Cutout Ratios Research Articles

On transient responses of sandwich plate with cutout using FEM

In the present research work, time-dependent transverse deflection responses of a sandwich composite plate with cutout have been analyzed by using lower-order theory in conjunction with the finite element approach. Initially, the sandwich structure with the cutout (square, pentagonal, hexagonal, and circular) is developed in the ANSYS platform using ANSYS parametric design language (APDL) code. The necessary material properties of the sandwich structure (face sheet and core) are assigned. The developed model has been discretized using 8 noded shell element (Shell 281). The structure is now assigned a simply supported end condition and uniformly distributed loading (UDL). Now, the numerical model’s accuracy is evaluated by comparing the simulated results to previously published literature’s results. The developed simulation model has been used further to investigate the effect of cutout ratios, cutout shape (square, pentagon, hexagon and circle) and core to face thickness ratio on the transient response of a square sandwich panel via new examples. The findings of the examples are analyzed and discussed in detail.

Comparative study of cross-ply laminated composite materials and effect of buckling response with and without cutouts

In this work, finite element analysis has been done along with experimental test and conducted using numerical and experimental tests of the buckling response of quasi-static compressive loading of six layers woven cross-ply laminated composite material [0º/90º/0º] with centrally square and circular cutouts. The effect of cut-out shape and its size with a buckling load were obtained experimentally and numerically. Compression experiment has been performed by using INSTRON machine, and the experimentally obtained buckling loads are compared with a numerical results obtained by ANSYS simulation program. Both experimental and numerical results are showing good agreement. It is noticed that the buckling load of the composite plate has been decreased with the increasing of the size of cutout. The cutout area, cutout ratio (d/w), fiber weight, plate thickness and fiber type of the plate has a major effect to the load of the cross-ply laminated composite plates.

Influence of porosity and nonuniform in-plane edge loads on vibration and buckling response of power law and sigmoid function based FG sandwich plates with geometrical discontinuities

Porosity defects can emerge during the manufacturing process of Functionally Graded Sandwich Plates (FGSPs). In practice, FGSPs have geometric discontinuities/cutouts and are exposed to Nonuniform In-plane Edge Loads (NIELs). The presence of porosity, cutout and NIELs causes a significant reduction in the stiffness of the plate affecting its vibration and buckling behavior. Therefore, in this paper vibration and buckling results obtained using the Finite Element (FE) method hitherto not reported in the literature are presented for porous FGSPs with cutouts and subjected to NIELs. Four types of porosity distribution models are explored, and the porosity imperfections are modeled as the criteria of stiffness reduction. Porosity-dependent material properties of FGSPs are evaluated using modified power law and sigmoid function. The current study incorporates two distinct kinds of sandwich configuration in such a way that there is no material mismatch along the thickness direction. The application of different cases of NIELs on the plate with cutouts leads to the development of nonuniform stresses. Hence a novel dynamic approach has been proposed to evaluate buckling loads by implementing two sets of boundary conditions. The first set of boundary conditions calculates pre-buckling stress, while second set calculates critical buckling loads. The generated results from the current FE formulation are compared with existing results in the literature to ensure accuracy. Finally, the effect of porosity distribution, NIELs, cutout ratio and its positions, support conditions, volume fraction exponents and geometric parameters on the vibration and buckling response are studied and discussed to arrive at appropriate conclusion.

Effects of different interlaminar hybridization and cutout sizes on the vibration and buckling characteristics of fiber metal composite laminates under partial edge loads

Fiber reinforced polymer composites are quickly gaining market share in structural applications, but further growth is limited by their lack of toughness. Fiber hybridization is a promising strategy to toughen composite materials. By combining two or more fiber types, these hybrid composites offer a better balance in mechanical properties than non-hybrid composites. This study presents the effect of different interlaminar hybridization and cutout sizes on the vibration and buckling characteristics of hybrid fiber metal laminates (HFMLs) subjected to partial edge loads by developing finite element formulation. Since the stress distribution within the plate element is highly non-uniform in nature, the dynamic approach has been used to solve the buckling problems wherein two sets of boundary conditions are used, one for pre-buckling stresses and other one for buckling load calculations. A 9-noded heterosis plate element has been used to discretize the plate by taking into account the effect of shear deformation and rotary inertia. The present study consists of aluminum metal face sheets bound with four layered symmetric hybrid cross-ply laminate schemes. In this scheme, six different hybrid combinations have been considered. The performance of each hybrid combination is investigated under various loading combinations. Further, the effect of different parameters such as boundary condition, cutout ratio, width and position of localized edge loads, plate aspect ratio, and hybrid configurations are included in this work. It is revealed from the study that the hybrid configurations under different cutouts significantly affect the vibration and buckling characteristics under different localized edge loads.

