• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.3
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• pp.35-42
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• 1987

For the analysis of natural vibrations of a rectangular stiffened plate with inner cutouts, an application of the Rayleigh-Ritz method is investigated. In construction of the trial function for the Rayleigh quotient, only the outer boundary conditions are satisfied with combination of Euler beam functions. As to the modeling of stiffened plates for the energy calculations, a lumping stiffener-effects method and the orthotropic plate analogy are considered for the purpose of comparison. Some numerical results obtained by the Rayleigh-Ritz method are compared with results by experiments and the finite element method. The following are major conclusions; (1) With the lumping stiffener-effects modeling the Rayleigh-Ritz method gives good results of both natural frequencies and mode shapes. The orthotropic plate analogy in cases of regularly stiffened plates is of restrictive use i.e. acceptable for a small cutout. (2) The natural frequency of a stiffened plate with inner cutouts between stiffeners is higher than that of without cutouts and increase as the hole area ratio increases as long as there are no discontinuous stiffeners due to the cutout.

• Structural Engineering and Mechanics
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• v.29 no.4
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• pp.455-467
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• 2008

This paper deals with the buckling and postbuckling responses and the progressive failure of square symmetric laminates with rectangular cutouts under uniaxial compression. A detailed investigation is made to show the effects of cutout size and cutout aspect ratio on prebuckling and postbuckling responses, failure loads and failure characteristics of $(+45/-45/0/90)_{2s}$, $(+45/-45)_{4s}$ and $(0/90)_{4s}$ laminates. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. In addition, the effects of boundary conditions on buckling load, failure loads, failure modes and maximum transverse deflection for a $(+45/-45/0/90)_{2s}$ laminate with and without cutout have also been presented. It is concluded that square laminates with small square cutouts have more postbuckling strength than without cutout, irrespective of boundary conditions.

• International Journal of Concrete Structures and Materials
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• v.11 no.2
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• pp.327-341
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• 2017

Openings in slabs are usually required for many different applications such as aeriation ducts and air conditioning. Opening in concrete slabs due to cutouts significantly decrease the member stiffness. There are different techniques to strengthen slabs with opening cutouts. This study presents experimental and numerical investigations on the use of Carbon Fiber Reinforced Polymers (CFRP) as strengthening material to strengthen and restore the load carrying capacity of R.C. slabs after having cutout in the hogging moment region. The experimental program consisted of testing five (oneway spanning R.C. flat slabs) with overhang. All slabs were prismatic, rectangular in cross-section and nominally 2000 mm long, 1000 mm width, and 100 mm thickness with a clear span (distance between supports) of 1200 mm and the overhang length is 700 mm. All slabs were loaded up to 30 kN (45% of ultimate load for reference slab, before yielding of the longitudinal reinforcement), then the load was kept constant during cutting concrete and steel bars (producing cut out). After that operation, slabs were loaded till failure. An analytical study using finite element analysis (FEA) is performed using the commercial software ANSYS. The FEA has been validated and calibrated using the experimental results. The FE model was found to be in a good agreement with the experimental results. The investigated key parameters were slab aspect ratio for the opening ratios of [1:1, 2:1], CFRP layers and the laminates widths, positions for cutouts and the CFRP configurations around cutouts.

• Steel and Composite Structures
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• v.7 no.1
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• pp.1-18
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• 2007

Additional cutouts in the floorbeam webs of orthotropic plated bridge decks relieve the highly stressed lower flange of the ribs passing through these floorbeam webs from possible fatigue damage. Conversely, the floorbeam webs themselves suffer from high stress concentrations, especially along the free edges of the additional cutouts. These stresses result from a combination of direct introduction of vertical traffic loads in the weakened web and from the truss action of the floorbeam. The latter differs from a simple beam action due to the presence of the openings and corresponds more to the behaviour of a Vierendeel truss. Close assessment of the appearing stresses, highly relevant for fatigue resistance, requires the use of elaborate finite element modelling. However, a full finite element analysis merely provides the results of total stresses, leaving the researcher or designer the difficult task of finding the origin of these stress components. This paper presents a calculation method for cutout stresses based on a combination of a framework analysis and a two dimensional finite element analysis of much smaller parts of the floorbeam. This method provides more insight in the origin of the stress components, as well as it simplifies any comparison of different additional cutout geometries, independent of the floorbeam topology.

