Transverse Shear Strains Research Articles

Stability Analysis of Shear Deformable Trapezoidal Composite Plates

The stability characteristics of shear deformable trapezoidal composite plates are studied here. Thestrain smoothing technique is employed to approximate the membrane strains and curvatures of the edge-based smoothing cells. The transverse shear strains within the Reissner–Mindlin quadrilateral element are obtained using the edge-consistent interpolation approach. At the beginning, the performance of the present numerical technique is examined for the buckling analysis of trapezoidal panels under in-plane compressive or shear stresses. Thereafter, new results on the buckling and postbuckling behaviors of trapezoidal composite plates are presented, for which comparable numerical results are rare in the literature. Representative numerical results are presented to highlight the interaction between the higher pre-buckling stresses and increased stiffness near the shorter edge with fiber orientation and loading direction on the buckling resistance of trapezoidal panels.

A sinusoidal beam theory for functionally graded sandwich curved beams

To the best of the authors’ knowledge, there is no research work available on FG sandwich curved beams in the whole variety of literature. Therefore, the analysis presented on static behaviour of FG sandwich curved beams in this study is the main contribution and the novelty of the present study. A sinusoidal beam theory considering the effects of transverse normal stress/strain is applied for the bending analysis of FG sandwich beams curved in elevation. The beam has functionally graded skins at top and bottom and isotropic core at the middle. Material properties of FG skins are varied through the thickness according to the power law distribution. The present theory accounts for sinusoidal variation of axial strain and cosine distribution of transverse shear strain through the thickness of the beam. Governing equations of equilibrium are derived using Hamilton’s principle. Analytical solutions for simply supported curved beam are obtained using Navier’s solution procedure. The non-dimensional numerical results are obtained for different radii of curvature and various power law coefficients. The present study contributes many new results on the bending analysis of functionally graded sandwich beams curved in elevation for the reference of future research in this area.

A Refined Simple First-Order Shear Deformation Theory for Static Bending and Free Vibration Analysis of Advanced Composite Plates.

A refined simple first-order shear deformation theory is developed to investigate the static bending and free vibration of advanced composite plates such as functionally graded plates. By introducing the new distribution shape function, the transverse shear strain and shear stress have a parabolic distribution across the thickness of the plates, and they equal zero at the surfaces of the plates. Hence, the new refined theory needs no shear correction factor. The Navier solution is applied to investigate the static bending and free vibration of simply supported advanced composite plates. The proposed theory shows an improvement in calculating the deflections and frequencies of advanced composite plates. The formulation and transformation of the present theory are as simple as the simple first-order shear deformation. The comparisons of deflection, axial stresses, transverse shear stresses, and frequencies of the plates obtained by the proposed theory with published results of different theories are carried out to show the efficiency and accuracy of the new theory. In addition, some discussions on the influence of various parameters such as the power-law index, the slenderness ratio, and the aspect ratio are carried out, which are useful for the design and testing of advanced composite structures.

An Efficient Beam Element Based on Quasi-3D Theory for Static Bending Analysis of Functionally Graded Beams.

In this paper, a 2-node beam element is developed based on Quasi-3D beam theory and mixed formulation for static bending of functionally graded (FG) beams. The transverse shear strains and stresses of the proposed beam element are parabolic distributions through the thickness of the beam and the transverse shear stresses on the top and bottom surfaces of the beam vanish. The proposed beam element is free of shear-looking without selective or reduced integration. The material properties of the functionally graded beam are assumed to vary according to the power-law index of the volume fraction of the constituents through the thickness of the beam. The numerical results of this study are compared with published results to illustrate the accuracy and convenience rate of the new beam element. The influence of some parametrics on the bending behavior of FGM beams is investigated.

Transverse Vibrations of an Orthotropic Plate with a Collection of Inclusions of Any Configuration with Different Types of Connections with the Matrix

Within the framework of an improved theory that takes into account transverse shear strains and inertial components, we construct the solution of the problem of stationary flexural vibration of an orthotropic plate containing a collection of arbitrarily located curvilinear inclusions. We analyze various types of connections of these inclusions with the plate. The outer boundary of the plate has an arbitrary geometric configuration. In this boundary, we impose mixed boundary conditions harmonic in time. The solution is constructed by using the indirect method of boundary element. We used the sequential approach to the representation of Green functions.

Bi-Axial Buckling of Laminated Composite Plates Including Cutout and Additional Mass.

