Cutout Shape Research Articles

Buckling analysis of thin cylindrical CFRP panel with oval cutout

Abstract The use of laminated composite is growing rapidly in many fields due to their high stiffness to weight and strength to weight ratios, low modulus of expansion, thermal conductivity etc. According to their applications, composite materials undergo different loading conditions. One of the common failures is buckling, when the laminate is subjected to axial compressive load. Hence buckling analysis of composite structure is very important from design point of view. Different cutout shapes of thin cylindrical shells have been studied for buckling, but oval shaped cutouts with different orientations seems scanty and requires more investigation. In the present study, buckling analysis of thin cylindrical carbon fiber reinforced polymer (CFRP) composite shell with oval cutout has been investigated. The effects of three types of variables viz. layup orientation, element type and cutout orientation are analyzed numerically. The results show that the buckling load and mode shape depend on all three variables. The four ply stack orientations panel show significantly higher buckling load than two ply stack, and large decrease in buckling load with respect to cutout orientation. The buckling modes are highly affected by the cutout orientation. The minimum value of buckling load with respect to cutout orientation depends upon layup configuration. The lowest value of buckling load has been obtained for configuration 2 at 90° cutout orientation.

Linear Buckling behaviour of Composite Laminate [(θ/-θ)] with various shaped cutout using FEM

In this paper, the buckling behavior has been investigated on square laminate made of Woven-glass-polyester composite with various shaped cutouts (i.e., circle, square, vertical rectangle, horizontal rectangle, vertical ellipse, horizontal ellipse) numerically. The composite laminates have been arranged in asymmetrical order as [(θ/-θ)]. The laminated plate that is subjected to uniaxial compression has been emphasized on the laminate along with the effect of layer orientation, effect of cutout ratio and effect of cutout angle. The result shows that the minimum buckling load is obtained at 45° and the maximum buckling load attained at 0° and 90°for all laminates by increasing the layer orientation. For cutout ratio, the maximum and minimum load is obtained for the smallest and largest cutout ratio in all cutout shapes. Increasing the cutout angle, the square cutout exhibits the minimum load at 60°. In elliptical cutouts, the load is decreasing and increasing gradually while they are aligned in along and perpendicular to the loading directions. The rectangular cutouts positioned vertically and horizontally the load is decreasing up to 30° and 60°and then increasing up to 90°.

Finite Element-Based Stochastic Nonlinear Progressive Failure Response of Piezo-Laminated Composite Plate with Elliptical Cutouts

This paper presents the second-order statistics of hygro-thermo-electrically-induced progressive failure in terms of first-ply failure load (FPFL) and last-ply failure load (LPFL) analysis for laminated composite material plate (LCMP) under out of plane mechanical loading with random system properties. Basic governing equation of nonlinear progressive failure analysis is based on shear deformation theory (higher order) with von-Karman nonlinear kinematics using Newton’s Raphson approach through Tsai–Wu failure criteria. The random input variables are assumed as uncorrelated type and are evaluated using second-order perturbation method (SOPT). Laminated composite plate with elliptical cutouts are subjected to uniformly distributed, point and hydrostatic load. The effect of boundary conditions, temperature variation, moisture content and voltage variations by utilizing piezoelectric layer position and various cutout shapes on the mean and corresponding covariance (COV) of FPFL and LPFL load are evaluated. Convergence of numerical analysis is performed, and results are validated with those available in literatures to check the efficiency of present methodology. It is observed that the presence of elliptical hole always causes an increase in the failure load of plates subjected to bending, even further increase for LPFL due to the reduction of stresses.

Free vibration of composite laminated plate with complicated cutout

This paper presents the free vibration analysis of a composite laminated square plate with complicated cutout. The problem formulation is based on the higher order shear deformation plate theory HDST C0 coupled with a curved quadrilateral p-element. The elements of the stiffness and mass matrices are calculated analytically. The curved edges are accurately represented using the blending function method. A calculation program is developed to determine the fundamental frequencies for different physical and mechanical parameters such as the cutout shape, plate thickness, fiber orientation angle, and boundary conditions. The results obtained show a good agreement with the available solutions in the literature. New results for the fundamentals frequencies of a composite laminated plate with complicated cutout are presented.