Effect of trapezoidal shaped laminated composite plate with and without cutout on vibration characteristics

Abstract In the present investigation, the influence of centrally placed circular cutouts, ply-orientation and boundary conditions on the vibration characteristics of laminated trapezoidal composite panels has been studied by using finite element technique. Towards this investigation, an eight node iso-parametric plate element has been used to discrete the laminated composite panel with seven degrees of freedom at each node. In the present mathematical formulation, the effect of shear deformation has been incorporated by using higher order shear deformation theory. Therefore, the present model is holds good for both thin and thick panels without applying any shear correction factors. The accuracy of the present model is confirmed by comparing present results with approachable literature. The parametric studies are carried out to examine the effect of various parameters such as different edge conditions, trapezoidal shape ratio, cutout ratio and aspect ratio of the trapezoidal laminated panel. It is observed from this study that the variation in natural frequency of the panel under different ply- orientations and boundary condition is predominant as compared to that of thick plate configuration.

Effect of sinusoidal and inverse sinusoidal In-plane loads on buckling and vibration characteristics of FRP panels with cutouts

Abstract The cutouts usually observed inside the aircraft and ship constructions toward facilitating water tubes, oil pipelines, electrical ducts, doorways, portholes and sometimes inspection objectives. These cutouts severely alter the vibration and buckling properties of the structural components. The panels examined under the work of uniaxial and bi-axial loading configurations. Furthermore, the consequences of different boundary conditions and cutout ratios are approached in this work. A 9-noded heterosis plate element utilized, involving the influence of shear deformation and rotary inertia. According to the outcomes, the size of cutout, ply-orientation and loading type seriously affects the vibration and buckling characteristics of laminated panels.

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°.

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.

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.

Free in-plane vibrations of annular sector plates with elastic boundary supports

In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular sector plates with elastic restraints along each of its edges. The in-plane displacement fields are universally expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. The expansion coefficients are considered as the generalized coordinates, and determined using the Rayleigh-Ritz technique. Several examples are presented to demonstrate the effectiveness and reliability of the current method for predicting the modal characteristics of annular sector plates with various cutout ratios and sector angles under different boundary conditions. It is also shown that annular and circle plates can be readily included as the special cases of the annular sector plates when the sector angle is set equal to 360°.

Vibration of Stiffened Plates with Cutout Subjected to Partial Edge Loading

The buckling and vibration characteristics of stiffened plates with cutout subjected to in-plane partial edge loadings at the plate boundary are studied using finite element method. Buckling loads and vibration frequencies are determined for different plate and cutout aspect ratios, various boundary conditions, partial edge loading at different locations, cutout ratios, various parameters of stiffeners by varying the number, size and location of the stiffeners. The analysis presented determines the stresses all over the region for different kinds of loading and edge conditions. 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 buckling and vibration characteristics are discussed and the free vibration results available in the literature for stiffened plates with/without cutout are compared.

압축하중을 받는 유공보강판 구조의 최종강도 설계식 개발

Ship structures are thin-walled structures and lots of cutouts, for example, of inner bottom structure, girder, upper deck hatch, floor and dia-frame etc. In the case where a plate has cutout it experiences reduced buckling and ultimate strength and at the same time the in-plane stress under compressive load produced by hull girder bending will be redistributed. In the present paper, we investigated several kinds of perforated stiffened model from actual ship structure and series of elasto-plastic large deflection analyses were performed to investigate into the influence of perforation on the buckling and ultimate strength of the perforated stiffened plate varying the cutout ratio, web height, thickness and type of cross-section by commercial FEA program(ANSYS). Closed-form formulas for predicting the ultimate strength of the perforated stiffened plate are empirically derived by curve fitting based on the Finite Element Analysis results. These formulas are used to evaluate the ultimate strength, which showed good correlation with FEM results. These results will be useful for evaluating the ultimate strength of the perforated stiffened plate in the preliminary design.

