Rectangular Cutouts Research Articles

709 矩形開口を有するクロスプライ積層円筒殻の軸圧縮座屈解析(材料力学II)

709 矩形開口を有するクロスプライ積層円筒殻の軸圧縮座屈解析(材料力学II)

Stress around square and rectangular cutouts in symmetric laminates

Abstract The solution presented in this paper is useful for finding the stress distribution around holes in symmetric laminates as well as in isotropic plates and also to determine the failure strength of the laminate on first ply failure basis by Tsai-Hill, Hashin-Rotem and Tsai-Wu criteria. This is a one stop solution for all kinds of in-plane loading on symmetric laminates as well as isotropic plates with any shape of cutout. Using Savin’s basic solution for anisotropic plates, the stress functions are derived for generalized mapping function for the hole and arbitrarily oriented in-plane loading. Square and rectangular holes in symmetric laminates of Graphite/epoxy and Glass/epoxy are studied. It is noted that the maximum stress and its location is mainly influenced by the type of loading. Larger stresses are noted for shear loading. The stress results are also obtained by ANSYS for comparison.

Monte Carlo calculation of monitor unit for electron arc therapy

Monitor unit (MU) calculations for electron are therapy were carried out using Monte Carlo simulations and verified by measurements. Variations in the dwell factor (DF), source-to-surface distance (SSD), and treatment are angle (a) were studied. Moreover, the possibility of measuring the DF, which requires gantry rotation, using a solid water rectangular, instead of cylindrical, phantom was investigated. A phase space file based on the 9 MeV electron beam with rectangular cutout (physical size = 2.6 x 21 cm2) attached to the block tray holder of a Varian 21 EX linear accelerator (linac) was generated using the EGSnrc-based Monte Carlo code and verified by measurement. The relative output factor (ROF), SSD offset, and DF, needed in the MU calculation, were determined using measurements and Monte Carlo simulations. An ionization chamber, a radiographic film, a solid water rectangular phantom, and a cylindrical phantom made of polystyrene were used in dosimetry measurements. Percentage deviations of ROF, SSD offset, and DF between measured and Monte Carlo results were 1.2%, 0.18%, and 1.5%, respectively. It was found that the DF decreased with an increase in a, and such a decrease in DF was more significant in the a range of 0 degrees-60 degrees than 60 degrees-120 degrees. Moreover, for a fixed a, the DF increased with an increase in SSD. Comparing the DF determined using the rectangular and cylindrical phantom through measurements and Monte Carlo simulations, it was found that the DF determined by the rectangular phantom agreed well with that by the cylindrical one within +/- 1.2%. It shows that a simple setup of a solid water rectangular phantom was sufficient to replace the cylindrical phantom using our specific cutout to determine the DF associated with the electron arc. By verifying using dosimetry measurements, Monte Carlo simulations proved to be an alternative way to perform MU calculations effectively for electron are therapy. Since Monte Carlo simulations can generate a precalculated database of ROF, SSD offset, and DF for the MU calculation, with a reduction in human effort and linac beam-on time, it is recommended that Monte Carlo simulations be partially or completely integrated into the commissioning of electron are therapy.

Postbuckling response and failure of symmetric laminated plates with rectangular cutouts under in-plane shear

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.

Postbuckling response and failure of symmetric laminated plates with rectangular cutouts under uniaxial compression

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 <TEX>$(+45/-45/0/90)_{2s}$</TEX>, <TEX>$(+45/-45)_{4s}$</TEX> and <TEX>$(0/90)_{4s}$</TEX> 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 <TEX>$(+45/-45/0/90)_{2s}$</TEX> 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.

Vibration control for plate-like structures using strategic cut-outs

Cut-outs are widely used in plates and shells to facilitate heat dissipation, and to provide access to different components. Because of the presence of the cut-outs, it is expected that the dynamic behavior will deteriorate, and vibration magnitudes will be exaggerated as compared to those of the case without a cut-out. Summary of an investigation is presented in this paper to explore the possibility of making a rectangular cut-out in a plate for the purposes of employing this cut-out as a dynamic vibration absorber. The process involves numerical modeling using standard finite elements. The numerical predictions are presented in the form of design charts to indicate the conditions under which vibration control may be possible. Then, two variations are presented for comparison purposes, namely a lumped-parameter tuned vibration absorber and an auxiliary flap, instead of an integral cut-out. Finally, simple experiments are described to test the validity of the numerical predictions.