A comprehensive study on the buckling behaviour of woven composite plates with major aerospace cutouts under uniaxial loading

Current research paper presents a comprehensive study based on Finite Element Method (FEM) to understand the effect of cutout shape and area on the buckling behaviour of E-glass composite plates. Considered plate has a dimension of 150 mm × 75mm × 3mm where loading edges are simple supported (shorter side) and other two edges are free. Major aerospace cutout shapes i.e. circular, square, elliptical (horizontal and vertical) and diamond are studied to understand their effect on plates’ critical buckling load. FE code Ansys is adopted to investigate the case studies. A limited number of experimental tests are also carried out in order to validate the FE code results. Overall, a good agreement between experimental and FE code results are found. From finite element analyses, it is found that for any cutout shape, as the cutout area increases, buckling load decreases significantly. Moreover, increasing the plate thickness by 0.5 mm can raise the buckling load up to 50%. More importantly, fibre orientation angle has most significant effect on the critical buckling load of plates where fibre orientation aligned with loading direction can increase the plates’ critical buckling load from 2.6 to 2.8 times than aligned with 900.

L-shaped plate model for the analysis of the warping deformation of perforated diaphragms in box girder

In order to estimate accurately the warping deformation of perforated diaphragms in girder distortion, a model of L-shaped plate is proposed in this paper based on the symmetry for the structure and loading, and the warping behavior under concentrated load at corner is investigated. The L-shaped plate is seen as an assembly of three rectangular portions connected by undetermined displacements and moments along the common boundary. Analytical functions for warping displacements of each rectangular portion are constructed according to elastic plate theory, and closed-form solutions are derived based on boundary conditions and compatibility between portions. Verifications are conducted by employing Finite Element Method and agreeable resultants are demonstrated for warping displacements and in-plane stress components, especially for the stress concentration around the corner of the cutout. Besides, a cutout ratio ρ is introduced to testify the feasibility of plate theory in solving the warping deformation of L-shaped plate. Results show that the rational range of cutout ratio for the model of L-shaped plate is identified 0.13<ρ < 0.25, and the variation of the shape of cutout hardly makes any significant influence on the warping deformation at loading corner for L-shaped plate.

Evaluation of a commercial Monte Carlo dose calculation algorithm for electron treatment planning

The RayStation treatment planning system implements a Monte Carlo (MC) algorithm for electron dose calculations. For a TrueBeam accelerator, beam modeling was performed for four electron energies (6, 9, 12, and 15 MeV), and the dose calculation accuracy was tested for a range of geometries. The suite of validation tests included those tests recommended by AAPM's Medical Physics Practice Guideline 5.a, but extended beyond these tests in order to validate the MC algorithm in more challenging geometries. For MPPG 5.a testing, calculation accuracy was evaluated for square cutouts of various sizes, two custom cutout shapes, oblique incidence, and heterogenous media (cork). In general, agreement between ion chamber measurements and RayStation dose calculations was excellent and well within suggested tolerance limits. However, this testing did reveal calculation errors for the output of small cutouts. Of the 312 output factors evaluated for square cutouts, 20 (6.4%) were outside of 3% and 5 (1.6%) were outside of 5%, with these larger errors generally being for the smallest cutout sizes within a given applicator. Adjustment of beam modeling parameters did not fix these calculation errors, nor does the planning software allow the user to input correction factors as a function of field size. Additional validation tests included several complex phantom geometries (triangular nose phantom, lung phantom, curved breast phantom, and cortical bone phantom), designed to test the ability of the algorithm to handle high density heterogeneities and irregular surface contours. In comparison to measurements with radiochromic film, RayStation showed good agreement, with an average of 89.3% pixels passing for gamma analysis (3%/3mm) across four phantom geometries. The MC algorithm was able to accurately handle the presence of irregular surface contours (curved cylindrical phantom and a triangular nose phantom), as well as heterogeneities (cork and cortical bone).

Crashworthiness design and optimisation of windowed tubes under axial impact loading

Thin-walled structures are frequently used as energy absorbers in the automotive, railway and aviation industries. This paper addresses the crashworthiness performance of thin-walled windowed tubes under dynamic impact loading. Different shapes of cut-outs were introduced to thin-walled tubes with different cross-sectional shapes to create windowed tubes. Explicit finite element code, LS-DYNA, was used to simulate the crushing behaviour of the windowed tubes under axial impact loading. The Finite Element (FE) model was validated by conducting experimental tests and showing that the numerical and experimental responses are comparable. The crashworthiness responses of the different windowed tubes were compared and the best performing tube was identified using a multi-criteria decision-making method known as Technique of Order Preference by Similarity to Ideal Solution (TOPSIS). It was found that a circular tube with a square window shape outperforms all other sections and exhibits the best energy absorption characteristics.Subsequently, a multi-objective optimisation analysis was performed to find the optimal configuration of the best tube. Response Surface Methodology (RSM) was used to develop models for the energy absorption responses of the tube. The design variables were selected to describe size, number, and distributions of the windows, while specific energy absorption (SEA) and peak crush force (PCF) were set as design responses. Parametric analysis was conducted to understand the effects of the design variables on the crashworthiness behaviour and the optimal configuration was identified.