In the presented paper, a study of bi-axial buckling of the laminated composite plate with mass variation through the cutout and additional mass is carried out using the improved shear deformation theory (ISDT). The ISDT mathematical model employs a cubic variation of thickness co-ordinates in the displacement field. A realistic parabolic distribution of transverse shear strains through the plate thickness is assumed and the use of shear correction factor is avoided. A C° finite element formulation of the mathematical model is developed to analyze the buckling behavior of laminated composite plate with cutout and additional mass. As no results based on ISDT for the considered problem of bi-axial buckling of the laminated composite plate with mass variation are available in the literature, the obtained results are validated with the data available for a laminated composite plate without cutout and additional mass. Novel results are obtained by varying geometry, boundary conditions and ply orientations.

Buckling analysis of composite lattice sandwich shells under uniaxial compression based on the effective analytical equivalent approach

In this paper, a new effective equivalent analytical approach is presented to compute the global buckling of composite lattice sandwich shells under uniaxial compression based on the first-order shear deformation theory (FSDT). The lattice core was transformed into a solid skin, as the middle skin of the sandwich shell by considering the transverse shear strains and the new force and moment effect analysis on the selected unit cell. The equivalent stiffness of the composite lattice sandwich shells is then calculated by superimposing the stiffness contribution of outer, middle and inner skins. Using the FSDT and Rayleigh-Ritz method, the related eigenvalue equations are solved, and the critical buckling load is obtained. Furthermore, a 3D finite element model is built using ABAQUS software for validation. For various test examples with different slenderness ratio, outer/inner thickness and ply stacking sequence, stiffener thickness and the number of unit cells, the efficiency and accuracy of the presented equivalent approach are confirmed by comparing the obtained results with FE and other work results. It is shown that for thick sandwich shells, the use of FSDT for determining their critical buckling load is necessary, more suitable and can give high computational efficiency.

The role of non-slender inner structural designs on the linear and non-linear wave propagation attributes of periodic, two-dimensional architectured materials

In the current work, we analyse the role of non-slender inner structural designs on the wave propagation characteristics of periodic, two-dimensional architectured materials. In particular, we study the effect of non-negligible inner transverse shear strains on the linear and non-linear dispersion characteristics of different periodic inner material designs, with square, triangular, hexagonal and re-entrant hexagonal unit-cells. Thereupon, we compare their non-slender, Timoshenko-based dispersion attributes with the ones obtained using the simplified Bernoulli-based formulation. In order to obtain the nonlinear dispersion diagram corrections, we make use of the Linstedt-Poincaré perturbation framework, after computing the architectured materials' Timoshenko-based, higher order inner stiffness characteristics. The results suggest that the primal linear eigenfrequencies of the periodic, non-slender structures are reduced over certain wavenumbers when Timoshenko effects are accounted for, with the magnitude of the reduction to depend on the Timoshenko factor β and on the unit-cell architecture. Contrariwise, the nonlinear, wave amplitude dependent corrections can be either amplified or reduced, depending on the propagating wavenumber and lattice design. The most significant effects are observed for the architectured structure's primal, shear mode.

Static analyses of laminated rhombic conoids

PurposeThis paper aims to present a new mathematical model for laminated rhombic conoids with reasonable thickness and depth. The presented model does not require the shear correction factor, as transverse strain variation through the thickness was assumed as a parabolic function. The zero transverse shear stress provision at the bottom and the top of rhombic conoids was enforced in the model. The presented model implemented a C0 finite element (FE) model, eliminating C1 continuity requirement in the mathematical model. The proposed model was validated with analytical, experimental and other methods derived from the literature.Design/methodology/approachA novel mathematical model for laminated composite skew conoidal shells has been proposed. Parabolic transverse shear strain deformation across thickness is considered. FE coding of the proposed novel mathematical model was done. Slope continuity requirement associated with present FE coding has been suitably avoided. No shear correction factor is required in the present formulation.FindingsThis is the first attempt to study the bending response of laminated rhombic conoids with reasonable thickness and depth. After comparisons, the parametric study was performed by varying the skew angles, boundary conditions, thickness ratios and the minimum rise to maximum rise (hl/hh) ratio.Originality/valueThe novelty of the presented model is reflected by the simultaneous addition of twist curvature in the strain field as well as the curvature in the displacement field allowing the accurate analysis of reasonably thick and deep laminated composite rhombic conoids. The behavior of conoids differs from that of usual shells such as cylindrical and spherical due to the conoid’s inherent twist curvature with its complex geometry and different location of maximum deflection.

