Elliptical Cutout Research Articles

Computational modeling and constructal design method applied to the mechanical behavior improvement of thin perforated steel plates subject to buckling

Perforated steel plates are structural components widely employed in engineering. In several applications these panels are subjected to axial compressive load, being undesired the occurrence of buckling. The present work associates the computational modeling and the constructal design method to obtain geometries, which maximizes the mechanical behavior for these components. A numerical model was used to tackle with elastic and elasto-plastic buckling. Square and rectangular plates with centered elliptical cutouts were considered and several hole volume fractions and ratios between the ellipse axes (H0/L0) were taken into account. Stress limit improvements around 100% were achieved depending only on the cutout shape.

Multiobjective optimization of laminated composite plate with elliptical cut-out using ANN based NSGA-II

Multiobjective optimization of laminated composite plate with elliptical cut-out using ANN based NSGA-II

Mechanical Characterization and Finite Element Investigation on Properties of PLA-Jute Composite

materials are on high demand in recent days amongst high performance products that need to be strong enough in severe loading conditions. It can be developed with a suitable combination of matrix and reinforcement materials to meet the requirement of specific applications. The present work attempts to form composite plates using a combination of natural polymers and fibers to improve certain properties. The focus is to develop a biodegradable composite of comparable properties with those available commercially. The formed plates are tested to determine different mechanical properties such as tensile strength, impact resistance, hardness etc. The thermal parameters are also determined by DSC (Differential scanning calorimetry) test. A finite element analysis is conducted and the results have been compared with Graphite epoxy composite for checking the effective use of this material. responses along with vibration behavior of laminated composite plates have been extensively investigated. Pandya and Kant (6) has proposed a C0 continuous displacement finite element formulation of laminated composite plates under transverse loading using Higher order Shear Deformation theory. The static behavior of laminated composite and sandwich plates is studied analytically using Navier's technique based on higher order refined theory by Kant and Swaminathan (7). Soltani et al. (8) has analyzed nonlinear tensile behavior of glass fibre reinforced aluminium laminates using finite element modeling. Attallah et al. (9) presented 3- D solutions of laminated composite plates by using a combined finite strip and state space approach. Bharet al. (10) analyzed the significance of the HSDT over the FSDT for laminated composite stiffened plates by using FEM. Grover et al. (11) investigated the static and buckling analysis of laminated composite and sandwich plates in the framework of a new inverse hyperbolic shear deformation theory and this theory is based on shear strain shape function. Kumar et al. (12) studied static analysis of thick skew laminated composite plate with elliptical cutout based on 3-D elasticity theories. Riyah and Ahmed (13 investigated stresses of composite plates with different types of cutouts. Rezaeepazhand and Jafari (14) analytically analyzed the stresses of composite plates with a quasi-square cutout subjected to uniaxial tension based on Lekhnitskii's theory. Static analysis of isotropic rectangular plate with various support conditions and loads are studied by Vanamet al. (15) using finite element analysis (FEA). A recent study detailed the effect of cutout orientation on SCF (16).

Post-buckling progressive damage of CFRP laminates with a large-sized elliptical cutout subjected to shear loading

Cutouts are always located in aerospace composite structures to meet specified requirements on the service and functions. The presence of cutout, especially large-sized cutout, would result in a significant stress concentration, and consequently a complicated failure mechanism. This paper presents an experimental and numerical study on the post-buckling damage process of high-performance carbon fiber reinforced polymer (CFRP), T800/X850, multidirectional composite laminated specimen. The simply supported specimen is with a central large-sized elliptical cutout and subjected to shearing load. In the numerical analysis, a damage model incorporating both advanced strain softening schemes and cross-coupling effect between the failure mechanisms is constructed for the damage simulation. Regularizations are implemented for coupling the damage variables to address the deficiencies of the existing model and access the real physical damage behavior of laminated composites. The strain invariant failure theory is employed for evaluation of delamination. To assess the objectivity of the present numerical model, the numerical predictions are compared with experimental data. The predicted damage and propagation patterns show good agreement with experiment results.

