In-plane Edge Loads Research Articles

A Parametric study on the effect of elliptical cutouts for buckling behavior of composite plates under non-uniform edge loads

The solution for the buckling problem of composite laminates is usually based on the assumption that the panels are subjected to uniform edge loads without any discontinuity or damage. Nevertheless, in practice, the panels are provided with various sized opening subjected to non-uniform edge loads. Hence in this work, a finite element analysis is carried out to study the buckling behaviour of composite laminates with various sized elliptical openings under non-uniform edge loads. In the FE formulation, the panels are discretised by adopting 9-noded heterosis element and incorporating the effect of shear deformation and rotary inertia. The correctness of the formulation is validated by correlating the results with available literature. The influence of different sized elliptical cutouts on the buckling behaviour is investigated under the compressive and tensile type of non-uniform in-plane edge loads. The effect of various parameters such as cutout size, ply-orientation, ellipse-orientation, boundary condition and panel thickness is included in this work. It is observed from this work that the elliptical vertical cutout has higher buckling resistance as compared to that of the elliptical horizontal cutout.

Buckling Characteristics of Laminated Functionally-Graded CNT-Reinforced Composite Plate under Nonuniform Uniaxial and Biaxial In-Plane Edge Loads

In this paper, the buckling response of laminated functionally-graded CNT-reinforced composite (FG-CNTRC) plate structure is predicted under various types of non-uniform edge compression loading. For the finite element (FE) discretization of the plate, a nine degree of freedom (DOFs)-type polynomial-based higher-order shear deformation theory (HSDT) is considered. The application of non-uniform edge load causes the in-plane stress distribution to be non-uniform. Hence, the in-plane stresses need to be evaluated prior to the buckling analysis. These in-plane stresses are calculated using the in-plane stress analysis method by FE approach or the in-plane elasticity approach. The differential equations are obtained by employing the Lagrange equation of motion and solved as a general eigenvalue problem, after the differential equations are converted into homogeneous equations by means of FE procedure. The accuracy and adaptability of the present model are validated by comparing the present result with the available literature. Further, the impact on the buckling response of the laminated FG-CNTRC plate is investigated by various parameters such as span thickness ratio, aspect ratio, various edge constraints, and different types of non-uniform edge load, CNT fiber gradation and temperature dependency material properties.

Instability and vibration analyses of FG cylindrical panels under parabolic axial compressions

This paper presents the semi-analytical development of the dynamic instability behavior and the dynamic response of functionally graded (FG) cylindrical shallow shell panel subjected to different type of periodic axial compression. First, in prebuckling analysis, the stresses distribution within the panels are determined for respective loading type and these stresses are used to study the dynamic instability behavior and the dynamic response. The prebuckling stresses within the shell panel are the same as applied in-plane edge loading for the case of uniform and linearly varying loadings. However, this is not true for the case of parabolic loadings. The parabolic edge loading produces all the stresses (

Effect of Reinforced Cutouts and Ply-Orientations on Buckling Behavior of Composite Panels Subjected to Non-Uniform Edge Loads

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.

Nonlocal vibration and biaxial buckling of double-viscoelastic-FGM-nanoplate system with viscoelastic Pasternak medium in between

The general equation for transverse vibration of double-viscoelastic-FGM-nanoplate system with viscoelastic Pasternak medium in between and each nanoplate subjected to in-plane edge loads is formulated on the basis of the Eringen's nonlocal elastic theory and the Kelvin model. The factors of the structural damping, medium damping, small size effect, loading ratio, and Winkler modulus and shear modulus of the medium are incorporated in the formulation. Based on the Navier's method, the analytical solutions for vibrational frequency and buckling load of the system with simply supported boundary conditions are obtained. The influences of these factors on vibrational frequency and buckling load of the system are discussed. It is demonstrated that the vibrational frequency of the system for the out-of-phase vibration is dependent upon the structural damping, small size effect and viscoelastic Pasternak medium, whereas the vibrational frequency for the in-phase vibration is independent of the viscoelastic Pasternak medium. While the buckling load of the system for the in-phase buckling case has nothing to do with the viscoelastic Pasternak medium, the buckling load for the out-of-phase case is related to the small size effect, loading ratio and Pasternak medium.