Fatigue cracking investigation on diaphragm cutout in a self-anchored suspension bridge with orthotropic steel deck

To investigate the mechanism of base-metal cracking on diaphragm cutout in a self-anchored suspension bridge with orthotropic steel deck (OSD), multi-scale finite element models were established to obtain stress response at cutout detail under the passage of wheel loads. Fatigue life was evaluated based on nominal stress method and hot-spot stress method. The results indicated that the length of the longitudinal influence line for detail stress to wheel loads approximately equalled to twice the diaphragm spacing. The wheel loading location of maximum stress was the front wheel of middle-axle group 0.3 m from the diaphragm, and the stress was dominated by in-plane stress. The nominal stress was hard to define at cutout detail for high stress concentration, and the hot-spot stress was preferred to fatigue assessment based on S-N curve of FAT125, also nominal stress should be extracted at the location 5.0 mm from cutout edge. Cutout shape of Highway Bridge in Eurocode was suggested, and diaphragm thickness should not be below 12 mm. The cutout cracking was caused by poor cutout shape, thin diaphragm, high truck traffic volume and overloaded wheel loads, while undesirable fabrication control and large residual stress might also contribute to the cracking.

Stress analysis of rectangular and square plates with various cutouts

The geometric irregularities present inside a structure results in an improper stress distribution caused during manufacturing, which not only affects the strength of the component but also its vibrational behaviour when operated in a fluctuating environment. The emphasis of this paper is to evaluate the stress behavioral characteristics of plates with different cutout shapes. Two different loading conditions with three different types of plates made of Mild Steel are used for this analysis. From the present investigation, it may be concluded that where the max stress occurs. The methodology adopted in this research work is based on the numerical technique of finite element method, which uses SOLID 185 in ANSYS 19.1 solver. For further analysis, the obtained results are validated with previous literature works which were found satisfactory when related to the present study. It may be noted that FEM provides good insight for the determination of stress and deflection, with different parameters.

Investigation on effect of geometric, material and load parameters on strength of composites with cutouts

Composite applications require presence of multiple holes for mechanical fasteners or cutouts in laminates. Unlike isotropic materials, composite materials experience change in stress values due to different parameters such as geometric, material and loading parameters. The present study is devoted to primarily determine whether geometric or material parameters have dominant influence on strength of composite laminates. Computational study using ABAQUS CAE software is employed for the analyses. Results reveal that geometric parameters have much significant influence on stress concentration factor and thereby the strength of composite laminates, when compared to material parameters. An elliptical cutout is seen to have comparatively more adverse effect on strength of laminate, when compared with other cutout shapes. Further, effect of load parameters - in-plane tension, compression and shear, is also studied. However, no significant effect was evidenced in stress concentration factor due to load parameters.

Investigation on effect of geometric, material and load parameters on strength of composites with cutouts

Composite applications require presence of multiple holes for mechanical fasteners or cutouts in laminates. Unlike isotropic materials, composite materials experience change in stress values due to different parameters such as geometric, material and loading parameters. The present study is devoted to primarily determine whether geometric or material parameters have dominant influence on strength of composite laminates. Computational study using ABAQUS CAE software is employed for the analyses. Results reveal that geometric parameters have much significant influence on stress concentration factor and thereby the strength of composite laminates, when compared to material parameters. An elliptical cutout is seen to have comparatively more adverse effect on strength of laminate, when compared with other cutout shapes. Further, effect of load parameters - in-plane tension, compression and shear, is also studied. However, no significant effect was evidenced in stress concentration factor due to load parameters.

A simple spline finite strip for buckling analysis of composite cylindrical panel with cutout

Abstract In this study, a new sub-parametric strip element is developed to simulate the axially loaded composite cylindrical panel with arbitrary cutout. For this purpose, a code called SSFSM is developed in FORTRAN to analyze the buckling of panels. The first order shear deformation theory is used to form the strain-displacement relations. Spline and Lagrangian functions are used to derive element shape functions in the longitudinal and transverse directions, respectively. The computational cost of the SSFSM is decreased dramatically, as mapping functions of the strip element are very simple. The results obtained from the SSFSM are compared with those of the literature and the results obtained by ABAQUS to show the validity of the proposed approach. A parametric study is performed to show the capability of the SSFSM in calculating the panel buckling load. Results indicate that increasing the panel thickness and panel central angles cause an increase in panel buckling load. The cutout shape is an important factor influencing the panel buckling load. For instance, when the angle between the direction of big chord of the elliptical cutout and compressive load direction are 0 and 90 degrees, the panel buckling load reaches its minimum and maximum magnitude, respectively.

