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A variant of the first-order shear deformation theory is presented for the flexure of shear deformable linear isotropic plates undergoing small deformations. The principle of stationary potential energy is utilized to obtain governing differential equations and variationally consistent boundary conditions. Unlike the Mindlin’s plate theory, the presented variant involves two coupled governing partial differential equations involving two unknown functions. This reduction will result in saving of the computational time involved for the plate boundary value problem, especially when external forces acting on the plate are variable/non-linear in nature. Solutions for the flexure of shear deformable isotropic plates by utilizing Levy’s method are obtained using analytical and numerical techniques. The fourth-order Runge–Kutta technique is utilized for obtaining numerical solutions. The effect of the plate thickness-to-length ratio on the flexure of shear deformable isotropic plates with two opposite edges simply-supported and remaining two edges having different combinations of boundary conditions are presented. These results are compared with corresponding results available in the literature.

A semi-analytical model is proposed for the stress and displacement analysis of all-round simply supported functionally graded (FG) piezoelectric laminated plates in this paper. Material electric a...

This study is motivated by the need to develop an efficient numerical model to simulate non-uniform interfacial degradation of reinforcing steel in concrete in an accelerated corrosion setup considering the influence of differential aeration, moisture and conductivity. In this study, a multi-physics finite element (FE) model is presented to simulate spatially and temporally non-uniform surface topography of corroding steel with rust layer, and eliminates the assumption of uniform mass loss and its linear variation with time as per available literature that uses classical approach of Faraday’s law. The model is validated experimentally with accelerated corrosion setup. Unlike previous studies, pore saturation (PS) is continuously monitored and its existing experimental correlations with conductivity and oxygen diffusivity are adopted so that the model can be extended to simulate natural corrosion to enhance the accuracy of service life predictions. These evaluations can be made completely nondestructive and in real-time eliminating the challenges in capturing the influence of environment by the use of alternative parameters such as relative humidity from real climate change predictions. The key findings from the investigation reveal that incorporating local environmental parameters measured in situ allows for the model to naturally evolve with anodic and cathodic locations on steel surface avoiding the need to assume predefined locations. It is envisioned that the developed multi-physics FE model can be used as a reliable substitute to accelerated corrosion experiment which is frequently used for durability studies of corroding reinforced concrete (RC) members. It is shown that the daily and cumulative mass loss evaluated from the degraded surface topography of the corroded rebar using the simulated model are in good agreement with those evaluated experimentally. Further, the maximum pit depth evaluated from the simulated surface is validated that has valuable applications in estimating degraded strength of corroding steel and service life of RC members.

In this paper, numerical results for flexure of shear-deformable isotropic square plates by utilizing recently proposed single variable new first-order shear deformation plate theory (SVNFSDT) are presented. For obtaining numerical results, fourth-order Runge-Kutta technique is used. It should be noted that the displacement functions of SVNFSDT give rise to constant transverse shear strains and hence constant transverse shear stresses through the plate thickness. Hence, similar to other first-order shear deformation plate theories reported in the literature, this theory also requires a shear correction factor. As opposed to Mindlin plate theory, SVNFSDT has only one fourth-order governing differential equation which is obtained by utilizing plate gross equilibrium equations. This theory presents physically meaningful boundary conditions. On similar lines of two-dimensional theory of elasticity approach for beam analysis, this theory also presents two different types of plate clamped edge boundary conditions. Illustrative examples presented in this paper consider Levy-type plates with two opposite plate edges simply supported and remaining two plate edges having either simply supported, clamped, or free boundary conditions with plate under the action of uniformly distributed transverse load. Numerical results for flexure of abovementioned cases of plates are presented for different values of plate thickness-to-length ratio. In order to demonstrate the efficacy of the presented numerical solution technique, obtained results are compared with corresponding results reported in the literature.

Flexural response of isotropic, orthotropic, and cross-ply laminated shear deformable plates has been presented in this paper using a new first-order shear deformation theory. The theory involves only two primary unknown functions, as compared to widely used Mindlin’s first-order shear deformation theory, which involves three primary unknown functions. This reduction in the number of primary variables make this theory simple and efficient to use. The principle of minimum total potential energy is utilised to obtain governing differential equations and variationally consistent boundary conditions. The Levy-type plates accompanied by the generalised segmentation technique is used to obtain the closed form analytical solution of isotropic, orthotropic and cross-ply laminated shear deformable plates with two opposite edges simply-supported and the other two edges having different combination of simply-supported, clamped and free boundary conditions. Comparative studies are performed to show the efficacy of the present theory. Effects of plate length-to-thickness ratio, aspect ratio and modulus ratio on transverse displacement and in-plane normal stresses are also presented and discussed. New benchmark solutions in the form of parametric study are presented for the future reference.

