Elliptical Cutout Research Articles

Validation of spline modeling for calculation of electron insert factors for varian linear accelerators.

There are several methods available in the literature for predicting the insert factor for clinical electron beams. The purpose of this work was to build on a previously published technique that uses a bivariate spline model generated from elliptically parameterized empirical measurements. The technique has been previously validated for Elekta linear accelerators for limited clinical electron setups. The same model is applied to Varian machines to test its efficacy for use with these linear accelerators. Insert factors for specifically designed elliptical cutouts were measured to create spline models for 6, 9, 12, 16, and 20 MeV electron energies for four different cone sizes at source‐to‐surface distances (SSD) of 100, 105, and 110 cm. Insert factor validation measurements of patient cutouts and clinical standard cutouts were acquired to compare to model predictions. Agreement between predicted insert factors and validation measurements averaged 0.8% over all energies, cones, and clinical SSDs, with an uncertainty of 0.6% (1SD), and maximum deviation of 2.1%. The model demonstrated accurate predictions of insert factors using the minimum required amount of input data for small cones, with more input measurements required for larger cones. The results of this study provide expanded validation of this technique to predict insert factors for all energies, cones, and SSDs that would be used in most clinical situations. This level of accuracy and the ease of creating the model necessary for the insert factor predictions demonstrate its acceptability to use clinically for Varian machines.

Buckling and postbuckling performance of composite fuselage panels with cutouts using continuous streamline fibres

In this paper the buckling and postbuckling behaviour of variable-stiffness composite fuselage panels with window openings based on streamline fibres is addressed. Streamlines of a fluid flow around a given body that represents the cutout are adopted to define the fibre trajectories that curve around the cutout in a continuous fashion. Plates and shells with circular and elliptical cutouts subjected to compressive and shear loads are investigated. Various design scenarios using different laminate layups are considered. As a first step, an optimum stacking sequence is obtained for maximum buckling capacity. Then, a postbuckling analysis is performed to evaluate the initial postbuckling stiffness that represents the strength of the laminates beyond buckling. The buckling and postbuckling performance of panels with streamline fibres is compared with that obtained for traditional panels with straight fibres. It is shown that significant improvements in the buckling capacity can be achieved using streamline fibres instead of straight ones. Moreover, laminates with streamline fibres optimized for maximum buckling loads exhibit a higher postbuckling strength than do the laminates with straight fibres.

Continuous Tow Steering Around an Elliptical Cutout in a Composite Panel

Cutouts are widely used to accommodate windows, openings for access purposes, or fasteners in the primary structural parts of airplanes. The presence of cutouts in composite panels results in stress or strain concentrations, leading to potentially reduced load-carrying capacity. Steering tows around cutouts using emerging techniques in three-dimensional (3-D) printing and advanced fiber placement can potentially alleviate such problems. Continuous tow steering around cutouts also eliminates fiber cutting, thereby precluding ply-level 3-D stress concentration, which could otherwise lead to delamination-induced damage. This work examines stress and strain concentrations, using continuous tow steering, around a representative wingbox access hole. Buckling response under compression loading together with stress and strain concentrations under both tensile and compression loads are examined. A steered configuration shows a 26% improvement in buckling performance in comparison with the equivalent straight-fiber configuration. Under tensile loading, the maximum stress and strain concentration factors around the cutout are 29 and 32% larger, respectively, for straight-fiber orientations than those with steered tows around the cutout. For the compression loading condition, the direct strain of the panel with straight-fiber orientations was found to be three times that of steered-fiber trajectories in the vicinity of the cutout.

Investigations on crush behavior and energy absorption characteristics of GFRP composite conical frusta with a cutout under axial compression loading

The changes in energy-absorption and deformation characteristics of thin-walled E-glass fiber reinforced composite conical frusta upon introduction cutouts were studied through quasi-static axial compression loading. The 15°, 18° and 21° semi-apical angled conical frusta with a circular, square, and elliptical cutout were axially compressed, and its crush-force-efficiency, energy-absorption, and specific-energy-absorption (SEA) characteristics were analyzed. Further, the ABAQUS® finite element software was used to simulate the crush behavior of perfect and imperfect conical frusta, and the corresponding results were compared with the experimental results, and the results are reported in this article.