Impact of fuselage cutouts on the stress and deflection behavior: numerical models and statistical analysis

Over the past several years, considerable studies have been made to understand the mechanisms of failure of composite structures and the effect of these mechanisms on the performance of structures components made of composite materials. The compressive response of composite materials has received considerable attention due to their significance in the aerospace industry and the complexity associated with compressive failure. Failure criteria for anisotropic composite materials, which have different strengths in tension and compression, have attracted numerous researchers over decades and it is still today an important research topic. The goal of this study is to create a validated model to evaluate the effect of cutout shape, size, and the lamination angles of layers on the failure criteria of the fuselages. To achieve this objective, finite element method and statistical analysis have been used. The results show that the various analytical and empirical approaches have been used to study the failure capability of the fuselage structure. The model is applicable to the air transport industry. The proposed model has been validated against the known shape of an aircraft.

Shape optimization of structures with cutouts by an efficient approach based on XIGA and chaotic particle swarm optimization

Structural shape optimization is one important and crucial step in the design and analysis of many engineering applications as it aims to improve structural characteristics, i.e., reducing stress concentration and structural weight, or improving the stiffness, by changing the structural boundary geometries. The goal of this paper is to present an efficient approach, which goes beyond limitations of conventional methods, by combining extended isogeometric analysis (XIGA) and chaotic particle swarm optimization algorithm for shape optimization of structures with cutouts. In this setting, mechanical response of structures with cutouts is derived by the non-uniform rational B-spline (NURBS) and enrichment techniques. The computational mesh is hence independent of the cutout geometry, irrelevant to the cutout shape during the optimization process, representing one of the key features of the present work over classical methods. The control points describing the boundary geometries are defined as design variables in this study. The design model, analysis model, and optimization model are uniformly described with the NURBS, providing easy communication among the three aforementioned models, resulting in a smooth optimized boundary. The chaotic particle swarm optimization (CPSO) algorithm is employed for conducting the optimization analysis. Apart from that, the CPSO has some advantages as it includes: (i) its structure is simple and easy to implement; (ii) without the need for the complicated sensitivity analysis as compared with the traditional gradient-based optimization methods; and (iii) effectively escaping from the local optimum. The accuracy and performance of the developed method are underlined by means of several representative 2-D shape optimization examples.

Free vibration studies on plates with central cut-out

The present work deals with the experimental and finite element free vibration studies on isotropic and laminated anti-symmetric angle-ply composite plates with central cut-out under clamped-free–clamped-free boundary condition. The natural frequencies were determined using the CQUAD8 finite element of MSC/NASTRAN and comparison made between the experimental values and the finite element solution. The effects of aspect ratio, cut-out size and cut-out shape on the natural frequencies of plates were studied. The experimental values of the first, second and third natural frequencies are in good agreement with those of the finite element solution in the case of both isotropic and laminated composite plates with and without cut-outs. The non-dimensional frequency coefficient Kf are found increases with increase in length-to-cut-out size ratio (d/a) irrespective of the cut-out shape. In case of laminated composite plates, the non-dimensional frequency coefficient Kf increases monotonically with an increase in the aspect ratio irrespective of hole size and shapes for all the three modes of vibration.

Energy effect removal technique to model circular/elliptical holes in relatively thick composite plates under in-plane compressive load

A new technique is introduced in this study to model laminates with circular and elliptical holes. Post-buckling and nonlinear behaviors of these perforated plates are examined when they are under uniaxial in-plane compressive load. Since the perforated plates are moderately thick, the plate theory used to embody the shear effects in the thickness direction is the first order shear deformation plate theory and Von Karman’s assumptions are also used to incorporate the geometric nonlinearity. The formulations are founded upon the principle of minimum potential energy and the approximation of displacement fields are based on Ritz method and obtained by Chebyshev polynomials. Convergence tests have been performed to determine the total number of terms to be used in the assumed displacement functions. The total potential energy of the perforated plate results from removing the energy contribution of the holes from the total potential energy of the perfect plate. All potential energy integrations are obtained numerically by applying the Guess quadrature rule, however, in the case of circular or elliptical cutouts, the required nodes of the Gauss-Chebyshev quadrature are arranged in two different ways; Cartesian and polar arrangements. The effects of cutout shape, size and location for perforated composite laminates with different boundary conditions are extensively investigated to show the capability of the proposed technique. The accuracy of the present work is investigated by comparing the results obtained from finite element method.