독립좌표연성법을 이용한 여러 개의 직사각형 구멍을 갖는 직사각형 평판의 자유진동해석

독립좌표연성법을 이용한 여러 개의 직사각형 구멍을 갖는 직사각형 평판의 자유진동해석

Composite plates with two concentric layups under compression

Abstract A new concept for designing composite panels with improved performance under compression is presented. In this concept, the panel consists of two different concentric layups. A Rayleigh–Ritz-based approach to model such rectangular panels under compression is presented. The buckling load and the in-plane stresses everywhere in the plate are determined using an energy minimization approach. The results are compared to detailed finite element models and, for special cases, to other published finite element solutions and are shown to be in good to excellent agreement except for cases where twisting–bending coupling (not accounted for by the present method) is significant. As shown by specific examples, the present method can be used to obtain lighter configurations than single-layup geometries. In addition, the method can be applied to plates with rectangular cutouts and plates with terminated stiffeners.

Damage simulation of repaired composite laminate with rectangular cut-out

Repaired composite laminate with rectangular cut-out is studied by tensile experiments and FEM simulation in this paper. A user damage subroutine is implemented to ABAQUS to simulate the damage of laminate. Good agreements between experimental data and numerical results are reached. From the experiment and FEM simulation results, the integrality of composite structure is destroyed due to the existence of cut-out. However, the asymmetry of repair gets this effect farther. From damage simulation, the initiation and development of three types of damages are predicted. The matrix cracking occurs at first, fiber–matrix shear and fiber break are subsequent. The effect of matrix cracking to the carrying capacity of structure is very small, but when fiber–matrix shear and fiber break occur, dangerous to structure, the carrying capacity of structure loses rapidly.

SU‐FF‐T‐439: Using Electron Beam Modifiers in the DPM Monte Carlo Code for Electron Beam Treatment Planning

Purpose: To investigate the feasibility of modeling patient‐specific beam modifiers for electron beams using the DPM MC code. Methods and material: We investigate the applicability of modeling a beam modifier ‘applicator’(vs. a multiple source model or beam fitting approach) inside the DPM code for electron beam dose calculation. DPM is only used for in‐phantom calculations; however, we have included beam modifiers such as Jaws, MLCs and now applicators within the code to improve its clinical applicability. Varian 21EX (Type III) was modeled for beam energies (6, 9 and 12 MeV) using the BEAMnrc MC code. The patient‐independent components were simulated once and the phase space (PS) is stored just below the ion chamber. As a first approximation, a preliminary model of the applicator blocks all the particles through the applicators but allows those in the open beam region. Verification of the beam modifier model with diode measurements and full PS simulations was performed using percent depth doses (PDDs) and profiles for various energies for the standard 15×15 cm2 cutout, and for square and rectangular cutouts from 4×4 to 25×25 cm2 in a homogeneous geometry. Results: PDD calculations with DPM beam modifiers showed agreement within 2% with measurements and full PS simulation for the 6MeV beam. The 9 and 12 MeV PDD calculations showed discrepancies up to 4% in the surface buildup region, and a slightly larger difference in the tail. A full 3‐d simulation currently takes roughly 10mins on 8 processors to achieve a relative uncertainty of less than 1% in voxels &gt; dmax/2 using a 2×2×2 mm3 voxel size. Conclusions: Preliminary investigation of dose calculations with beam modifiers in DPM MC code shows good agreement with measurement. Future work will focus on modeling 16 and 20 MeV beams and their verification in a homogeneous and heterogeneous medium.