유공보강판의 좌굴 및 극한강도 특성에 관한 연구

선체는 기본적으로 판부재들의 조합으로 구성되어 있으며 상당수는 유공판(Perforated plate)으로 이루어져있다. 선체에 설치된 유공판으로서는 선체 상갑판 해치(하역시설로 사용), 선저부의 거더와 플로어(중량경감과 선박 건조 및 검사시 통로확보용), 다이어프램(중량경감 및 파이프 관통의 목적)등이 있다. 이들 유공판에 압축하중이 작용하면 좌굴과 극한강도 특성이 크게 변화할 뿐만 아니라 수반되는 면내응력도재 분포하게 되어 심각한 문제를 발생한다. 실적선에서는 유공주위에 스티프너 보강을 통하여 취약한 좌굴강도 보완하고 있으며, 유공을 고려한 실선에서 사용 중인 유공보강판 모델을 적용하여 좌굴강도 및 극한강도를 파악할 필요성이 있다. 이와 같은 측면에서 각 조선소에서는 각국 선급들이 제시하는 유공판의 좌굴설계식을 사용하여 강도계산을 하고 있으나 임의의 유공크기에 대한 좌굴강도 및 극한강도 평가법을 찾기란 매우 어려운 일이다. 본 연구에서는 실선에서 사용 중인 유공보강판의 모델을 조사하여 비선형 유한요소법(ANSYS)을 사용하여 면내 압축하중이 작용하는 경우에 대해서 유공비, 웹 치수, 두께 그리고 보강재 단면을 변화시켜가며, 극한강도 시리즈 해석을 수행하고 압축극한강도에 미치는 영향을 검토하였다. In ship structures many of the structural plates have cutouts, for example, at inner bottom structure, girder, upper deck hatch, floor and dia-frame etc. In the case where a plate has a cutout it experiences reduced buckling and ultimate strength and at the same time the in-plane stress under compressive load produced by hull girder bending will be redistributed In general, actual ship structure adopted reinforcement of stiffener around the cutout in order to preventing from buckling so it need to examine a buckling and ultimate strength behaviour considering a cutout because In many ship yards used class rule for calculating buckling strength but it is difficult to evaluate perforate stiffened plate with random size. In the present paper, we investigated several kinds of perforated stiffened model from actual ship and then was performed finite element series analysis varying the cutout ratio, web height, thickness and type of cross-section using commercial FEA program(ANSYS) under compressive load.

Dynamic stability of stiffened plates with cutout subjected to harmonic in-plane partial edge loading

The dynamic instability characteristics of eccentrically stiffened plates with cutout subjected to harmonic in-plane partial edge loadings at the plate boundaries are studied using finite element method. The instability regions are determined for a wide range of excitation frequencies with different boundary condition, partial edge loading at different locations, cutout ratios and various parameters of stiffeners using Bolotin's method and Hill's infinite determinants by varying the number, size and location of the stiffeners. In the structural modeling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained.

VIBRATION AND STABILITY BEHAVIOR OF LAMINATED COMPOSITE CURVED PANELS WITH CUTOUT UNDER PARTIAL IN-PLANE LOADS

The present paper is concerned with the vibration, buckling and dynamic instability behavior of laminated composite, cross-ply, doubly-curved panels with a central circular hole subjected to in-plane static and periodic compressive loads. A generalized shear deformable Sanders' theory is used to model the curved panels, considering the effects of transverse shear deformation and rotary inertia. Bolotin's approach is used for studying the dynamic instability regions of doubly-curved panels. The effects of non-uniform edge loads, curvature with different cutout ratios, static and dynamic load factors, and lamination parameters on curved panels are investigated with the results discussed.

Transverse Vibration of Thick Annular Sector Plates

This paper investigates the free vibration of thick sector plates with different supporting edge conditions. The Rayleigh-Ritz procedure is used in the energy functional, which includes the effect of shear deformation and rotatory inertia in deriving the governing eigenvalue equation. Sets of mathematically complete two-dimensional polynomials (P-2) are used as the admissible displacement and rotational functions. A basic function (B) is introduced to satisfy the prescribed free, simply supported and clamped supporting edge conditions. This resulting PB-2 Rayleigh-Ritz method is applied to obtain solutions for thick sector plates of different radii (cutout ratios), sector angles, relative thickness ratios and with various end conditions along the radial and circumferential edges. The present results, wherever possible, are compared with existing published values from the open literature.

Optimization on the end-shaping of a quadrupole magnet

In order to achieve the widest possible aperture of accelarator magnets, end-shaping is a well known method. To do this one has to deal with the three-dimensional fringe field inherent to each geometry. This may be done experimentally by a cut-and-try method or theoretically by a three-dimensional computer code. In any case, considerable time has to be consumed if one wants to get a conclusion which is a general as possible and which is useful in designing magnets. Fringe field optimazation on the end-shaping of the conventional quadrupole magnet was done by a cut-and-try method, where a very simple geometry of the end pole was chosen to get a general conclusion. The “cut-out ratio diagram” given as a conclusion is useful to designers of the conventional quadrupole magnet.