Hygro-Thermo-Mechanical Vibration and Buckling Analysis of Composite Laminates with Elliptical Cutouts under Localized Edge Loads

Perforated composite laminates are frequently encountered in multiple engineering applications as sub-components of complicated structures. In many of these applications, the primary objective of using the panel is to resist buckling under diverse environmental and loading conditions. This paper is mainly focused on the vibration and buckling responses of composite laminates with elliptical cutouts subjected to localized edge loads under different hygrothermal environments. Toward this, a nine-noded heterosis plate element has been utilized to discretize the plate by adopting a refined meshing pattern around the elliptical cutout. The geometric nonlinearity has been incorporated to predict free vibrations under the hygrothermal environment. Considering the plethora of applications of composite laminates in hygrothermal conditions, a new temperature/moisture-dependent model is presented by taking into consideration various mechanical loadings. For a given environmental and loading condition, the stress distribution within the perforated panel is highly non-uniform in nature and hence, a novel dynamic approach has been proposed to solve buckling problems by adopting two sets of boundary conditions. A MATLAB program has been developed to investigate the effect of various parameters such as elliptical cutout size, elliptical orientation, elliptical cutout eccentricity, thickness and boundary conditions of the laminated composite plate under diverse hygrothermomechanical loading conditions. A notable difference in the critical buckling load is observed when the locally prestressed perforated panels are subjected to complex hygrothermal environments, especially at larger elliptical cutouts and hence the importance of localized edge loads under hygrothermal environment is emphasized.

Local Elasto–plastic Buckling of Isotropic Plates With Cutouts Under Tension Loading Conditions

The motivation of the presented study was the observation of the existence of local loss of stability “tension buckling” in the experimental tests of composite and metallic plates with cut-outs subjected to tension. Because of this, the numerical analyses of the aluminum plate with elliptical or circular cutouts at the center and subjected to tensile load are studied in the paper. Although the whole structure is uniformly stretched, the circumferential compressive stresses in the vicinity of the cutout edge are observed. First of all, the linear buckling analysis is carried out for different sizes of the holes. Based on these results, the size of the hole is chosen, where the circumferential stress magnitude in the vicinity of the cutout is the lowest or even comparable to the yield stress of the material. The computations are made for three different values of thickness. Finally, the nonlinear buckling analysis is carried out without and with the plasticity effects included. Generally, in the case of the circular and vertically oriented elliptical cut-out, the loss of stability in the tensed plate is always observed. However, in elastic-plastic analyses, the values of the critical parameters significantly differ from the results obtained for elastic buckling. Finally, the critical geometries for further experimental tests were defined.

Determination of Optimal Flat-End Head Geometries for Pressure Vessels Based on Numerical and Experimental Approaches.

The experimental and numerical analyses of the pressure vessels with different flat ends are presented and discussed in the paper. The main aim of the study is to propose the optimal flat head end geometry. The analyses are focused on the comparison of standardized geometries and with the proposed elliptical cut-out. The experimental tests with the application of strain-gauge measurements and numerical modeling of the pressure vessel are conducted. The behavior under low and high pressures and the influence of the residual welding stresses, material properties, and geometrical tolerances on the level of the plastic deformation in the flat end is discussed. It is presented that the rules given in the recent standard are not sufficient for optimal selection of the optimal geometry. It is observed that in certain geometries the deviations of the pipe thickness may lead to a significant increase of the equivalent stresses. The residual welding stresses have a significant influence on the stress and strain level—particularly in the stress relief groove (SRG). The performed study and comparison of the different geometries allow for the proposal of the optimal shape of the flat end. It appeared that the pressure vessels with SRG are the most optimal choice, particularly when elliptic shapes are in use. In some cases (i.e., pipe with wall-thickness equal to 40 mm and the flat end with circular SRG), the optimal configuration is reached for dimensions beyond the admissible by code range.