Buckling analysis of cylindrical shells with cutouts including random boundary and geometric imperfections

In this paper, the effect of random geometric imperfections on the critical load of isotropic, thin-walled, cylindrical shells under axial compression with rectangular cutouts is presented. Second moment characteristics of geometric imperfections are estimated by data of available measurements, a simulation procedure based on the Karhunen–Loève expansion is applied for generating realizations of geometric imperfections. Nonlinear static finite-element analyses are carried out for the calculation of the response statistics of the critical load of the cylindrical shells. Cumulative distribution functions of the critical load as obtained by direct Monte Carlo simulation are presented. Furthermore, the individual and combined effects of random boundary and geometric imperfections on the limit loads of isotropic, thin-walled, cylindrical shells under axial compression are also treated. Again, second moment characteristics of these imperfections are estimated by data of available measurements of imperfections, a simulation procedure also based on the Karhunen–Loève expansion is applied for generating realizations of both boundary and geometric imperfections. A nonlinear static finite-element analysis using the general purpose code STAGS [C.C. Rankin, F.A. Brogan, W.A. Loden, H.D. Cabiness. STAGS (STructural Analysis of General Shells) User Manual, LMSC P032594, Version 3.0. Lockheed Martin Missiles and Space Co., Inc., Palo Alto, CA, USA, 1998] is carried out for the calculation of the buckling response of the cylindrical shells. Finally, the cumulative distribution functions of the limit load using direct Monte Carlo simulation are shown.

Stability analysis of composite laminate with and without rectangular cutout under biaxial loading

Abstract Composite plates with cutouts are extensively used in many mechanical structures. The presence of a cutout complicates the stress distribution in the plate. In this study an attempt has been made to incorporate the effect of prebuckled stress on the stability analysis of moderately thick/very thick composite laminated plates with cutouts under in-plane compressive loading using a “Simple higher order shear deformation theory” based on four unknown displacement functions ( u 0 , v 0 , w b , w s ). The finite element method is employed to study the critical buckling load of laminated plates. The change in critical buckling response of both thick and thin rectangular symmetric laminates with respect to the fibre orientation angle has been studied. The interaction curves (between N x and N y for different parameters of the laminates) are studied in detail.

독립좌표연성법을 이용한 원형 구멍을 갖는 단순지지 직사각형 평판의 자유진동해석

This paper is concerned with the vibration analysis of a simply-supported rectangular plate with a circular cutout. Even though there have been many methods developed for the free vibration of the rectangular plate with a rectangular cutout, very few research has been carried out for the rectangular plate with a circular cutout. In this paper, a new methodology called independent coordinate coupling method, which was developed to save the computational effort for the free vibration analysis of rectangular plate with a rectangular cutout, is applied to the case of circular cutout. The independent coordinate coupling method employs the global coordinate system for the plate and the local coordinate system for the cutout. In the case of the rectangular plate with a circular cutout, the global coordinate system is the Cartesian coordinate system and the local coordinate system is the polar coordinate system. By imposing the compatibility condition, the relationship between the global coordinates and the local coordinates is derived. This equation is then used for the calculation of the mass and stiffness matrices resulting in eigenvalue problem. The numerical results show the efficacy of the proposed method.

A Tube with a Rectangular Cut-Out. Part 1: Subject to Pure Bending

A Tube with a Rectangular Cut-Out. Part 1: Subject to Pure Bending

A tube with a rectangular cut-out. Part 1: Subject to pure bending

The response to pure bending of tubes with rectangular cut-outs is considered. Experiments on 1000-mm long, 100-mm diameter, and 2.55-mm wall thickness DIN 2391 ST NBK supported steel tubes are described. Such a thickness-to-diameter ratio is typical of structural columns, rather than shell structures. Tubes containing cut-outs with an axial dimension of up to 30 mm and a circumferential size of up to 180° were tested. It was found that plastic hinge mechanisms dominated the response when the cut-out was on the compressive side, whereas fracture behaviour dominated the response when the cut-out was on the tensile side. Finite element and semi-empirical analyses were carried out to predict the global load-deformation behaviour of the tubes. All analyses gave reasonable predictions of the experimental results for the majority of the cut-out parameters investigated. The aim of this study is to investigate the feasibility of using cut-outs to initiate and control the toppling of offshore jacket structures.