Three dimensional (3-D) elasticity solution is presented for simply supported functionally graded (FG) material plate by using a semi analytical approach . Formulation is based on solution of a two-point boundary value problem (BVP) governed by a set of coupled first order ordinary differential equations (ODEs) through thickness of plate. Fourth-order Runge–Kutta algorithm is used for numerical integration of these ODEs. A comprehensive comparison of the present formulation with other 3-D elasticity approaches available in the literature is also attempted. The proposed semi-analytical model is very simple, efficient and highly accurate. Both displacements and stresses are evaluated simultaneously with the same degree of accuracy which is the main feature of the present development.

In this work, the influence of uniaxial and biaxial nonuniform edge loads on buckling characteristics of composite laminates with and without cutout is investigated by using a finite element method. Furthermore, this investigation addresses the effects of different degree of edge restraints on buckling analysis. Regarding this, a nine node heterosis plate element has been adapted by employing the effects of shear deformation and rotary inertia. The influence of different parameters, such as ply-orientations, nonuniform edge loads, boundary conditions, and cutout sizes, has been considered and studied in detail. It is clearly illustrated that cutout sizes under different loading conditions have remarkable effects on buckling behavior of composite laminates.

Displacement and stress analysis of an all-round simply supported piezoelectric laminate has been carried out with a new model. Formulation part has been developed using elasticity approach and the methodology is free from any a-priory assumption in thickness direction. The mathematical model is a set of mixed first ordered ordinary differential equations (ODEs). Solution is obtained using numerical integration in through-thickness direction. Accuracy of the proposed model is assessed by comparing numerical results for single layer piezoelectric plate as well as for multi-layered laminates with exact solutions available in literature and are found to be in good agreement with the same. Additional investigation has been performed to establish a few future references. (C) 2016 Elsevier Ltd. All rights reserved.

Analytical solutions for laminated and functionally graded sandwich open cylindrical shells under mechanical and thermal loads are presented using a refined higher order shear and normal deformation theory. Temperature variation through thickness is assumed as thickness coordinate polynomial. Present study also extends the classical thickness criteria with more reliable extension to moderately thick shells. Navier solution method is used to solve system of equations derived using principle of minimum potential energy for all edges diaphragm supported. Two kinds of sandwich panels with core or face sheets made of thickness graded material are studied. Several examples are numerically evaluated to establish the accuracy of present models.

Buckling loads of laminated panels calculated by analytical approaches are usually based on the assumptions that the panels are subjected to uniform in-plane edge loads without cutouts, despite of the fact that real structural components are subjected to various kinds of non-uniform in-plane edge loads along with different sized cutouts. The main objective of this paper is to study the effects of reinforced/unreinforced circular cutouts and non-uniform in-plane edge loads on the buckling behavior of composite panels with different ply-orientations by the finite element technique. Furthermore, it addresses the effects of different boundary conditions and thickness of panels. To carry out the analyses, a nine-noded heterosis plate element and a compatible three-noded beam element are developed, including the effect of shear deformation and rotary inertia for both the plate and the stiffeners. In structural modeling, the plate and the stiffener elements are treated separately, with their displacement compatibility maintained using transformation matrices. It has been illustrated in this study that presence of larger-sized reinforced cutouts predominantly increases the buckling strength of the panel as compared to those with smaller sized cutouts.

Uneven distribution of fibers can adversely affect the mechanical behavior of unidirectional composites. A micromechanical model based on finite element analysis is presented to evaluate elastic and strength properties of such composites under normal loading. Analysis starts with identification of micro unit cells/micro repetitive unit cells and/or representative volume elements. Because of uneven distribution/random distribution of the fibers, fiber volume fraction can be different for different micro unit cells present at different locations in the transverse cross-section of the unidirectional composite. Configuration of the micro unit cell is worked out at the outset considering the fiber distribution having the hexagonal arrangement, but with different volume fraction at different locations. For such micro unit cells, elastic and strength properties are obtained based on finite element analysis starting with the elastic and strength properties of fiber and matrix. With the properties obtained for different micro unit cells, elastic and strength properties of the unidirectional composite with micro unit cells having hexagonal arrangement of fibers with different volume fraction at different locations in the transverse cross-section are determined. Further, elastic and strength properties are evaluated for micro unit cells with uneven distribution of fibers in the transverse cross-section.