Buckling optimization of laminated composite plate with elliptical cutout using ANN and GA

Buckling optimization of laminated composite plates is significant as they fail because of buckling under in-plane compressive loading. The plate is usually modeled without cutout so that the buckling strength is found analytically using classical laminate plate theory (CLPT). However in real world applications, the composite plates are modeled with cutouts for getting them assembled and to offer the provisions like windows, doors and control system. Finite element analysis (FEA) is used to analyze the buckling strength of the plate with cutouts and it leads to high computational cost when the plate is optimized. In this article, a genetic algorithm based optimization technique is used to optimize the composite plate with cutout. The computational time is highly reduced by replacing FEA with artificial neural network (ANN). The effectiveness of the proposed method is explored with two numerical examples.

Thermo-mechanical buckling analysis of functionally graded plates with an elliptic cutout

In this paper, buckling of functionally graded plates (FG plates) with an elliptical cutout under combined thermal and mechanical loads is investigated using Finite Element Method. Unlike other studies in which the plates are exposed to thermal or mechanical loads, in this study it is assumed that the mechanical and thermal loads are applied simultaneously. The material properties are assumed to vary across plate thickness according to power law distribution of the volume fraction of constituents. The plate formulation is based on the First order Shear Deformation Theory (FSDT) and element stiffness matrices are derived based on the principle of minimum potential energy. A flexible mesh generation algorithm is prepared in which the mesh density around the hole can be controlled easily. After validating the results of developed FE code with those available in the literature, the effect of boundary condition, plate aspect ratio and cutout radius ratio on thermo-mechanical buckling behavior of FG plates is studied and stability diagrams are presented. Finally useful conclusions are presented.

Acoustic Emission based Monitoring of Cut-out Geometry Effects in Carbon-Epoxy Laminates under Uni-axial Compression

In this paper, symmetric cross ply CFRP laminates were fabricated using hand layup with LY556 epoxy resin as matrix and the specimens were cut without cut-out, with circular, vertical elliptical and horizontal elliptical cut-outs according to the ASTM D 7137 standard using water jet cutting. The CFRP specimens with and without cut-outs were subjected to compression under controlled condition accompanied by acoustic emission (AE) monitoring. The ultimate compressive strength for specimens with and without cut-outs were determined and compared. The optimum cut-out with lesser reduction in compressive strength was determined. The nature and dominance of different failure modes in each type of cut-out were investigated using AE. Finally the result gives useful information about improved design of laminated composites with cut-outs suitable for different applications.

Exact solution for free vibration analysis of an eccentric elliptical plate

The method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions is used to investigate the free flexural vibrations of a fully clamped thin elastic panel of elliptical planform containing an elliptical cutout of arbitrary size, location, and orientation. The first five natural frequencies are calculated for various plate/cutout aspect ratios and selected cutout location/orientation parameters. Also, a number of representative vibration mode shapes are depicted in graphical form. The accuracy of solutions is demonstrated through proper convergence studies, and the validity of results is established with the aid of a commercial finite element package as well as by comparison with those in the existing literature.

Free vibration analysis of an elliptical plate with eccentric elliptical cut-outs

The elaborated collocation multipole method is employed to obtain a semi-analytical solution, involving proper products of angular and radial Mathieu functions, for the free flexural vibrations of a fully clamped thin elastic plate of elliptical planform containing multiple elliptical cutouts of arbitrary size, location, and orientation. The problem boundary conditions are satisfied by uniformly collocating points on the boundaries, and exactly calculating the normal derivative of plate displacement at the collocation points through use of appropriate directional derivative in each coordinate system. The multipole expansion is truncated to yield a coupled algebraic linear system of equations that is then solved for the nontrivial eigensolutions. Extensive numerical simulations present the first three calculated natural frequencies and the associated deformed mode shapes of an elliptical plate with elliptical/circular cutouts, for a wide range of plate/cutout aspect ratios, and cutout location/orientation parameters. The accuracy of solutions is checked through appropriate convergence studies, and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data available in the existing literature.

