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1.
Numerical experiments are performed on the determination of the fundamental frequency of transverse vibration of simply supported rectangular plates having rectangular holes with free edges. This constitutes a rather common technological situation since holes are present in plates or slabs due to operational conditions, namely passage of conduits or ducts, electric conductors, etc., Satisfying exactly the governing natural boundary conditions at the hole edges is practically an impossible task. This study reviews numerical experiments where the displacement function is expanded into a double Fourier series which constitutes the exact solution when the plate is simply connected. Satisfactory convergence is achieved when the plate is doubly connected. 相似文献
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《中国海洋工程》2020,(4)
An investigation is conducted on the static ultimate limit state assessment of ship hull plates with elastically restrained edges subjected to axial compression. Both material and geometric non-linearities were considered in finite element(FE) analysis. The initial geometric imperfection of the plate was considered, while the residual stress introduced by welding was not considered. The ultimate strength of simply supported ship hull plates compared well with the existing empirical formula to validate the correctness of the applied boundary conditions, initial imperfection and mesh size. The extensive FE calculations on the ultimate strength of ship hull plates with elastically restrained edges are presented. Then a new simple empirical formula for plate ultimate strength is developed, which includes the effect of the rotational restraint stiffness, rotational restraint stiffness, and aspect ratios. By applying the new formula and FE method to ship hull plates in real ships, a good coincidence of the results between these two methods is obtained, which indicates that the new formula can accurately predict the ultimate strength of ship hull plates with elastically restrained edges. 相似文献
4.
A new approach for the solution of the two-dimensional guillotine-cutting problem in ship production
A. Cemil Dikili 《Ocean Engineering》2004,31(8-9):1193-1203
A new approach has been developed for the arrangement of rectangular pieces in plates for the guillotine-cutting problem as encountered in ship production and similar manufacturing processes. The algorithm is quite novel in the sense that instead of making preliminary specifications and ignoring all the alternative arrangements, as is the case for most of the current models, it selectively considers feasible arrangements by eliminating the majority of the probable arrangements that render the problem insolvable. Intermediate steps of the algorithm produce results which cannot be obtained through integer programming. Losses are distributed to the minimum number of plates. The number of arrangement plans is also minimized. Overall the solution of the problem has been drastically simplified to allow even hand calculations instead of long computer runs. 相似文献
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The eigenfunction expansion method (will be referred to as error function method in this paper) of analysing reflection and transmission of ocean waves at a semi-infinite thin elastic plate [J Geophys Res 95 (1990) 11629; Phil Trans R Soc Lond A 347 (1994) 185] is modified and extended to cases with simply supported and built-in edges. The form of the error function in the eigenfunction expansion method of Fox and Squire [J Geophys Res 95 (1990) 11629] has been modified based on a dimensional analysis and also extended to plates with either a simply supported or a built-in edge. The modified error function does not include the so-called Lagrange multipliers used in the original method and therefore the modified solution is independent of the selection of the Lagrange multipliers. It is demonstrated that the modified error function method satisfies the relation of energy conservation very well for the three edge conditions examined. The relation of energy conservation for plates is derived for elastic plates with simply supported and built-in edges and it is found that the relation of energy conservation for a free edge is also held for simply supported and built-in edges.In addition, a minor modification has also been made to the eigenfunction method (will be called inner product method in this study) of Sahoo et al. [Proceedings of 10th International Offshore and Polar Engineering Conference 3 (2000) 594]. It will be shown that the modified inner product method becomes mathematically well defined. The modified coefficient matrixes for different edge conditions are diagonal and thus the linear simultaneous equations can be solved very easily. It is also demonstrated with examples that the extended error function method and the modified inner product method give identical results. 相似文献
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The dynamic instability of laminated sandwich plates subjected to in-plane partial edge loading is studied for the first time using an efficient finite element plate model. The plate model is based on a refined higher order shear deformation plate theory, where the transverse shear stresses are continuous at the layer interfaces with stress free conditions at plate top and bottom surfaces. Interestingly the plate model having all these refined features requires unknowns at the reference plane only. However, this theory requires C1 continuity of transverse displacement, which is difficult to satisfy arbitrarily in any existing finite element. To deal with this, a new triangular element developed by the authors is used in the present paper. 相似文献
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Sh. Hosseini Hashemi Mahmoud Karimi H. Rokni Damavandi Taher 《Ocean Engineering》2010,37(2-3):174-185