Closed-form methodology for the bending of symmetric composite plates with cutouts and non-uniform lay-up

The present work is focused on the development of a Lekhnitskii-based closed-form methodology for the analysis of composite plates with elliptical cutouts and non-uniform lay-up, under bending loads. Due to an innovative approach, the methodology capable of dealing with changes of the plate’s thickness, stacking sequence, and the inclusion of local reinforcements. The article considers only the bending response of the plates, under the assumption of symmetric laminates. The motivation to carry out this investigation is to simplify the labour of the calculation engineers during the first phases of the component’s design, allowing an efficient evaluation of the most promising configurations by means of conducting parametric analyses.

A particle method development for analysing the post-buckling behaviour of composite plate with cut-out

In this research, nonlinear buckling and post-buckling behaviours of composite plates with the ‎circular/elliptical cut-out are investigated using particle semi-energy (PSE) method. The semi-‎energy is based on the solution of compatibility equation via an Airy force and out-of-plane ‎displacement functions. The‏ ‏unknown parameters of these functions are determined by ‎minimizing the potential energy. The integrals of potential energy are replaced with ‎summations at perforated plate particle (node). The cut-out is modelled easily using these ‎nodes. The advantages of this method are modelling cut-out by nodes easily and proposing ‎just one of the displacement fields (i.e. out-of-plane). Based on the results, there is a good ‎agreement (1.25%) between the post-buckling loads derived from PSE of this paper and ‎experimental test of other literature. The accuracy of the finite element method (FEM) is 7.5% ‎with respect to experimental test. The influences of rotating elliptical cut-out and replacing it ‎with two circular cut-outs via same areas on post-buckling load are investigated‎

Progressive failure analysis of laminated plate containing elliptical cutout

PurposeThe prediction of accurate failure strength and a composite laminate failure load is of paramount importance for reliable design. The progressive failure analysis helps to predict the ultimate failure strength of the laminate, which is more than the first ply failure (FPF) strength. The presence of a hole in the laminate plate results in stress concentration, which affects the failure strength. The purpose of the current work is to analyze the stress variation and progressive failure of a symmetric laminated plate containing elliptical cutouts under in-plane tensile loading. The effect of various parameters on FPF and last ply failure (LPF) strength is studied.Design/methodology/approachThe ply-by-ply stresses around elliptical cutouts are obtained analytically using Muskhelishvili's complex variable formulation. To predict the progressive failure, Tsai–Hill (T-H) and Tsai–Wu (T-W) failure criteria are used, and depending on the mode of failure, lamina modulus is degraded.FindingsThe study has revealed that fiber orientation and stacking sequence for given loading have the most significant effect on the laminate's failure strength.Originality/valueComplex variable method and conformal mapping are simple and proficient for studying failure analysis of a laminated plate with elliptical cutout.

Applicability Evidence of Constructal Design in Structural Engineering: Case Study of Biaxial Elasto-Plastic Buckling of Square Steel Plates with Elliptical Cutout

The application of the Constructal Design method in Heat Transfer and Fluid Mechanics areas is an already consecrated approach to geometrically evaluate these flow engineering systems. However, this approach in Mechanics of Materials realm is not yet widely used, since one can find only few publications about it in literature. The Constructal Design is based on the Constructal Law, a physical law that explains the universal phenomenon of evolution of any finite size flow system. Therefore, the main goal here is to show that the Constructal Design can also be used in dedicated Structural Engineering problems as an effective method for geometric evaluation. The obtained results prove the Constructal Design applicability definitively in Mechanics of Materials.

Stress analysis of infinite laminated composite plate with elliptical cutout under different in plane loadings in hygrothermal environment

AbstractThis paper presents the solution of stress distribution around elliptical cutout in an infinite laminated composite plate. Analysis is done for in plane loading under hygrothermal environment. The formulation to obtain stresses around elliptical hole is based on Muskhelishvili’s complex variable method. The effect of fibre angle, type of in plane loading, volume fraction of fibre, change in temperature, fibre materials, stacking sequence and environmental conditions on stress distribution around elliptical hole is presented. The study revealed, these factors have significant effect on stress concentration in hygrothermal environment and stress concentration changes are significant with change in temperature.