Multiscale modeling of 3D layer-to-layer orthogonal interlock woven composite structure for elastic and strength behavior is presented. Due to the inherent nature of weaving, 3D woven composites can be represented by repetitive unit cells at the meso level. The present study focuses on identifying different types of repetitive unit cells considering both the geometry and the boundary conditions. For a typical 3D layer-to-layer orthogonal interlock woven composite, there are eight types of meso repetitive unit cells taking into account both the geometry and the boundary conditions. Additionally, for a practical situation, fiber volume fraction (Vf) in the impregnated strand is not uniform throughout the cross-section. In other words, Vf would be different for different micro repetitive unit cells. The properties of the macro structure, i.e. the 3D woven composite structure has been determined by applying periodic boundary conditions at micro and meso levels and iso-strain conditions at the macro level using finite element analysis. The continuity between the blocks is provided by merging the nodes in the intersection regions. The effect of different Vf at different locations in the transverse cross-section of the strand on the elastic and the strength properties of 3D layer-to-layer woven composite structure is presented.

An effort has been made in this paper to analyze a simple diaphragm supported single layer piezoelectric plate for electromechanical loading by using mixed semi-analytical model developed by Kant et al. (2007). The mathematical model consists of defining a two-point boundary value problem (BVP) governed by a set of coupled first order ordinary differential equations (ODEs). The accuracy and effectiveness of the proposed model are assessed by comparing the numerical results with available three dimensional (3D) elasticity solutions. Numerical results for different length to width ratio and for various aspect ratios have been presented for future reference.

An effort has been made in this paper to analyze a simple diaphragm supported single layer piezoelectric plate for electromechanical loading by using mixed semi-analytical model developed by Kant et al. (2007). The mathematical model consists of defining a two-point boundary value problem (BVP) governed by a set of coupled first order ordinary differential equations (ODEs). The accuracy and effectiveness of the proposed model are assessed by comparing the numerical results with available three dimensional (3D) elasticity solutions. Numerical results for different length to width ratio and for various aspect ratios have been presented for future reference.

In this study, the influence of centrally placed circular and square cutouts on vibration and buckling characteristics of different ply-oriented laminated panels under the action of compressive and/or tensile types of non-uniform in-plane edge loads are investigated. The panels are inspected under the action of uniaxial compression, uniaxial tension and biaxial, compression-tension, loading configurations. Furthermore, the effects of different degrees of edge restraints and panel aspect ratios are also addressed in this work. Towards this, a nine-node heterosis plate element has been adopted which includes the effect of shear deformation and rotary inertia. According to the results, the tensile buckling loads are higher than that of compressive buckling loads. However, the tensile buckling load continuously reduces with the increased cutout sizes irrespective of ply-orientations. This is also true for compressive buckling loads except for some particular ply-orientations with higher sized cutouts.

A transition element is developed for the local global analysis of laminated composite beams. It bridges one part of the domain modelled with a higher order theory and other with a 2D mixed layerwise theory (LWT) used at critical zone of the domain. The use of developed transition element makes the analysis for interlaminar stresses possible with significant accuracy. The mixed 2D model incorporates the transverse normal and shear stresses as nodal degrees of freedom (DOF) which inherently ensures continuity of these stresses. Non critical zones are modelled with higher order equivalent single layer (ESL) theory leading to the global mesh with multiple models applied simultaneously. Use of higher order ESL in non critical zones reduces the total number of elements required to map the domain. A substantial reduction in DOF as compared to a complete 2D mixed model is obvious. This computationally economical multiple modelling scheme using the transition element is applied to static and free vibration analyses of laminated composite beams. Results obtained are in good agreement with benchmarks available in literature.

Solution is obtained for functionally graded (FG) narrow beams under plane stress condition of elasticity by using the mixed semi analytical model developed by Kant et al. (Int J Comput Methods Eng Sci Mech 8(3): 165–177, 2007a). The mathematical model consists in defining a two-point boundary value problem (BVP) governed by a set of coupled first-order ordinary differential equations (ODEs) in the beam thickness direction. Analytical solutions based on two dimensional (2D) elasticity, one dimensional (1D) first order shear deformation theory (FOST) and a new 1D higher order shear-normal deformation theory (HOSNT) are also established to show the accuracy, simplicity and effectiveness of the developed mixed semi analytical model. It is observed from the numerical investigation that the present mixed semi analytical model predicts structural response as good as the one given by the elasticity analytical solution which in turn proves the robustness of the present development.