A modified first order shear deformation theory for Reissner-Mindlin composite panels with internal delamination

In this paper, an extended first order shear deformation theory is proposed for Reissner-Mindlin laminated composite panels with internal delamination. The distinctive feature of the present theory is that a contact mechanism is involved in the governing equations based on FSDT by introducing a constitutive relation between the contact force and the transverse deflection and are expressed in terms of the displacements and the rotation functions. The proposed theory is applied to investigate the structural failure of a delaminated Reissner-Mindlin composite panel subjected to in-plane compression. Numerical solutions are computed by developing MATLAB program for different values of thickness-to-width ratio, material properties, aspect ratio and delamination conditions and are compared with those obtained from the modified classic laminated plate theory established in previous works and with ABAQUS results. Both theories and ABAQUS analysis predict a consistent global buckling mode without opening in between the delamination. The comparisons of the two solutions not only validate the efficiency and accuracy of the proposed M-FSDT but also evidence that neglecting the transverse shear strain may lead to the overestimation of the load capacity of the panel up to more than 35% when the thickness-to-width ratio is greater than 0.15.

Static, free vibration, and buckling analysis of plates using strain-based Reissner\u2013Mindlin elements

A quadrilateral and a triangular element based on the strain approach are developed for static, free vibration and buckling analyses of Reissner–Mindlin plates. The four-node triangular element SBTP4 has the three essential external degrees of freedom at each of the three corner nodes and at a mid-side node; whereas the quadrilateral element SBQP has the same degrees of freedom at each of the four corner nodes. Both elements use the same assumed strain functions which are in the linear variation where bending and transverse shear strains are independent and satisfy the compatibility equations. The use of the strain approach allows obtaining elements with higher-order terms for the displacements field. The formulated elements have been proposed to improve the strain-based rectangular plate element SBRP previously published. Several numerical examples demonstrate that the present elements are free of shear locking and provide high-accuracy results compared to the available published numerical and analytical solutions.

A higher-order shear deformable mixed beam element model for accurate analysis of functionally graded sandwich beams

In this paper, a new higher-order shear deformation beam theory is developed by introducing the stress equilibrium condition. On the basis of the new shear deformation theory, novel shear deformable mixed beam elements with independent internal force fields and displacement fields are developed for accurate analysis of the functionally graded sandwich beams. Furthermore, a shear deformable beam element with additional interpolated axial displacement is also constructed in order to get reliable reference solutions. Two examples are presented to investigate the solution accuracy of different beam elements. Numerical results indicate that the present mixed beam elements can accurately predict the stress distributions over the cross section and ultimately give accurate displacement solutions. Moreover, the characteristics of axial displacement distributions and transverse shear strain distributions for functionally graded sandwich beams are discussed and the difficulty of getting accurate solutions by introducing a single form higher-order displacement function is pointed out. In these cases, the equilibrium-based beam theory and the corresponding mixed beam elements are more effective and reliable to obtain accurate solutions. Finally, the numerical stability for different beam elements is investigated and the results indicate the present higher-order shear deformable mixed beam element has excellent numerical stability.

Dynamic Analysis of Laminated Composite Plate Integrated with a Piezoelectric Actuator Using Four-Variable Refined Plate Theory

This paper presents an analytical solution based on four-variable refined plate theory for dynamic analysis of cross-ply composite laminates integrated with piezoelectric fiber-reinforced composite actuator attached to the upper surface. This theory considers parabolic transverse shear strains through the plate thickness. Equations of motion for simply supported rectangular plates are derived using Hamilton’s principle, and Navier’s method is employed to solve the equations. An unconditionally stable implicit Newmark scheme is used for temporal discretization. The accuracy of the present analytical solution is proved by comparing the results with those obtained by the finite element analysis. The effects of different parameters such as thickness-to-side ratio, aspect ratios and types of mechanical and electrical loading on the deflections and stresses are investigated.

Polygonal shell elements with assumed transverse shear and membrane strains

In this study, a new polygonal shell element is developed to provide greater flexibility in mesh design of complex shell structures. Wachspress coordinates are used to construct shape functions for polygonal shell elements. An assumed covariant shear strain field with respect to the element natural coordinate system is defined by employing the mixed interpolation of tensorial components approach to avoid transverse shear locking in polygonal shell elements. Moreover, an assumed covariant membrane strain field is constructed by using characteristic geometry and displacement vectors defined on quadrilateral subdomains of polygonal shell elements to alleviate membrane locking due to the element curvature. Some benchmark shell problems are solved to evaluate the performance of the proposed polygonal shell elements. Numerical experiments show that they converge much better than triangular shell elements and comparable to quadrilateral shell elements.

Temperature Stresses in a Functionally Graded Cylindrical Shell

For functionally gradient isotropic circular cylindrical shells, we propose the nonstationary heatconduction and thermoelasticity equations with appropriate boundary conditions. The thermoelasticity equations take into account both transverse shear and transverse normal strains. The temperature distribution over the thickness of the shell is assumed to be linear. As the shell material, we take a metal–ceramics composite. The volume fractions of these components vary across the thickness of the shell according to a power law. The solution of the quasistatic problem of thermoelasticity for a finite simply supported shell subjected to local heating is obtained by the methods of Fourier and Laplace transformations.

