Postbuckling of shear deformable stiffened anisotropic laminated cylindrical shell under axial compression

A postbuckling analysis is presented for a shear deformable anisotropic laminated cylindrical shell with stiffener of finite length subjected to axial compression. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on a higher order shear deformation shell theory with von Kármán-Donnell-type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The ‘smeared stiffener’ approach is adopted for the beam stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, grid, axial, ring stiffened, and unstiffened shells. The results confirm that there exists a compressive stress along with an associate shear stress and twisting when the anisotropic shell is subjected to axial compression. The postbuckling equilibrium path is unstable for the moderately thick cylindrical shell under axial compression and the stiffened shell structure is imperfection-sensitive.     

加筋板的轴压强度受加筋随机点蚀的影响研究

船舶与海洋结构在服役期间会遭受电化学和微生物侵蚀等多种腐蚀环境影响,加筋板作为此类结构的主要受力构件,其表面易产生不规则形态的点蚀,引起构件的强度退化。利用ANSYS有限元软件构建加筋腹板遭受随机点蚀损伤的加筋板有限元模型,研究带板长宽比、带板长细比、加筋长细比和腐蚀体积损失率对加筋板极限强度的影响。研究结果表明,加筋遭受同等腐蚀体积损失率下,带板长宽比变化对极限强度退化的影响很小,但带板长细比和加筋长细比变化产生的影响明显;带板长细比越大,极限强度退化越严重,而加筋长细比越大,极限强度退化反而越小。针对文中研究的加筋板,当加筋长细比为 0.2时,腐蚀体积率为14%的随机点蚀导致结构极限强度退化程度达到约14.0%。因此,加筋的随机点蚀损伤会显著削弱加筋板结构的极限强度,其影响不可忽略。     

Finite element analysis of ship structures using a new stiffened plate element

A new stiffened plate element is developed for the three-dimensional finite element analysis of ship structures. The plate element can accommodate any number of arbitrarily oriented stiffeners and obviates the use of mesh lines along the stiffeners. The new element provides a very economic global analysis of the complete ship structure with fewer elements and without any loss of accuracy. The global analysis of a rectangular box shaped vessel is carried out with the present element and compared with the general-purpose finite element software NISA. An Offshore Tug/Supply Vessel is analysed for crest at perpendiculars.     

Elastic lateral-torsional buckling analysis of permanent means of access structure

International Maritime Organization (IMO) adopted a new regulation to request permanent means of access (PMA) for a regular inspection of ship structure. Horizontal platforms for an inspector to walk on should be provided at specified locations. The platform is attached perpendicular to longitudinal bulkheads or side shell like a common longitudinal stiffener. Since the platform is much wider than ordinary stiffeners, a mid-flat-bar is welded in the middle of the platform. The wide platform (i.e. the tall web plate) makes PMA structure prone to lateral torsional buckling prior to overall flexural Euler buckling subjected to axial compression. This study employs the Rayleigh-Ritz method to treat the elastic lateral-torsional buckling of the PMA structure. The deformation of the cross-section can be expressed using six independant parameters. Compared to the previous research for an ordinary stiffened plate (Hughes and Ma, 1996a), two additional parameters are employed to model the deformation of the mid flat bar. This study also proposes a new strain distribution of lateral bending introducing two respective neutral axes for the flange and the mid-flat-bar. Two mathematical models are developed for two cases; one without associated plating, and the other with both the plating and its rotational restraint. In the former, the coupling between the lateral torsional buckling (“tripping”) and the Euler buckling is investigated. In the latter, a plate rotational spring constant is suggested based on extended deformed shape of the plating. For each model, the validity of the proposed method is verified by a comparison with a number of linear buckling analyses carried out using the NASTRAN finite-element program.     

循环载荷作用下损伤船体梁极限强度研究

为了研究循环载荷作用下扶强材初始损伤对其极限强度的影响,进行了14组扶强材的循环加载试验和分析。构造了考虑材料累积损伤完整、断筋和大变形的扶强材单元极限承载力计算公式,提出了相应循环载荷作用下损伤扶强材单元的端缩曲线表达式和船体梁极限强度计算的简化逐步破坏法。编制了循环载荷作用下船体梁损伤极限强度计算程序,进行了船体梁极限强度计算,并与有限元结果进行对比。研究结果表明：改进的损伤扶强材模型可较为准确地描述扶强材材料损伤的完整、断筋和大变形的极限承载力退化情况,扶强材腹板断裂的损伤相较初始大变形及材料累积损伤形式承载力下降程度更明显;所提出的循环载荷作用下损伤船体梁极限强度计算的简化逐步迭代方法,能定量地计算扶强材在不同类型损伤下的极限承载力退化程度,具有较高精度,方便易行,可应用于工程设计。     

Analysis and reversal of dry and hydroelastic vibration modes of stiffened plates