The effects of cut-outs on lateral buckling behavior of laminated composite beams

This paper addresses the effects of different cutouts on the lateral buckling behavior of composite beams made of polymer matrix composites. Cut-outs like circular, rectangular, square, elliptical and triangular are generally used in composites as design requirements. This paper includes two parts; first part is an experimental part and second is a numerical part. In the experimental part, samples with square, circular and without cutouts are used and critical lateral buckling loads are determined experimentally. In the second part, finite element analysis is performed to predict the effects of different cutouts (square, circular, triangular and elliptical), location and size of cutouts on the lateral buckling behavior of the beam. The results show that cutout shape has important effect on the lateral buckling load. The elliptical cutout is the best and square cutout is the worst cutout type. It is also concluded that fiber orientation angle, cutout location and size affect the lateral buckling load.

Exact solution for free in-plane vibration analysis of an eccentric elliptical plate

A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters.

The effects of cutouts on buckling behavior of composite plates

AbstractCutouts such as circular, rectangular, square, elliptical, and triangular shapes are generally used in composite plates as access ports for mechanical and electrical systems, for damage inspection, to serve as doors and windows, and sometimes to reduce the overall weight of the structure. This paper addresses the effects of different cutouts on the buckling behavior of plates made of polymer matrix composites. To study the effects of cutouts on buckling, loaded edges are taken as fixed and unloaded edges are taken as free. Finite element analysis is also performed to predict the effects of different geometrical cutouts, orientations, and position of cutouts on the buckling behavior. The results show that fiber orientation angle and cutout sizes are the most important parameters on the buckling loads. For all types of cutouts the buckling loads decrease dramatically by increasing the fiber orientation angle. It is observed that minimum buckling load is reached when 45° fiber angle is used, and after this angle critical buckling load begins to increase. Also, it is concluded that while fiber orientation angle is 0°, elliptical cutout has the highest buckling load and while fiber orientation angle is 45°, circular cutout has the highest buckling load.

An analytical method for the determination of stress and strain concentrations in textile-reinforced GF/PP composites with elliptical cutout and a finite outer boundary and its numerical verification

Stress concentrations in the vicinity of cutouts can often be regarded to be the limiting factor for a whole structure. As a further development of prior research at the Institute of Lightweight Engineering and Polymer Technology, an analytical method for the determination of the whole stress-strain fields in the vicinity of holes in multilayered textile-reinforced composites has been developed, which takes into consideration the influences of a finite outer boundary of the specimen. The analytical method is based on the classical laminate theory and the use of complex-valued potential functions. To account for the shape of the specimen, the method of conformal mappings is applied for the inner boundary, while a combination of boundary collocation and least squares method is used for the outer boundary. The method allows a layer-by-layer analysis of stress concentrations. For the verification of the developed calculation model, extensive experimental and numerical finite-element (FE) studies have been carried out on multilayered GF/PP plates with different laminate layups, notches, and specimen dimensions. The comparison of the experimentally or numerically determined results with the analytically calculated ones shows a very good correlation, of which the numerical studies are presented here for the first time. In a second step, the applicable boundary conditions on the outer boundary have been extended in such a way that varying stress and moment resultants can be applied, so that the calculation method can be used as an analytical sub-model in combination with FE techniques.

Buckling Analysis of Laminated Composite Panel with Elliptical Cutout Subject to Axial Compression

A buckling analysis has been carried out to investigate the response of laminated composite cylindrical panel with an elliptical cutout subject to axial loading. The numerical analysis was performed using the Abaqus finite-element software. The effect of the location and size of the cutout and also the composite ply angle on the buckling load of laminated composite cylindrical panel is investigated. Finally, simple equations, in the form of a buckling load reduction factor, were presented by using the least square regression method. The results give useful information into designing a laminated composite cylindrical panel, which can be used to improve the load capacity of cylindrical panels.