In this study Free vibration analysis of vertical rectangular Mindlin plates resting on Pasternak elastic foundation and fully or partially in contact with fluid on their one side is investigated for different combinations of boundary conditions. The plate is assumed to be one of vertical rectangular walls of a container in contact with fluid. In order to analyze the interaction of the Mindlin plate with the elastic foundation and fluid system, three displacement components of the plate are expressed in the Ritz method by adopting a set of static Timoshenko beam functions satisfying geometric boundary conditions in a Cartesian co-ordinate system. The method of separation of variables and the method of Fourier series expansion is used to model fluid and to obtain the exact expression of the motion of fluid in the form of integral equations. The fluid domain is finite in depth and width but infinite in the length direction. To demonstrate the accuracy of the present solution, convergence study is first carried out and then a few comparison studies are carried out with the available data in the literature. Finally, natural frequencies of rectangular plates are presented in tabular and graphical forms for different fluid levels, foundation parameters, aspect ratios, thickness to width ratios and boundary conditions. 相似文献
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In this study, a two-dimensional floating pier consists of single rectangular impermeable pontoon with side supporting pile-columns is studied. The purpose of this study is to present a theoretical solution for the linearized problem of incident waves exerting on a floating pier with pile-restrained. All boundary conditions are linearized in the problem, which is incorporated into a scattering problem and radiation problem with unit displacement. The method of separation of variables is used to solve for velocity potentials. For the radiation problem with unit heave and pitch amplitude, the boundary value problem with non-homogeneous boundary condition beneath the structure is solved by using a solution scheme. By calculating the wave force from velocity potential and solving the equation of motion of the floating structure simultaneously a close form theoretical solution for the problem is developed. The finite element method was also applied to calculate the dynamic responses on the supporting piles subjected to the pontoon motions and incident waves. 相似文献
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The two-dimensional nonlinear time domain free surface flow problem is analysed using potential flow theory. The problem is solved by a time marching method. At each time step two numerical approaches are used. One is based on the boundary element method in the complex plane. The complex potential is assumed to vary linearly within each element and the solution is obtained by imposing the boundary conditions at the nodes of the elements. The other approach is based on the finite element formulation. Triangular elements and linear shape functions are used. The solution is obtained by the Galerkin method. Numerical results are obtained for the wave elevation generated by a vertical wave maker. Results are also provided for a circular cylinder oscillating below the free surface. For these cases the finite element method is found to provide substantially more efficient computations than the boundary element method using equivalent discretizations. 相似文献
10.
G. X. WuR. Eatock Taylor 《Applied Ocean Research》1994,16(6):363-372
The two-dimensional nonlinear time domain free surface flow problem is analyzed by the finite element method. Two approaches are used. One is based on the velocity potential which is approximated by means of shape functions. The solution is obtained through use of a variational statement, and the velocity is obtained subsequently by the Galerkin method. The other approach is to write both potential and velocity in terms of the shape functions at the same time. Their solutions are derived from the same equation by using another variational statement. Numerical results are given for the vertical wave maker problem and for a transient wave in a rectangular container. They are compared with analytical solutions, and very good agreement is found. 相似文献
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P.M. CiancioJ.A. Reyes 《Ocean Engineering》2003,30(11):1323-1333
This paper deals with the determination of the critical load in the buckling of isotropic, circular annular thin plates whose thickness varies slightly according to an exponential law.The outer edge of the plate is elastically restrained against rotation while the inner boundary is free. Classical small-deflection theory is used. An hidrostatic pressure acting in the middle plane is considered.The eigenvalues of the problem are obtained by means of an analytical approach based on the optimized Rayleigh-Ritz method. It is shοwnι that the results are in good agreement from an engineering viewpoint, with those available in the literature. 相似文献
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研究重力式海洋平台沉箱的表面裂纹最大深度,通过考虑沉箱有一个内表面裂纹,将问题简化为无裂纹重力式平台问题和带裂纹矩形板问题的叠加,应用有限元方法对重力式海洋平台无裂纹情形进行了静力分析,得到了与裂纹位置对应处的环向拉应力。计算裂纹矩形板的应力强度因子,得到海洋环境荷载下沉箱内表面裂纹的最大深度为0.066 8m,计算结果可供海洋平台的设计参考。 相似文献
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Diana V. Bambill Raúl E. Rossi Verónica Jederlinic Carlos A. Rossit 《Ocean Engineering》1997,24(1):45-49
Transverse vibrations of a rectangular plate with three edges elastically restrained against rotation while the fourth is free are studied using (a) an analytical approach based on the optimized Rayleigh-Ritz method and (b) the finite element method. The study was motivated by the necessity of finding out how the lower frequencies of vibration were affected by introducing a step discontinuity in the plate thickness. This variation in the plate thickness was practiced in order to obtain a reduction in the total plate weight. 相似文献
14.
The present study deals with numerical experiments performed using the doublesine Fourier expansion and the Ritz method to determine natural frequencies of vibration of simply supported rectangular plates with free rectangular holes parallel to the plate sides.The problem is of basic structural interest in naval and ocean engineering systems since holes are frequently practiced in plate-type structural elements to allow for the passage of ducts, elevators, etc… 相似文献
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针对受均匀轴向压力的矩形开孔板剩余极限强度的问题,考虑矩形板中间开圆孔和腰圆孔两种典型形状,四种边界条件下,以板的柔度系数、开孔率为主要影响参数通过大量非线性有限元数值计算分析,采用一种新的拟合方式提出了矩形开孔板轴向受压剩余极限强度的简化计算公式,新经验公式能够很好地反映开孔所导致板极限强度的衰减趋势。将所提出的经验公式计算结果分别与相应的试验结果、非线性有限元计算结果及其他经验公式计算结果进行对比分析。结果表明所提出的经验公式相比已有的经验公式计算更为准确,适用范围更广,可以用来预报不同边界条件下轴向均匀受压开孔矩形板的极限强度。 相似文献
16.