Buckling response of laminated composite stiffened plates subjected to partial in-plane edge loading

ABSTRACTThis article presents the buckling analysis of laminated composite stiffened plates subjected to partial in-plane edge loading. The finite element method is used to carry out the analysis. The eight-noded isoparametric degenerated shell element with C0 continuity and first-order shear deformation and a compatible three-noded curved beam element are used to model the plate skin and the stiffeners, respectively. The eigen value analysis is carried out to track the buckling load. The convergence study is performed for some specific problems and the results are compared with the available results in the literature. It is observed that the convergence of results is very fast for this finite element model. Effect of different parameters like orientation of fibers, number of layers, and loading types are considered in the present investigation. It is also observed that all these parameters have significant effect on the buckling response of the composite stiffened plate.

Thermomechanical buckling of hybrid cross-ply laminated rectangular plates

A thermomechanical buckling analysis is presented for simply supported rectangular symmetric cross-ply laminated composite plates that are integrated with surface-mounted piezoelectric actuators and are subjected to the combined action of in-plane compressive edge loads, two types of thermal loads, and constant applied actuator voltage. The formulation of equations is based on the classical laminated plate theory and the von-Karman non-linear kinematic relations. The analysis uses an exact method to obtain closed-form solutions for the buckling load. The effects of applied actuator voltage, thermal and mechanical loads, plate geometry, and lay-up configuration of the laminated plates are investigated. The novelty of the present work is to obtain closed-form solutions for electro-thermomechanical buckling of hybrid composite plates, and to cover non-uniform temperature distribution loading. The results for various states are verified with known data in the literature.

Vibration and buckling analyses of laminated panels with and without cutouts under compressive and tensile edge loads

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 nonuniform 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.

Dynamics Behavior of a Guided Spline Spinning Disk, Subjected to Conservative In-Plane Edge Loads, Analytical and Experimental Investigation

The governing linear equations of transverse motion of a spinning disk with a splined inner radius and constrained from lateral motion by guide pads are derived. The disk is driven by a matching spline arbor that offers no restraint to the disk in the lateral direction. Rigid body translational and tilting degrees-of-freedom are included in the analysis of total motion of the spinning disk. The disk is subjected to lateral constraints and loads. Also considered are applied conservative in-plane edge loads at the outer and inner boundaries. The numerical solution of these equations is used to investigate the effect of the loads and constraints on the natural frequencies, critical speeds, and stability of a spinning disk. The sensitivity of eigenvalues of spline spinning disk to the in-plane edge loads is analyzed by taking the derivative of the spinning disk's eigenvalues with respect to the loads. An expression for the energy induced in the spinning disk by the in-plane loads, and their interaction at the inner radius, is derived by computation of the rate of work done by the lateral component of the edge loads. Experimental idling and cutting tests for a guided spline saw are conducted at the critical speed, super critical speeds, and at the flutter instability speed. The cutting results at different speeds are compared to show that the idling results of a guided spline disk can be used to predict stable operation speeds of the system during cutting.

Buckling behaviour of laminated composite skew plates with various boundary conditions subjected to linearly varying in-plane edge loading

In the present study, the buckling behaviour of laminated composite skew plates with different boundary conditions subjected to linearly varying in-plane loads are presented. The skew plate is modelled based on higher order shear deformation theory, which accurately predicts the buckling behaviour for the thick plate. The in-plane stress distribution within the skew plate due to linearly varying in-plane load is equal to the applied in-plane edge load in the pre-buckling range. Using these in-plane stress distributions, the total potential energy functional is formulated. Total potential energy is a function of the total strain energy of skew plate and potential energy due to in-plane stress distributions. The total strain energy of skew plate contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total potential energy functionals mapped from physical domain to computational domain over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram–Schmidt orthogonalization process. Using a Rayleigh-Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials, the total potential energy functional is converted into sets of algebraic equations. Finally, these algebraic equations are rearranged as a linear eigenvalue problem, which is solved to obtain the critical buckling loads. The numerical results are presented for different skew angles, boundary conditions, length to thickness ratios, aspect ratios and in-plane loadings. It is observed that the critical buckling load increase with the increase of skew angle as well as change in the mode shape at a lower aspect ratio with the increase of skew angle.