Bending and buckling of three-dimensional graphene foam plates

Abstract Bending and buckling behaviors of three-dimensional graphene foam (3D-GrF) plates are investigated in the framework of the two-variable refined plate theory (TRPT). The material properties of three-dimensional graphene foams vary continuously along thickness direction of the plate. The TRPT considers the effect of transverse shear strains that vary quadratically along the thickness of the plate. In addition, this theory does not need to consider the shear correction factor. By using Hamilton’s principle, the governing equations are obtained. Analytical solutions for the bending problem of 3D-GrF plates are derived via Navier’s method. Additionally, buckling problem of 3D-GrF plates with various boundary conditions are analyzed by employing the Galerkin method. Results obtained in this study are verified by comparing with the published ones. Finally, the influences of pore distribution, porosity coefficient, transverse distributed load, aspect ratio, length-to-thickness ratio, mode number and axial compression ratio on bending and buckling behaviors of 3D-GrF plates are discussed.

Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory

In this paper, a new refined hyperbolic shear deformation beam theory for the bending analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the bending response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equilibrium equations are derived from the principle of virtual work. Navier type solution method was used to obtain displacement and stresses, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG beams.

High-Order Layerwise Formulation of Transverse Shear Stress Field for Laminated Composite Beams

This paper presents a high-order layerwise theoretical framework for laminated composite beams based on a piecewise description of the transverse shear-stress field. Linear and quadratic variations in the transverse shear-stress field are assumed in each discrete layer, and compatibility conditions of the shear stress are a priori fulfilled through the introduction of shear-stress variables defined on the layer surfaces. Based on the stress–strain relations, the transverse shear strain is obtained, and the in-plane displacement is determined by integrating the transverse shear strain along the thickness direction. By imposing continuity conditions of the displacements, a displacement field expression that contains only displacement variables is formulated. Moreover, a two-node beam element associated with the present model is developed, where Hermite cubic interpolation functions are used for the transverse displacement variable, and linear interpolation functions are employed for the remaining displacement variables. Comparisons with the exact solution, various displacement-based theories, and high-fidelity finite element models demonstrate the high accuracy of the present model in predicting the stress and displacement distributions. In addition, the introduction of sublayers to improve the modeling accuracy and the influence of the stiffness ratio between layers on the effectiveness of the proposed model are addressed.

Enhanced drag-reduction over superhydrophobic surfaces with sinusoidal textures: A DNS study

Direct Numerical Simulation (DNS) studies of a fully developed turbulent channel flow are performed with sinusoidal surface texture to assess its ability to enhance turbulent skin-frictional drag reductions over superhydrophobic surfaces (SHS). The streamwise sinusoidal microgroove structure generates asymmetric secondary flows to induce an in-plane stationary distribution of spanwise velocity that oscillates in the streamwise direction. The transverse motions over a sinusoidal texture behave analogously to an existing drag-reduction technique by spanwise wall oscillations. The friction-drag levels and slip-lengths are precisely quantified for various streamwise wavelength configurations, and an optimum wavelength for the maximum reduction in turbulent drag is determined. The response of the near-wall turbulent structures to the sinusoidal microgrooves is also analysed. The transverse Stokes strain generates spanwise tilting in the near-wall streaks for large wavelengths, inducing an apparent drop in the wall-normal ejections and sweeps, thereby reducing the turbulent contribution to the wall-shear-stress. The transverse shear strain above the sinusoidal microgroove is demonstrated to be resembling a Stokes spatial layer (SSL), by comparing with existing analytical solutions of strain profiles for wall-forcing by spanwise spatial oscillations.

Investigation of porosity effect on flexural analysis of doubly curved FGM conoids

Abstract The flexural analysis of doubly curved functionally graded porous conoids was performed in the present paper. The porosities inside functionally graded materials (FGMs) can occur during the fabrication and lead to the occurrence of micro-voids in the materials. The mathematical model includes expansion of Taylor’s series up to the third degree in thickness coordinate and normal curvatures in in-plane displacement fields. Since there is a parabolic variation in transverse shear strain deformation across the thickness coordinate, the shear correction factor is not necessary. The condition of zero-transverse shear strain at upper and lower surface of conoidal shell is implemented in the present model. The improvement in the 2D mathematical model enables to solve problems of moderately thick FGM porous conoids. The distinguishing feature of the present shell from the other shells is that maximum transverse deflection does not occur at its centre. The improved mathematical model was implemented in finite element code written in FORTRAN. The obtained numerical results were compared with the results available in the literature. Once validated, the current model was employed to study the effect of porosity, boundary condition, volume fraction index, loading pattern and others geometric parameters.