This paper deals with the solution of the title problem in the case where the outer boundary is subjected to uniform, hydrostatic pressure while the inner edge of the plate is free. It is assumed that the plate thickness varies (a) in a discontinuous fashion and (b) linearly.An approximate approach is proposed using polynomial coordinate functions which identically satisfy the boundary conditions at the outer edge, only. The eigenvalues are determined using the optimized Rayleigh-Ritz method and good engineering agreement is shown to exist with buckling parameters obtained by means of a finite element code. 相似文献
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For a semi-submersible platform in repair, the eight old main brackets which connect columns with pontoons need to be replaced by new ones. In order to ensure the safety of the cutting operation of the old main bracket and calculate the initial stress condition of new main bracket, the structural stress monitoring of eight key spots is carried out, and then the calibrated finite element model is established according to the field monitoring results. Before cutting the main bracket and all associated structures, eight rectangular rosettes were installed, and a tailored cutting scheme was proposed to release the initial stress, in which the main bracket and associated column and pontoon plates were partly cut. During the cutting procedure, the strains of the monitoring spots were measured, and then the structural stress of the monitored spots were obtained. The stress variation characteristics at different spots during the initial cutting operation were shown and the initial stress condition of the monitored spots was figured out. The loading and support conditions of the semi-submersible platform were calibrated based on the measured initial stress condition, which made the finite element model more credible. The stress condition with the main bracket and associated structures being entirely cut out is analyzed by the Finite Element Method(FEM), which demonstrates the cutting operation to be safe and feasible. In addition, the calibrated finite element model can be used to calculate the initial stress condition of the new main bracket, which will be very helpful for the long-term stress monitoring on the main bracket. 相似文献
18.
This paper is concerned with the hydroelastic responses of a mat-like, rectangular very large floating structure (VLFS) edged with a pair of horizontal/inclined perforated anti-motion plates in the context of the direct coupling method. The updated Lagrangian formulae are applied to establish the equilibrium equations of the VLFS and the total potential formula is employed for fluids in the numerical model including the viscous effect of the perforated plates through the Darcy''s law. The hybrid finite element-boundary element (FE-BE) method is implemented to determine the response reduction of VLFS with attached perforated plates under various oblique incident waves. Also, the numerical solutions are validated against a series of experimental tests. The effectiveness of the attached perforated plates in reducing the deflections of the VLFS can be significantly improved by selecting the proper design parameters such as the porous parameter, submergence depth, plate width and inclination angle for the given sea conditions. 相似文献
19.
《Applied Ocean Research》2005,27(4-5):224-234
The modified scaled boundary finite-element method (SBFEM), keeping the advantages of the original SBFEM, eliminates the restriction of the scaling center location so that this approach can solve two-dimensional problems with parallel side-faces. In this paper, the modified SBFEM is applied to solutions of two types of problems—wave diffraction by a single and twin surface rectangular obstacles and wave radiation induced by an oscillating mono-hull and twin-hull structures in a finite depth of water. For wave diffraction problems, numerical results agree extremely well with the analytic solution for the single obstacle case and other numerical results of a different approach for the twin obstacle case. For wave radiation problems, the particular solutions to the scaled boundary finite-element equation are presented for cases of heave, sway and roll motions. The added mass and damping coefficients for heave, sway and roll motions of a two-dimensional rectangular container are computed and the numerical results are compared with those from independent analytical solution and numerical solution using the boundary element method (BEM). It is found that the SBFEM method achieves equivalent accuracy to the conventional BEM with only a few degrees of freedom. In the last example, wave radiation by a two-dimensional twin-hull structure is analyzed. Comparisons of the results with those obtained using conventional Green's function method (GFM) demonstrate that the method presented in this paper is free from the irregular frequency problems. 相似文献
20.
Murat Altekin 《Ocean Engineering》2010,37(11-12):1048-1060
Bending analysis of orthotropic super-elliptical plates of uniform thickness was investigated. Optimum location of the point supports was searched by minimizing the maximum absolute deflection. The support location which minimizes the bending moments at the supports was reported. The Ritz method was used and the total potential energy functional was modified by introducing the Lagrange multipliers to improve the accuracy of the stress resultants. The deflection and the bending moments computed at various points for a large variety of plate shapes ranging from an ellipse to a rectangle were checked with those of rectangular and elliptical plates. Good agreement was obtained for both cases. The structural response was found to be sensitive to support position. 相似文献