Post-Buckled Vibration Characteristic of Composite Cylindrical Shell Panels Under Parabolic In-Plane Edge Compression

In this paper, post-buckled vibration of cross-ply thick laminated cylindrical shell panels subjected to nonuniform (parabolic) uniaxial and biaxial compression is studied. The mathematical model is based on a higher order shallow shell theory incorporating von Kármán-type geometric nonlinearities and initial geometric imperfections. In the first step, the plate membrane problem is solved to evaluate the stress distribution within the plate in the pre-buckling range as the applied in-plane edge load is nonuniform. By using the above stress distributions, the governing shell panel post-buckling equations are derived through Hamiltonian principle. The governing nonlinear partial differential equations are reduced into a set of nonlinear algebraic equations for post-buckling analysis and nonlinear ordinary differential equations in the case of free vibration analysis using Galerkin's method. The equilibrium paths through limit points are traced using Newton–Raphson method in conjunction with Riks approach. The free vibration frequency of pre-bucked and post-buckled cylindrical panels loaded with uniaxial or biaxial nonuniform in-plane edge load are studied. Free vibration frequency for symmetric (0/90/0) cross-ply laminated cylindrical shell panels under uniaxial and biaxial parabolic in-plane load with initial imperfections are presented for different post-buckled deflections. Limit loads and snap-through behavior of shell panels and corresponding free vibration results are co-related for better understanding of the problem.

Elastic buckling behavior of rectangular plates with holes subjected to partial edge loading

Cut-outs or openings are inevitable part of steel structural systems since they are required as access ports for mechanical and electrical systems or to reduce the amount of material that is used. When such perforated plates experience compression loads, they may buckle or show instability due to axial compression. In this study, the buckling of perforated square and rectangular plates subjected to in-plane compressive edge loading is investigated using the finite element method. To analyze the behavior of the plates the following four edge loading cases were applied; concentrated edge loading, asymmetric partial loading at the opposite edges, partial loading at the center of the opposite edges and partial loading at the two ends of the opposite edges. The plate aspect ratio, the length and location of the edge loading and diameter of the circular hole are taken as the variables that have a buckling effect on the behavior of the plate. The results show that the square plates are highly sensitive to buckling when the loading at the center of the plates.

Buckling and vibration of laminated composite circular plate on winkler-type foundation

Buckling and vibration characteristics of circular laminated plates under in-plane edge loads and resting on Winkler-type foundation are solved by the Ritz method. Inclusive numerical data are presented for the first three eigen-frequencies as a function of in-plane load for different classical edge conditions. Moreover, the effects of fiber orientation on the natural frequencies and critical buckling loads of laminated angle-ply plates with stacking sequence of ((β / -β / β / -β))s, are studied. Also, selected deformation mode shapes are illustrated. The correctness of results is established using finite element software as well as by comparison with the existing results in the literature.

Buckling and Vibration of Symmetrically Laminated Composite Elliptical Plates on an Elastic Foundation Subjected to Uniform In-Plane Force

AbstractBuckling and vibration characteristics of thin, symmetrically laminated, elliptical composite plates under initial in-plane edge loads and resting on Winkler-type elastic foundation are presented based on the classical laminated-plate theory. The governing equations were obtained from the variational approach and solved by the Ritz method. Extensive numerical data are provided for the first three natural frequencies as a function of in-plane load, and critical buckling loads as a function of aspect ratio for various classical edge conditions (free, clamped, and simply supported). Moreover, the effects of fiber orientation on the natural frequencies and buckling loads of laminated angle-ply plates, with stacking sequence of [(β/−β/β/−β)]s, were studied for chosen foundation parameter. Selected deformation buckling mode shapes are illustrated. The accuracy of calculations was checked by performing good convergence studies, and the correctness of results is established by comparison to existing resul...

Buckling and postbuckling response of sandwich panels under non-uniform mechanical edge loadings

The buckling and postbuckling responses of cylindrical sandwich panels, subjected to non-uniform in-plane loadings are investigates in this paper by analytical method. A fourth and fifth order expansions are used respectively for the transverse and tangential displacement of the core to model the core compressibility effect. The stress distribution within the panels due to the applied non-uniform in-plane edge loadings are determined by prebuckling analysis. The governing partial differential equations describing the buckling and postbuckling behavior of cylindrical sandwich panels are derived using the principle of minimum total potential energy. Galerkin’s method is used to reduce the governing partial differential equations to a set of non-linear algebraic equations. Newton–Raphson method in conjunction with Riks approach is employed to solve the algebraic equations. Numerical results are presented for both flat and cylindrical sandwich panels subjected to various non-uniform in-plane edge loadings. The sandwich panels used in the present investigation are made up of isotropic and composite materials.