A partial discretization formulation with two-noded finite elements (FEs) under plane stress conditions has been developed for flexural analysis of composite and sandwich beams subjected to transverse loading. The methodology consists in defining a two-point boundary value problem (BVP) governed by a set of coupled first-order ordinary differential equations (ODEs) with four degrees of freedom (u, w, τxz and σz) per node. Continuity of interlaminar transverse stresses and displacements at laminae interfaces is implicitly enforced in the formulation. All the fundamental elasticity relationships between the components of stress, strain and displacement fields are explicitly maintained throughout the elastic continuum. Results have been obtained for cross-ply composite and sandwich beams. Excellent agreement with available analytical, mixed semianalytical and FE solutions is observed. Some new results with clamped support conditions have also been obtained and are presented to serve as benchmark solutions for future reference and to show the generality of the formulation.

A novel semi-analytical model is presented here for accurate estimation of stresses and displacements in composite and sandwich laminates. Displacements and corresponding transverse stresses are considered as primary variables of interest. Formulation is based on solution of a two-point boundary value problem (BVP) governed by a set of linear first-order ordinary differential equations (ODEs) through the thickness of a laminate. These first-order ODEs are numerically integrated by using fourth-order Runge–Kutta–Gill routine. Present model is free from any simplifying assumptions and also satisfies the continuity requirements of displacements and interlaminar transverse stresses at the laminae interfaces. Solutions for a wide range of composite and sandwich laminates are obtained to validate the present formulation. Results obtained through this technique are seen to compare well with the available three dimensional (3D) elasticity and other two dimensional (2D) analytical and 2D/3D finite element (FE) solutions. Few new benchmark solutions are also presented for future reference., © Elsevier

A simple, semi-analytical model with mixed (stresses and displacements) fundamental variables starting from the exact three dimensional (3D) governing partial differential equations (PDEs) of laminated composite and sandwich plates for thermo-mechanical stress analysis has been presented in this paper. The plate is assumed simply supported on all four edges. Two different temperature variations through the thickness of plates are considered for numerical investigation. The accuracy and the effectiveness of the proposed model are assessed by comparing numerical results from the present investigation with the available elasticity solutions. Some new results for sandwich laminates are also presented for future reference.

A simple, semi-analytical methodology defining a two-point boundary value problem (BVP) governed by a set of linear first-order ordinary differential equations (ODEs) with mixed primary variables whose number equals the order of partial differential equations (PDEs) for narrow layered beams is proposed in this paper. These primary quantities consist of displacements ( u , w ) and the corresponding transverse stresses ( τ xz , σ z ). Continuity of transverse stresses and displacements through the thickness of a laminated beam is enforced naturally in the formulation. The accuracy and the effectiveness of the proposed methodology is addressed by comparing numerical results from the present formulation with available closed-form analytical and finite element (FE) solutions.

A novel Normal and Shear Deformation Theory (NSDT) for analysis of laminated composite and sandwich beams, taking into account shear deformation as well as normal deformation, is developed. The paper investigates flexural behaviors of thick laminated and sandwich beams under plane stress conditions using NSDT. A generalized displacement-based refined formulation is elucidated with inclusion of various warping functions in terms of thickness coordinates to represent shear and normal deformation effects. These effects become pronounced in thick laminated beams and particularly in sandwich beams with transversely flexible core. Present formulation satisfies the shear stress free surface conditions at the top and bottom surfaces of the beam with realistic through-the-thickness variation of transverse shear stresses. The results obtained are compared with higher order theories available in literature. It is observed that NSDT predicts displacement and stresses accurately compared to other higher order theories.

Two Dimensional Stress Analyses of Laminates under Thermal Load

Analysis of a piezoelectric laminate under plane strain condition of elasticity (cylindrical bending) has been performed with mixed semi-analytical model developed by Kant et al. (2007). The in-plane displacement, transverse displacement, transverse normal and shear stresses, electric potential and transverse electric displacement have been considered as fundamental dependent variables. The mathematical model consists of defining a two-point boundary value problem (BVP) governed by a set of coupled first order ordinary differential equations (ODEs). The accuracy and efficiency of the proposed model are assessed by comparing the numerical results from the present investigation with available elasticity solutions. (C) 2014 Elsevier Ltd. All rights reserved.