A Tube with a Rectangular Cut-Out. Part 2: Subject to Axial Compression

Simply supported steel tubes with rectangular cut-outs of different sizes positioned at their mid-length were subject to axial compression to assess the effect of the cut-outs on the deformation behaviour. Experiments on 1000 mm long, 100 mm diameter, and 2.55 mm wall thickness DIN 2391 ST NBK supported steel tubes are described. The experimental tubes were relatively thick walled, with a thickness-to-diameter ratio typical of structural columns, rather than shell structures. The radial position of the cut-outs was such that the reduced cross-section was symmetric with respect to the direction of rotation of the pinned ends. Several permutations of the axial and circumferential dimensions of the cut-out were tested so that the effect of changing these dimensions could be assessed. Finite-element and semi-empirical analyses were carried out to predict the global load-deformation behaviour of the tubes. Both analyses gave good predictions of the experimental results for the majority of the cut-out parameters investigated. The motivation for the study was to investigate the feasibility of using cut-outs to initiate and control the toppling of offshore jacket structures.

Ultimate Strength of Ship Plating under Axial Compression

The failure of a ship hull girder is governed by buckling and plastic collapse of the deck, bottom and side shell steel stiffened plates. The stiffened steel plating in ships is generally subjected to both in-plane and out-of-plane loading and is more important to understand the characteristics of these panels under buckling. Tests are reported on the collapse load of stiffened plates with and without cutout and with reinforced cutout under uniaxial compression. A generalized computer program for the semi-analytical solutions proposed by various investigators based on strut approach and orthotropic plate approach, and a finite element analysis program based on orthotropic plate approach are developed. The panels are also analysed using the finite element analysis software ANSYS. An approximate method based on strut approach is proposed to calculate the collapse load of stiffened plates with cutouts and initial imperfections. The reduction in strength of the panels due to the presence of square cutout, rectangular cutout and increase in strength due to reinforcement around rectangular cutout are calculated based on the test results. Comparisons are made between the test results and predictions based on semi-analytical solutions and finite element analyses, and the uncertainty parameters calculated are discussed. Based on this study it is concluded that the cutout can be reinforced with a maximum increase in strength up to 19% for plate initiated failures.

CRACK PROPAGATION IN RECTANGULAR THIN‐WALLED PLATES WITH CONCENTRATORS SUBECTED TO CYCLING LOADING

The paper presents the results of experimental investigations of the crack propagation process in thin‐walled elements made from optically active materials (polycarbonate), making the visualization of the field possible isochromatics at the front of the crack. Influence of the orientation of principal directions was analyses An experimental investigation of thin‐walled plate with circular and rectangular cutouts subjected to cycling shear loading was made. Using the photo‐stress method, propagation of the crack and the field of isochromatics were recorded over time. In parallel, the areas of initiation of fatigue fractures were identified. The results presented in the paper constitute a fragment of a larger process of investigation of thin-walled structures at the stress pattern in conditions of fatigue crack propagation to failure.

Free vibration of square laminates with delamination around a central cutout using HSDT

A finite element formulation based on Higher Order Shear Deformation Theory and Hamilton’s principle is developed to study the free vibration response of thick square composite plates having a central rectangular cutout, with and without the presence of a delamination around the cutout. An attempt is made to gain a complete understanding of the effect of a rectangular cutout on natural frequencies of the laminate. The concept of a frequency envelope is found to be quite convenient for this purpose. A systematic study is carried out to investigate the effect of material orthotropy, boundary conditions and side-to-thickness ratio on the free vibration response. In addition, effects of delamination size and its location around the cutout on the natural frequency of a thick square laminate are examined. A comparison is also made between results obtained using First Order Shear Deformation Theory and Higher Order Shear Deformation Theory.

Displacement amplitudes and flexural moments for a rectangular plate with a rectangular cutout under a uniformly distributed static load

Displacement amplitudes and flexural moments for a rectangular plate with a rectangular cutout under a uniformly distributed static load