Elasto Buckling Behaviour Of Gfrp Laminated Plate With Central Holes

In various cases, it is roughly unavoidable to have holes in the plate elements for inspection, maintenance, and service purposes. In such cases, the presence of these holes redistributes the membrane stresses in the plates and may reduce their stability significantly. The buckling of such perforated plates has received the attention of many researchers over the past years. This paper deals with the buckling analysis of symmetrically and laminated composite plates under two sides simply supported and two sides free boundary condition. The effects on buckling load by various cut out shapes (circular, square and elliptical) and sizes are investigated. It was observed that the plate with the circular cutout yielded the greatest critical buckling load when compared with the square and elliptical cutouts.

Topological sensitivity derivative with respect to area, shape and orientation of an elliptic hole in a plate

The topological sensitivity derivative of a functional expressed in terms of displacement, strain or stress fields and boundary tractions is derived for the case of an elliptical hole introduced in the plate. The derivative is specified with respect to the hole area, the length of ellipse axes and their orientation in terms of primary and adjoint state fields. The shape sensitivity derivative for a finite hole can be applied and the topological derivative with respect to the hole area is obtained in the limiting case. The transition to a plane crack occurs for vanishing length of minor axis and the topological derivative with respect to crack length is then derived from the general formulae. The results can be useful in optimal design procedures by selecting positions, shape and orientation of elliptical cutouts.

Elasto-plastic buckling analysis for perforated steel plates subject to uniform compression

This study investigates the elasto-plastic buckling behaviour of simply supported square and rectangular thin steel plates having elliptic cut-outs by means of finite element method. Plates with simply supported in the out-of-plane direction are applied uniform compression in long-edge direction. A50 steel was used in the analysis and the focus was on the effect of plate aspect ratio, elliptical hole size, elliptical hole angle, elliptical hole location and slenderness ratio on buckling behaviour. It was found in the study that as the plate slenderness ratio increases, the critical buckling stress decreases for all the perforated plates.

Analytical and experimental analysis of stress concentration in notched multilayered composites with finite outer boundaries

A solution method for stress concentration problems of fibre- and textile-reinforced multilayered composites with account of the influence of a circular or elliptical cut-out and of the finite outer boundary of a composite plate is presented. The method is based on complex-valued displacement functions and conformal mappings in combination with the boundary collocation and least squares methods. This allows a layer-by-layer calculation of full stress, strain, and displacement fields in a generally multilayered anisotropic plate. To verify the calculation model, extensive experimental studies have been carried out. For all the combinations of multilayered GF/PP plates, laminate lay-ups, and notch and specimen dimensions investigated so far, a very good agreement between the analytical calculations and experimental results is found to exist.

Dynamic crushing characteristics of high strength steel cylinders with elliptical geometric discontinuities

Thin-walled members are commonly used as energy absorbers in engineering structures and often contain cutouts. This study performed numerical simulations of high strength steel cylindrical shells with elliptical cutouts subjected to dynamic axial impact. The LS-DYNA code was the primary analytical tool used to analyze the influence of cutout locations, cutout shapes and symmetry of cutout on the energy absorption capabilities and the crush characteristics of tubes with a cutout. For high strength steel tubes made from a rate sensitive material, the stress–strain curves of different strain rates were used to elucidate the effect of dynamic impact on the strain rate. Our results show that collapse crushing behavior is strongly influenced by the location and symmetry of cutouts and the variation of major axis influences the peak crush load.

Buckling of steel cylindrical shells with an elliptical cutout

Numerical simulation and analysis of steel cylindrical shells with various diameter and length having an elliptical cutout, subjected to axial compression were systematically carried out in this paper. The investigation examined the influence of the cutout size, cutout angle and the shell aspect ratios L/D and D/t on the pre-buckling, buckling, and post-buckling responses of the cylindrical shells. For several specimens, an experimental investigation was also carried out via an INSTRON 8802 servo hydraulic machine and the results obtained from the experiments were compared with numerical results. A very good accordance was observed between the results obtained from the finite element simulation and the experiments. Furthermore, some equations in the form of a buckling load reduction factor were developed.