Physical testing of composites to determine their elastic and strength properties is difficult owing to their inherent heterogeneous character. Multiscale analysis presents a sequential approach to the prediction of these properties at micro, meso and macro levels for 2D laminates and 3D composites. The homogenized properties at any length scale are always derived from the well-defined properties of the constituent phases of the composite. The micromechanical analysis of the repetitive unit cells (RUCs), along with the periodic boundary conditions, initiates the computation of homogenized properties of the composites. In this paper, different types of RUCs have been identified and appropriate periodic boundary conditions are formulated to determine the homogenized properties of the composites which can be further used for meso and macro-mechanical analyses. An algorithm based on the available literature is used to generate the random distribution of unidirectional fibers and check for their compatibility. In the random fiber generation, two types of models have been analyzed, the first is the random fiber unit cell with periodicity, and the second is without considering any periodicity at the edges of the RUC. This also leads to the evolution of a representative volume element (RVE). This paper also attempts to inspect the progressive degradation in properties of a debonded unidirectional composite by using contact criteria at the fiber-matrix interface.

A unique finite element model for static and free vibration analyses of thick and thin composite laminates is presented. The model is a combination of 3D mixed layerwise and equivalent single layer (ESL) theories. The ESL is employed in the global part of domain. On the other hand, a stack of 3D elements are used for estimation of the local parameters. The transverse inter laminar stresses are determined by using 18 noded 3D mixed layerwise element with 6 DOF per node in the local region. This mixed element incorporates the interlaminar stresses as the nodal DOF in addition to displacements for ensuring continuity of the transverse stresses in the thickness direction. Nine noded 2D elements with 12 DOF per node are used in the global domain. A transition has been developed for connection and compatibility of differently modelled sub-domains. Hamilton's variational principle has been used for the free vibration analysis. Present static and vibration analyses of laminates are in good agreement with the available elasticity and closed form solutions. The presented combined mesh modelling reduces number of elements to map the entire domain as compared to full 3D model. This results in substantial reduction of DOF and improves the computational efficiency. (C) 2015 Published by Elsevier Ltd.

Fatigue analysis of a simply supported composite plate with laminate configuration of [0n/90n]s under central patch impulse loading is presented using an analytical method. The method mainly consists of two steps, one, evaluation of vibration induced stresses for the given central patch impulse loading using modal analysis, and two, fatigue analysis using S–N curve approach, residual strength approach as well as failure function approach. The stress state in the plate was evaluated using viscous damping model as a function of time. The stress-time history was converted into block loading consisting of many sub-blocks. In the present study, the block loading consisted of four sub-blocks and a total of 175 numbers of cycles. The block loading was repeated after every 5 s. Next, fatigue analysis was carried out based on the block loading condition evaluated. Number of loading blocks for fatigue failure initiation and the location of failure were obtained. Studies were also carried out using two-dimensional (2D) finite element analysis (FEA). Number of loading blocks required to cause fatigue failure initiation under central patch impulse loading was found to be 3120 and 3170 using the analytical method and 2D FEA, respectively.

A semi-analytical approach for evaluation of stresses and displacements in composite and sandwich laminates Under cylindrical bending subjected to transverse load has been developed in this paper. Two dimensional (21)) partial differential equations (PDEs) of such a laminate are obtained by imposing plane-strain conditions of elasticity. The fundamental dependent variables are so selected in this formulation that they satisfy the continuity of displacements and transverse interlaminar stresses at the laminate interface through the thickness. The set of governing PDEs are transformed into a set Of Coupled first-order ordinary differential equations (ODEs) in thickness direction by assuming Suitable global orthogonal trigonometric functions for the fundamental variables satisfying the boundary conditions. These ODEs are numerically integrated by a specially formulated ODE integrator algorithm involving transformation of a two-point boundary value problem (BVP) into a set of initial value problems (IVPs). Numerical studies on both composite and sandwich laminates for various aspect ratios are performed and presented. Accuracy of the present approach is demonstrated by comparing the results with the available elasticity solution. It is seen that the present results are in excellent agreement with the elasticity solutions. Some new results for sandwich laminates and for uniform loading condition are presented for future reference. Copyright (c) 2006 , Ltd.