Optimum Design of Perforated Orthotropic and Laminated Composite Plates under in-plane loading by genetic algorithm

In this paper, the parameters influencing the stress distribution around regular polygon cutouts in orthotropic plates and symmetrical composite laminates are studied, and then the genetic algorithm is used to determine the optimal values of effective parameter for attaining the lowest normalized stress and the highest failure strength. The parameters examined for this purpose are cutout geometry, curvature radius of cutout corners, cutout orientation, fiber angle, and load angle and stacking sequence of laminated composite. An analytical method is used to calculate the stress distribution around different cutouts under different in-plane loads. Using conformal mapping and complex variable method, the Lekhnitskii’s method that is originally introduced for circular and elliptical cutouts is expanded for cutouts with different shapes. The results show that the failure strength of perforated plates can be improved by choosing the appropriate shape of cutout and the optimal values of the effective parameters. The results show that contrary to expectation, the best cutout geometry is not always a circle, as in some cases by choosing the appropriate values of bluntness parameter, cutout orientation, and stacking sequence for a laminate with non-circular cutout the failure strength higher than that of a circular cutout can be achieved.

Elastoplastic analysis of FGM plate with a central cutout of various shapes under thermomechanical loading

ABSTRACTThe present work aims to study the elastoplastic buckling, postbuckling, and failure behavior of perforated Ni/Al2O3 functionally graded material (FGM) plate with various shaped cutouts (i.e., circular, square, diamond, and elliptical) of various sizes under thermomechanical loading conditions using finite element method (FEM). The nonlinear FEM formulation is based on the first-order shear deformation theory and von Kármán’s nonlinear kinematics in which the material nonlinearity is incorporated. The nonlinear temperature-dependent thermoelastic material properties of FGM plate are varied in the thickness direction by controlling the volume fraction of the constituent materials (i.e., ceramic and metal) as per a power law, and Mori–Tanaka homogenization scheme is applied to evaluate the properties at a particular thickness coordinate of FGM. In accordance with the Tamura–Tomota–Ozawa model (TTO model), the ceramic phase of FGM is considered to be elastic, whereas the metal phase is assumed to be elastoplastic. Further, the elastoplastic analysis of FGM is assumed to follow J2 plasticity with isotropic hardening. After validating the present formulation with the results available in the literature, various numerical studies are conducted to examine the effects of material inhomogeneity, thermal loading, cutout shape, and size on the elastoplastic buckling, postbuckling, and failure behavior of perforated FGM plate. It is observed that for smaller cutout sizes, the FGM plate with square shape cutout possesses maximum value of ultimate failure load; however, for larger cutout size, the FGM plate with diamond cutout depicts highest ultimate failure load. Furthermore, for all cutout shapes, the ultimate failure load of FGM plate decreases with an increase in cutout size. It is also revealed that irrespective of shape and size of cutout, the material plastic flow has considerable effect on postbuckling path of FGM plate, and under thermomechanical loading conditions, the FGM plate shows destabilizing response after the point of maximum postbuckling strength.

Numerical Study of the Effect of Presence of Geometric Singularities on the Mechanical Behavior of Laminated Plates

In this paper, an effort is made to understand the effects of geometric singularities on the load bearing capacity and stress distribution in thin laminated plates. Composite plates with variously shaped cutouts are frequently used in both modern and classical aerospace, mechanical and civil engineering structures. Finite element investigation is undertaken to show the effect of geometric singularities on stress distribution. In this study, the stress concentration factors (SCFs) in cross-and-angle-ply laminated as well as in isotropic plates subjected to uniaxial loading are studied using a quadrilateral finite element of four nodes with thirty-two degrees-of-freedom per element. The varying parameters such as the cutout shape and hole sizes (a/b) are considered. The numerical results obtained by the present element are compared favorably with those obtained using the finite element software Freefem++ and the analytic findings published in literature, which demonstrates the accuracy of the present element. Freefem++ is open source software based on the finite element method, which could be helpful to study and improving the analyses of the stress distribution in composite plates with cutouts. The Freefem++ and the quadrilateral finite element formulations will be given in the beginning of this paper. Finally, to show the effect of the fiber orientation angle and anisotropic modulus ratio on the (SCF), number of figures are given for various ratio (a/b).