RSM and ANN modeling of the energy absorption behavior of steel thin-walled columns: a multi-objective optimization using the genetic algorithm

In many industries, it is necessary to use structures that exhibit a proper stability against the design loads and depreciate the energy in a controlled manner. In this study, the energy absorption characteristics of thin-walled structures with rectangular cross sections are investigated under the quasi-static loading. The section of structures has a different aspect ratio, and in all of them, an elliptical cutout with a different diameter ratio exists on the larger side. In all instances, the area of the cross section and cutout is constant. Hence, an experimental design with two design parameters consisting of the shell aspect ratio and the diameter ratio of the cutout was conducted by applying the central composite design method. Energy absorption parameters were modeled using the artificial neural network and the response surface method. A systematic crashworthiness study was carried out with a multi-objective optimization design using the genetic algorithm. The results showed that the optimal amount of the specific energy absorption was 14.48 kJ/kg and the optimal amount of the peak crushing load was 37.77 kN which was obtained in the aspect ratio of 1 and the diameter ratio of 0.7. The validity of the results was confirmed by empirical experiments.

Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

Abstract Recently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

Thermal buckling of curvilinearly stiffened laminated composite plates with cutouts using isogeometric analysis

This research presents the Non-Uniform Rational B-Splines (NURBS) based isogeometric finite element analysis of stiffened laminated composite plates. A first-order shear deformation theory is used to derive the governing equations by employing a variational formulation. Isotropic, orthotropic and laminated composite plates stiffened with multiple curvilinear stiffeners of different profiles are investigated. A novel way to achieve displacement compatibility between the panel and stiffeners interfaces is introduced. An easy way of modeling plates with complicated cutouts by using edge curves and generating a ruled NURBS surface between them is described. Influence on the critical thermal buckling load due to the presence of circular and elliptical cutouts is also investigated. Results of parametric studies are presented which show the influence of ply orientation, size and orientation of the cutout, and the position and profile of the curvilinear stiffener. The numerical examples show high reliability and efficiency of the proposed formulation when compared to other published solutions and those obtained using ABAQUS, a commercial software.

Non-linear deflection and stress analysis of laminated composite sandwich plate with elliptical cutout under different transverse loadings in hygro-thermal environment

Abstract In this paper, non-linear transverse deflection, stress and stress concentration factors (SCF) of isotropic and laminated composite sandwich plate (LCSP) with and without elliptical cutouts subjected to various trans-verse loadings in hygrothermal environment are studied. The basic formulation is based on secant function-based shear deformation theory (SFSDT) with von-Karman nonlinearity. The governing equation of non-linear deflection is derived using C0 finite element method (FEM) through minimum potential energy approach. Normalized trans-verse maximum deflections (NTMD) along with stress concentration factor is determined by using Newton’s Raphson method through Gauss point stress extrapolation. Influence of fiber orientations, load parameters, fiber volume fractions, plate span to thickness ratios, aspect ratios, thickness of core and face, position of core, boundary conditions, environmental conditions and types of transverse loading in MATLAB R2015a environment are examined. The numerical results using present solution methodology are verified with the results available in the literatures.

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.

Nonlinear and post-buckling responses of FGM plates with oblique elliptical cutouts using plate assembly technique

The aim of this study is to obtain the nonlinear and post-buckling responses of relatively thick functionally graded plates with oblique elliptical cutouts using a new semi-analytical approach. To model the oblique elliptical hole in a FGM plate, six plate-elements are used and the connection between these elements is provided by the well-known Penalty method. Therefore, the semi-analytical technique used in this paper is known as the plate assembly technique. In order to take into account for functionality of the material in a perforated plate, the volume fraction of the material constituents follows a simple power law distribution. Since the FGM perforated plates are relatively thick in this research, the structural model is assumed to be the first order shear deformation theory and Von-Karman\'s assumptions are used to incorporate geometric nonlinearity. The equilibrium equations for FGM plates containing elliptical holes are obtained by the principle of minimum of total potential energy. The obtained nonlinear equilibrium equations are solved numerically using the quadratic extrapolation technique. Various sets of boundary conditions for FGM plates and different cutout sizes and orientations are assumed here and their effects on nonlinear response of plates under compressive loads are examined.

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.