Strengthening of existing old structures has traditionally been accomplished by using conventional materials and techniques, viz., externally bonded steel plates, steel or concrete jackets, etc. Alternatively, fibre reinforced polymer composite (FRPC) products started being used to overcome problems associated with conventional materials in the mid 1950s because of their favourable engineering properties. Effectiveness of FRPC materials has been demonstrated through extensive experimental research throughout the world in the last two decades. However there is a need to use refined analytical tools to simulate response of strengthened system. In this paper, an attempt has been made to develop a numerical model of strengthened reinforced concrete (RC) beams with FRPC laminates. Material models for RC beams strengthened with FRPC laminates are described and verified through a nonlinear finite element (FE) commercial code, with the help of available experimental data. Three dimensional (3D) FE analysis has been performed by assuming perfect bonding between concrete and FRPC laminate. A parametric study has also been performed to examine effects of various parameters like fibre type, stirrup's spacing, etc. on the strengthening system. Through numerical simulation, it has been shown that it is possible to predict accurately the flexural response of RC beams strengthened with FRPC laminates by selecting an appropriate material constitutive model. Comparisons are made between the available experimental results in literature and FE analysis results obtained by the present investigators using load-deflection and load-strain plots as well as ultimate load of the strengthened beams. Furthermore, evaluation of crack patterns from FE analysis and experimental failure modes are discussed at the end.

Two dimensional (2D) stress analysis is performed in this paper for functionally graded (FG) beam under the plane stress condition of elasticity by using semi analytical approach developed by Kant et al. [6]. Modulus of elasticity is assumed to be varied exponentially through the thickness of beam. The mathematical model consists in defining a two-point boundary value problem (BVP) governed by a set of coupled first-order ordinary differential equations (ODEs) in the beam thickness direction. Elasticity solutions presented by Sankar [9] is used to show the accuracy, simplicity and effectiveness of present semi analytical solution. It is observed from the numerical investigation that the present mixed semi analytical model predicts structural response as good as the one given by the elasticity solution, which in turn proves the robustness of the presented formulation.

An exact analytical solution based on the propagator matrix method and a semianalytical solution based on a higher-order mixed approach (displacement and stress interpolation) have been presented in this paper to evaluate the natural frequencies as well as the stress and displacement mode shapes of simply supported, cross-ply laminated and sandwich plates. Continuity of the transverse stresses and displacements has been maintained at the laminae interfaces. Results have been presented for orthotropic plates, symmetric as well as nonsymmetric cross-ply composite and sandwich laminates. Results from the propagator matrix agree well with the published results for frequencies as well as for displacement and stress mode shapes. Furthermore, the frequencies and displacement and stress eigenvectors obtained from the proposed layerwise mixed method are in excellent agreement with those obtained by three-dimensional elasticity theory. Results obtained from the present equivalent single layer theory are in good agreement with those obtained from the displacement based higher order methods. The high accuracy of the present methods is further confirmed by comparing the response of a sandwich plate with significantly different layer properties for which the conventional displacement based formulations yield inaccurate solutions.

First-ply failure (FPF) analyses of composite laminated plates have been presented in this paper. A 3-D layer-wise mixed finite element model developed by the authors (Ramtekkar, G.S., Desai, Y.M. and Shah, A.H. (2002). Mixed Finite Element Model for Thick Composite Laminated Plates, Mechanics of Advanced Materials and Structures, 9(2): 133-156.) has been employed for the computation of components of stress and strain. FPF has been predicted by using the maximum stress, the maximum strain, Tsai-Hill, Tsai-Wu and Hoffman failure theories. It has been observed that the 3-D failure theories have yielded approximately the same failure load as their 2-D counterparts because the failure of a lamina (ply) under flexure is primarily associated with the in-plane stress state. It has been demonstrated that the present methodology predicts the FPF load for cross-ply laminated plates very well. Results have been presented for cross-ply-angle-ply, symmetric-anti-symmetric and thin-thick plates to show important observations.

The bending analysis of sandwich plates consisting of very stiff face sheets and a comparatively flexible core material offers challenge due to large variation in the magnitude of stress and strain components in the face and in the core regions of the plate. Similarly, the displacement fields do vary in zigzag manner at the layer interface of stiff face sheet and the soft core, thereby making the transverse strains highly discontinuous at such layer interfaces. All these behavioural aspects indicate that only an individual layerwise model can appropriately analyze sandwich plates. A layerwise (three-dimensional), mixed, 18-node finite element (FE) model developed by Ramtekkar et al. [Mech. Adv. Mater. Struct. 9 (2002) 133] has been employed for the accurate evaluation of transverse stresses in sandwich laminates. The FE model consists of six degrees-of-freedom (three displacement components and three transverse stress components tau(xz), tau(yz), sigma(z), where z is the thickness direction) per node which ensures the through thickness continuity of transverse stress and displacement fields. Results obtained by using the FE model have shown excellent agreement with the available elasticity solutions for sandwich plates. Additional results on the variation of transverse strains have also been presented to highlight the magnitude of discontinuity in these quantities due to difference in properties of the face and the core materials of sandwich plates. (C) 2003 Elsevier Ltd.