• Structural Engineering and Mechanics
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• v.34 no.2
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• pp.175-188
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• 2010

This paper deals with the buckling and postbuckling responses, and the progressive failure of square laminates of symmetric lay-up with a central rectangular cutout under in-plane shear load. A detailed investigation is made to show the effects of cutout size and cutout aspect ratio on the buckling and postbuckling responses, failure loads and failure characteristics of $(+45/-45/0/90)_{2s}$, $(+45/-45)_{4s}$ and $(0/90)_{4s}$ laminates. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. In addition, the effects of boundary conditions on buckling loads, failure loads, failure modes, and maximum transverse deflection for a $(+45/-45/0/90)_{2s}$ laminate with and without a square cutout have been presented. It is concluded that because of early onset of delamination at the net section of cutouts before first-ply failure, total strength of the laminate with very small cutouts can not be utilized.

• Steel and Composite Structures
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• v.21 no.1
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• pp.37-55
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• 2016

In this study, the influence of centrally placed circular and square cutouts on vibration and buckling characteristics of different ply-oriented laminated panels under the action of compressive and/or tensile types of non-uniform in-plane edge loads are investigated. The panels are inspected under the action of uniaxial compression, uniaxial tension and biaxial, compression-tension, loading configurations. Furthermore, the effects of different degrees of edge restraints and panel aspect ratios are also addressed in this work. Towards this, a nine-node heterosis plate element has been adopted which includes the effect of shear deformation and rotary inertia. According to the results, the tensile buckling loads are higher than that of compressive buckling loads. However, the tensile buckling load continuously reduces with the increased cutout sizes irrespective of ply-orientations. This is also true for compressive buckling loads except for some particular ply-orientations with higher sized cutouts.

• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.609-624
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• 1997

The optimization of cutouts in composite plates was investigated by implementing a procedure known as Evolutionary Structural Optimization. Perforations were introduced into a finite element mesh of the plate from which one or more cutouts of a predetermined size were evolved. In the examples presented, plates were rejected from around each evolving cutout based on a predefined rejection criterion. The limiting ply within each plate element around the cutout was determined based on the Tsai-Hill failure criterion. Finite element plates with values below the product of the average Tsai-Hill number and a rejection criterion were subsequently removed. This process was iterated until a steady state was reached and the rejection criterion was then incremented by an evolutionary rate and the above steps repeated until the desired cutout area was achieved. Various plates with differing lay-up and loading parameters were investigated to demonstrate the generality and robustness of this optimization procedure.

• Journal of Korean Society of Steel Construction
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• v.23 no.5
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• pp.607-614
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• 2011

This study deals with thegeometrical nonlinear dynamic behavior of laminated plates made of advanced composite materials (ACMs), which contain central cutouts. Based on the first-order shear deformation plate theory (FSDT), the Newmark method and Newton-Raphson iteration wereused for the nonlinear dynamic solution. The effects of the cutout sizes and lay-up sequences on the nonlinear dynamic response for various parameters werestudied using a nonlinear dynamic finite element program that was developed for this study. The several numerical results agreed well with those reported by other investigators for square composite plates with or without central cutouts, and the new results reported in this paper showed significant interactions between the cutout and the layup sequence in the laminate. Key observation points are discussed and a brief design guide for laminates with central cutouts is given.

• Steel and Composite Structures
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• v.42 no.4
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• pp.427-446
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• 2022

Cutouts in the beams or plates are often unavoidable due to inspection, maintenance, ventilation, structural aesthetics purpose, and sometimes to lighten the structures. Therefore, there will be a substantial reduction in the strength of the structure due to the introduction of the cutouts. However, these cutouts can be reinforced with the different patterns of ribs (stiffener) to enhance the strength of the structure. The present study highlights the influence of the elliptical cutout reinforced with a different pattern of ribs on the stability performance of such stiffened composite panels subjected to non-uniform edge loads by employing the Finite element (FE) technique. In the present formulation, a 9-noded heterosis element is used to model the skin, and a 3-noded isoparametric beam element is used to simulate the rib that is attached around a cutout in different patterns. The displacement compatibility condition is employed between the plate and stiffener, and arbitrary orientations are taken care by introducing respective transformation matrices. The effect of shear deformation and rotary inertia are incorporated in the formulation. A new mesh configuration is developed to house the attached ribs around an elliptical cutout with different patterns. Initially, a study is performed on the panels with different stiffener schemes for various ply orientations and for different stiffener depth to width ratios (d_s/b_s) to determine an optimal stiffener configuration. Further, various parametric studies are conducted on an obtained optimal stiffened panel to understand the effect of cutout size, cutout orientation, panel aspect ratio, and boundary conditions. Finally, from the analysis, it can be observed that the arrangement of the stiffener attached to a panel has a major impact on the buckling capacity of the stiffened panel. The stiffener's depth to width ratio also significantly influences the buckling characteristic.

• Steel and Composite Structures
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• v.34 no.2
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• pp.227-239
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• 2020

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.