiar local (Winkler) model once the Pasternak modulus is set to zero. The same governing equations are obtained for a curved plate (shell) subjected to in-plane equi-biaxial loading. Fourier transforms and the Wiener–Hopf technique are employed. The solution is obtained for the case when the Pasternak modulus is greater than the Winkler modulus. Superposition and a two-step procedure are employed: First, an infinite uncracked plate subjected to general loading is considered; then, the bending moment and shearing force distribution acting along the crack line are adopted as the (continuous) loading condition to be fed in the solution for the cracked plate. Results are obtained as a function of the ratio of the Pasternak over the Winkler foundation stiffness times the tile flexural rigidity. It is established that the elastic foundation significantly affects the mechanical behavior of the elastic plate. In particular, the Winkler model substantially underestimates the stress state near the crack tip. Stress-intensity factors are determined, and they are employed as a guideline for increasing the composite toughness. The analytical solution presented in this paper may serve as a benchmark for a more refined numerical analysis.

Irreversible deformation of metal matrix composites: A study via the mechanism-based cohesive zone model

An elastic–plastic interface model at finite deformations is utilized to predict the irreversible deformation of metal matrix composites (MMCs) under the transverse loading and unloading conditions. The associated benefit of the cohesive model is to provide a physical insight on the main irreversible deformation mechanisms, i.e., the geometrically nonlinear, localized plastic deformation and damage induced debonding, at the interface of MMCs. The extensive parametric study is conducted using this cohesive model to investigate the effects of the cohesive parameters on the stress–strain response of MMCs under transverse loading. Further, the ductile mechanism of the matrix is considered to characterize the competition between the plastic flow of the matrix and the inelastic interface induced irreversible deformation. Moreover, the predictions using the cohesive model are compared with those available experimental data in the literature to demonstrate the inelastic behaviors, including the interfacial plasticity and damage induced debonding, as well as the plastic flow of the matrix. The numerical results of the stress–strain responses for both loading and unloading conditions show good agreements with those obtained by the experiment. The deformation and failure modes of MMCs predicted by the model are also consistent with the observations of the experiment.

Structural behavior of cast-in-place and precast concrete barriers subjected to transverse static loading and anchored to bridge deck overhangs

In this study, experimental testing was performed on cast-in-place and precast barriers subjected to quasi-static loading and anchored to 6 m long bridge decks with a 1 m overhang. The three select...

Stability and Nonlinear Vibrations of Closed Cylindrical Shells Interacting with a Fluid Flow (Review)

Results of systematic study of the stability and nonlinear vibrations of thin cylindrical shells interacting with a fluid flow are presented. The main patterns of dynamical deformation of shells during divergence and flutter are considered. The effect of different structural features (initial geometrical imperfections, added concentrated masses, boundary conditions, longitudinal and transverse static loads) on the critical (divergence and flutter) velocities is analyzed. The amplitude–frequency response of shells to external periodic radial loads and internal periodic pressure caused by small pulsations of the fluid velocity is determined. A method is proposed to solve nonlinear problems describing nonstationary processes of passing resonance zones by shells interacting with the fluid flow

622 軸直角方向負荷下のねじ締結体のすべり・ゆるみ挙動

The thread joint has been frequently used for the efficient productivity and maintainability as a machine element. However, many troubles such as loosening of bolted joints or fatigue failure of bolt were often experienced. Many attentions must be paid on the improvement of the strength and the reliability of the thread joints. It is generally said that the fastening axial force rapidly decreases by the rotation loosening of nuts if the relative slippage on the interfaces between nuts and fastened body goes beyond a certain critical limit. This critical relative slippage (Scr) that prescribes the upper limit for preventing the loosening behavior has been estimated according to the theoretically obtained equation considering the bending deformation of bolt and the geometrical constraint condition. In this paper, we present the investigated results of the deformation behavior of bolt-nut joint under transverse loading condition. The bending moment of bolt is measured by the quasi-static loading test. The reaction force moment by nut used in the equation for estimating the Scr is evaluated by the comparison of experimental and analytical results from estimated equation. The new equation for estimating the reaction force moment which agrees with measured value is examined and proposed.

Free-edge effect on the effective stiffness of single-layer triaxially braided composite

Abstract Free-edge effect is known to play an important role in the failure of triaxially braided composites, especially under transverse tension loading conditions. However, there is little understanding available regarding the free-edge effect on the elastic property of the material. The emphasis of the present study is to examine the impact of the free-edge effect on the effective elastic response of a single-layer triaxially braided composite. Transverse tension straight-sided coupon specimens with various widths are tested and analyzed. The experimental results demonstrate an obvious increase in the tangent modulus and failure strength as the specimen width increases. The surface out-of-plane displacement contours present a continuous out-of-plane warping behavior distributed periodically along the free edges in an antisymmetric way. A meso-scale finite element model is utilized to study the coupon specimens; it is found to correlate well with the experimental data in predicting elastic properties and out-of-plane warping behavior. The results indicate that free-edge effect is an inherent factor of the antisymmetric braided architecture of bias fiber bundles. By conducting a dimensional analysis, the relationships between effective moduli and specimen width are quantified using Weibull equations; this method could potentially be used to predict the material properties of large structural components using small-scale test data.

Effect of Joint Geometry on the Behavior and Failure Modes of Sandwich T-Joints Under Transverse Static and Dynamic Loads

Due to wide spread application of adhesive T-joints in various industries, a review of properties and strength of their fracture modes under static and dynamic loadings is required. By defining the ability of failure in the joint material and fracture of adhesive in the numerical model, fracture modes of sandwich T-joints have been investigated. This paper presents numerical results on the performance of sandwich T-joints subjected to static tensile, static transverse, and dynamic transverse loading. The results of available experiments in the literature have been used to validate the detailed numerical models capable of simulating the damage processes observed. In general, the failure load predicted by the finite element (FE) analysis is within 5% of the experimental results.