A unified mixed, higher-order analytical formulation has been presented in this paper to predict general buckling as well as wrinkling of a general multi-layer, multi-core sandwich plate having any arbitrary sequence of stiff layers and cores. Assumptions of thin stiff layers and anti-plane core, which are usually made in the analysis of sandwiches, have been eliminated in the present formulation. Displacements as well as the transverse stress continuities have been enforced in the formulation by incorporating them as the degrees-of-freedom. The modal transverse stresses have been obtained directly as eigen vectors and thus their separate calculations have been advantageously avoided. Two sets of mixed models have been proposed on the basis of individual layer as well as equivalent single layer (ESL) theories by selectively incorporating non-linear components of Green's strain tensor. Solutions from the models have been shown to be in excellent agreement with the available three-dimensional elasticity solutions as well as with the available experimental results. It has been demonstrated that the ESL theories cannot accurately evaluate the overall buckling as well as the wrinkling loads of sandwiches. Limitations of the typical simplifying assumptions have also been highlighted. (C) 2003 Elsevier Ltd.

The phenomenon of ratchetting is defined as constant accumulation of plastic strain or deformation under combined steady state and cyclic loading. It can reduce the fatigue life or can cause failure of piping components or systems subjected to seismic or other cyclic loads. The uniaxial ratchetting characteristics of SA333 Gr.6 steel have been investigated at room temperature in the present paper. The specimens were subjected to cyclic axial stress with a constant mean stress of 200 MPa and a varying amplitude stress of 149, 174, 199 and 224 MPa. Tests were also performed on 203.2 mm, Sch 80, SA333 Gr. 6 carbon steel straight pipe. The pipe was subjected to a constant internal pressure of 18 MPa and a cyclic bending load. The effects of amplitude of load on the rate of ratchetting have also been investigated in the present paper. The uniaxial experiments showed that specimens exhibited shakedown at low stress amplitude after some strain accumulation. However, specimens experienced continuous ratchetting at higher stress amplitudes with no shakedown before failure. Ovalization of the pipe cross-section was observed when the pipe was subjected to constant internal pressure and cyclic point load. Local bulging was observed at higher loading. The pipe did not show any shakedown behaviour for the given cycles of loading and exhibited continuous ratchetting under the varying amplitude loading., © Elsevier

Guided waves in a layered elastic plate of rectangular cross section (finite width and thickness) has been studied in this paper. A semianalytical finite element method in which the deformation of the cross section is modeled by two-dimensional finite elements and analytical representation of propagating waves along the length of the plate has been used. The method is applicable to arbitrary number of layers and general anisotropic material properties of each layer, and is similar to the stiffness method used earlier to study guided waves in a laminated composite plate of infinite width. Numerical results showing the effect of varying the width of the plate on the dispersion of guided waves are presented and are compared with those for an infinite plate. In addition, effect of thin anisotropic coating or interface layers on the guided waves is investigated. (C) 2002 .

A novel, analytical mixed theory based on the potential energy principle has been presented in this paper to investigate buckling response of laminated composite plates subjected to mechanical and hygrothermal loads. Two sets of higher-order mixed models have been proposed on the basis of an individual layer as well as equivalent single layer theories by selectively incorporating nonlinear components of Green’s strain tensor. Displacements, as well as transverse stress continuities, have been enforced in the formulation of models by incorporating displacements and transverse stresses as the degrees-of-freedom. The modal transverse stresses have been obtained as eigenvectors and thus their separate calculations have been advantageously avoided. Solutions from the models have been shown to be in excellent agreement with the available three-dimensional elasticity solutions. Few benchmark solutions have also been presented for the bi-axial compression-tension loading.

A six-node. plane-stress mixed finite element model has been developed by using Hamilton's energy principle for the natural vibrations of laminated composite beams. Continuity, of the transverse stress and displacement fields has been enforced through the thickness of the laminated beam in the formation for proper modelling. The transverse stress components have been invoked as the nodal degrees of freedom by applying elasticity relations. Natural Frequencies of laminated composite beams obtained through the present formulation have been shogun to be in good agreement with the data available in the literature. Various mode shapes have also been presented as benchmark solutions. (C) 2002 . .