Buckling of Laminated Composite Stiffened Panels Subjected to Linearly Varying In-Plane Edge Loading

The presence of in-plane loading may cause buckling of stiffened panels. An accurate knowledge of critical buckling load and mode shapes is essential for reliable and lightweight structural design. This paper presents parametric studies on simply supported laminated composite blade-stiffened panels subjected to linearly varying in-plane edge/compressive loading. Studies are carried out by changing the panel orthotropy ratio, stiffener depth, pitch length (number of stiffeners), smeared extensional stiffness ratio of stiffener to that of the plate and load distribution parameter. Based on the studies, a few important parameters influencing the buckling behavior are identified and their significance is discussed. Further, the interaction equations for combined loadings are validated by carrying out numerical studies.

Nonlinear low-velocity impact analysis of temperature-dependent nanotube-reinforced composite plates

A nonlinear analysis is presented for impact response of carbon nanotube-reinforced composite (CNTRC) structures under thermal conditions. Two plate configurations (i.e., single-layer and sandwich plates) are considered, and the nanotube reinforcement is either uniformly-distributed or functionally-graded in the plate thickness direction. The material properties of nanotube reinforced composites are estimated using micromechanical models. The equations of motion are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity, and the thermal effects are included by considering the nanotube reinforced composites as temperature-dependent. The equations of motion are solved with a two-step perturbation technique, and the initial stresses caused by either the thermal or in-plane edge loads as in-plane boundary conditions are introduced. The influences of material property gradient, volume fraction distribution, temperature change, initial stress, initial velocity of the impactor, and core-to-face sheet thickness ratio on impact response of plate structures are discussed. The analysis presented can help better understand the nonlinear impact response of functionally-graded materials and facilitate design and optimization of nanocomposite structures against impact and under thermal and other environments.

Dynamical Analysis of Stiffened Plates under Patch Loading

The vibration characteristics of stiffened plates with cutouts subjected to in-plane partial edge loadings at one end at the plate boundaries are studied using the finite element method. Buckling loads and vibration frequencies are determined for different cutout ratios and extent of partial edge loading at one end. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The main elegance of the formulation lies in the treatment of the stiffeners. The stiffeners can be placed anywhere within the plate element, and need not be placed on the nodal lines. The vibration characteristics are discussed and the results are compared with those available in the literature. Numerical results are presented for a range of cutout to plate size from 0 to 0.8.

Nonlinear dynamic response of sandwich plates with FGM face sheets resting on elastic foundations in thermal environments

This paper presents an investigation on the nonlinear dynamic response of sandwich plates with FGM face sheets resting on elastic foundations in thermal environments. The material properties of FGM layer are assumed to be graded in the thickness direction according to the Mori–Tanaka scheme. The governing equations of the plate that includes plate–foundation interaction are solved by a two-step perturbation technique. The thermal effects are also included and the material properties of both FGM face sheets and homogeneous core layer are assumed to be temperature-dependent. Two cases of the in-plane boundary conditions are considered. Initial stresses caused by thermal loads or in-plane edge loads are introduced. The numerical illustrations concern the nonlinear dynamic response of sandwich plates resting on Pasternak elastic foundations under different sets of thermal environmental conditions, from which results for single-layer FGM plates are also obtained for comparison purposes. The numerical results show that foundation stiffness and initial stress have a significant effect on the dynamic response of both single-layer and sandwich FGM plates. They also show that the core-to-face sheet thickness ratio has a significant effect on the dynamic response of sandwich FGM plates. The results reveal that the volume fraction distribution of FGM layer has a significant effect on the dynamic response of single-layer FGM plates, whereas this effect is less pronounced for the sandwich plate with FGM face sheets.

Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments

This paper presents an investigation on the nonlinear dynamic response of carbon nanotube-reinforced composite (CNTRC) plates resting on elastic foundations in thermal environments. Two configurations, i.e., single-layer CNTRC plate and three-layer plate that is composed of a homogeneous core layer and two CNTRC surface sheets, are considered. The single-walled carbon nanotube (SWCNT) reinforcement is either uniformly distributed (UD) or functionally graded (FG) in the thickness direction. The material properties of FG-CNTRC plates are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The motion equations are based on a higher-order shear deformation theory with a von Karman-type of kinematic nonlinearity. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The equations of motion that includes plate-foundation interaction are solved by a two-step perturbation technique. Two cases of the in-plane boundary conditions are considered. Initial stresses caused by thermal loads or in-plane edge loads are introduced. The effects of material property gradient, the volume fraction distribution, the foundation stiffness, the temperature change, the initial stress, and the core-to-face sheet thickness ratio on the dynamic response of CNTRC plates are discussed in detail through a parametric study.