A layerwise, mixed, 18-node finite-element (FE) model has been developed to analyze laminated composite plates by using the minimum potential energy principle. Continuity of transverse stresses and displacement fields has been enforced through the thickness direction, Z, of a laminated plate by considering six degrees-of-freedom (three displacement components in the coordinate axes directions and three transverse stress components tau(xz), tau(yz), sigma(z)) per node. Because the transverse stress components have been invoked as nodal degrees of freedom by using the fundamental elasticity relationship between the components of stress and displacement, the model has an added feature of maintaining the fundamental elasticity relation among the stress, strain, and displacement fields throughout the elastic continuum, which has not been observed in various mixed formulations available in the literature. Results obtained by using the present FE model have shown excellent agreement with the available elasticity solutions for thin and thick composite laminates as well as sandwich plates.

A novel, 6-node, two-dimensional mixed finite element (FE) model has been developed to analyze laminated composite beams by using the minimum potential energy principle. The model has been formulated by considering four degrees of freedom (two displacement components u, w and two transverse stress components sigma(z), tau(xz)) per node. The transverse stress components have been invoked as nodal degrees of freedom by using the fundamental elasticity equations. Thus, the present mixed finite element model not only ensures the continuity of transverse stress and displacement fields through the thickness of the laminated beams but also maintains the fundamental elasticity relationship between the components of stress, strain and displacement Fields throughout the elastic continuum. This is an important feature of the present formulation, which has not been observed in various mixed formulations available in the literature. Results obtained from the model have been shown to be in excellent agreement with the elasticity solutions for thin as well as thick laminated composite beams. A few results for a cross-ply beam under fixed support conditions are also presented.

A simple, nine degrees-of-freedom model has been presented to describe vibrations of an inclined cable by using a generalized finite element approach. All three translations of a vibrating cable and of the support points have been included in the model for its use over a wide range of cable supported structures. The model has been validated for free as well as forced responses of inclined cables by comparing the results with analytical solutions. Some illustrative examples are considered to demonstrate the applicability of the model for analyzing vibrating cables and guyed towers subjected to gusty wind. It has been demonstrated that the model can be utilized to expeditiously predict the dynamic response of cable supported structures., © Elsevier

Vibration induced fatigue analysis of cross-ply [0(n)/90(n)](s) cantilever beam under tip impulse loading is presented. As a first step, vibration induced stress for the given tip impulse loading was evaluated using modal analysis. Viscous damping model was used for evaluating the stress state as a function of time. The stress-time history was converted into block loading consisting of many sub-blocks. The block loading consisted of four sub-blocks and a total of 135 numbers of cycles. The block loading was repeated after certain time duration. Further, fatigue analysis was performed based on the block loading condition evaluated. Fatigue failure initiation was examined using S-N curve based approach, residual strength approach as well as failure function approach. Number of blocks to failure initiation and the location of failure were obtained. Analysis of cross-ply [0(n)/90(n)](s) cantilever beam under tip static loading was also conducted for comparison. Studies are also presented using 3D finite element analysis (FEA). Number of blocks required to cause fatigue failure initiation under tip impulse loading was found to be 332 and 331 using the analytical method and 3D FEA, respectively for the geometry of the beam, material properties and loading condition considered. (C) 2012 Elsevier Ltd. All rights reserved.

The objective of this paper is to consider the dynamic motions of second order, weakly non-linear, discrete systems. The main attention is focused on a comparison, for such systems, of the method of Krylov-Bogoliubov (KB) and an enhanced Galerkin (EG) method which produce seemingly different solutions. Despite the apparent differences, the two methods are shown to give identical first order periodic and quasi-periodic solutions, and the same stability conditions for internal and external resonances, as well as a non-resonance. The ease of applying one or the other method depends upon whether a system is resonant and upon the number of participating modes. Both approaches are used here to analyze illustrative examples that are pertinent to galloping.

Efficient perturbation schemes are developed to compute the large amplitude, low frequency, galloping vibrations of a multi-span, overhead transmission line. Systematic procedures are formulated to assess the stability of a conductor's wind and ice loaded static profile by employing a multiple-degree-of-freedom finite element model. The use of the computationally most demanding part of the finite element analysis, namely a time marching process, is minimized by employing the averaging methods of Krylov-Bogoliubov and Galerkin. The methods are applied successfully to simulate field galloping records and their usefulness and advantages are demonstrated through illustrative examples. Alternative designs of transmission line clearances and span lengths can be assessed readily, with the help of the procedures, to achieve a cost-effective solution.