This work describes the theoretical modal analysis model for the stiffened bottom plate of a tank that is filled with fluid having an undisturbed free surface. In the analysis model, the effects of bending, transverse shear and rotary inertia in both the plate and the stiffener are considered. Analytical results concerning the natural frequencies of the stiffened plate correlate well with experimental modal testing (EMT) results for above the second mode. To overcome the complexities in the modal analysis of the fluid–structure interaction, the Mindlin plate theory and the potential flow theory are applied; the velocity potential is also expressed using double finite Fourier transforms. Additionally, a parametric study was also performed for eigenfrequencies of the plate with a stiffener, in terms of the ratio of the depth of the stiffener to the thickness of the plate and that of the width of the stiffener to the thickness of the plate. Analysis results revealed the phenomenon of “mode reversal”, i.e. the first and second mode shapes of the plate with a deep stiffener in contact with air and water, respectively, are reversed. An occurring condition of “mode reversal” is derived and verified by both finite element analysis and EMT.     

Dynamic instability of laminated sandwich plates subjected to in-plane partial edge loading

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.     

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.     

水下加筋圆柱壳结构声散射特性研究

采用有限元/边界元(FEM/BEM)方法对水下加筋圆柱壳结构的声散射特性进行分析。考虑入射声场激发弹性结构振动产生二次辐射声场,总声场为入射场与散射场之和。基于Mindlin理论建立结构受迫振动的有限元模型,考虑入射声场为简谐激励,采用模态叠加法求出结构振动表面速度。根据声学边界元相关理论,利用有限元方法计算得出的弹性结构表面动力相应,可求出弹性结构的散射声场。研究结果表明,在同一波数下,不加筋结构后向散射强于加筋结构;加筋结构的散射指向性图案分叉较为明显;同种结构在波数增加的时候后向散射强度逐渐增大,前向散射强度逐渐减弱。     

On the effective breadth of stiffened platings

A stiffened plate is one of the principal structural components of the hull. During the design phase it is useful to study this structure considering it as a system consisting of monodimensional elements. Therefore, it is appropriate to identify the plate breadth that collaborates with the stiffener in the simplified calculation.The aim of this work is to investigate the effective breadth, regarding both stiffness and strength. The analysis is performed comparing various numerical solutions supplied by a finite-element program with solutions based on the beam theory. Analytic expressions and graphs, derived from the results of the parametric investigation, are proposed to design this kind of structure.     

Finite element modeling of heating phenomena of cracks excited by high-intensity ultrasonic pulses

A three-dimensional thermo-mechanical coupled finite element model is built up to simulate the phenomena of dynamical contact and frictional heating of crack faces when the plate containing the crack is excited by high-intensity ultrasonic pulses. In the finite element model, the high-power ultrasonic transducer is modeled by using a piezoelectric thermal-analogy method, and the dynamical interaction between both crack faces is modeled using a contact-impact theory. In the simulations, the frictional heating taking place at the crack faces is quantitatively calculated by using finite element thermal-structural coupling analysis, especially, the influences of acoustic chaos to plate vibration and crack heating are calculated and analysed in detail. Meanwhile, the related ultrasonic infrared images are also obtained experimentally, and the theoretical simulation results are in agreement with that of the experiments. The results show that, by using the theoretical method, a good simulation of dynamic interaction and friction heating process of the crack faces under non-chaotic or chaotic sound excitation can be obtained.     

The new simple design equations for the ultimate compressive strength of imperfect stiffened plates

The new simple design equations for predicting the ultimate compressive strength of stiffened plates with initial imperfections in the form of welding-induced residual stresses and geometric deflections were developed in this study. A non-linear finite element method was used to investigate on 60 ANSYS elastic–plastic buckling analyses of a wide range of typical ship panel geometries. Reduction factors of the ultimate strength are produced from the results of 60 ANSYS inelastic finite element analyses. The proposed design equations have been developed based on these reduction factors. For the real ship structural stiffened plates, the most general loading case is a combination of longitudinal stress, transverse stress, shear stress and lateral pressure. The new simplified analytical method was generalized to deal with such combined load cases. The accuracy of the proposed equations was validated by the experimental results. Comparisons show that the adopted method has sufficient accuracy for practical applications in ship design.     

周向变刚度环肋圆柱壳应力分析研究

采用大曲率梁理论和弹性基础梁带理论,建立潜艇特殊舱段结构的力学模型。利用能量法求出肋位处耐压船体壳板中面周向应力。建立环肋圆柱壳微分方程并根据边界条件求解,得到周向变刚度环肋圆柱壳应力计算方法。通过理论分析和模型试验验证了本计算方法。     

加筋板轮印载荷分布特性的试验与数值分析

轮印载荷的分布对于直升机甲板加筋板结构的设计至关重要。通过在橡胶块上加压的方式模拟轮印载荷,直接测量橡胶块与加筋板结构之间的接触压力,揭示轮印载荷分布特性,得到轮印载荷在加强筋和铺板之间的分布具有较强的不均匀性。利用ABAQUS软件进行轮印载荷分布的数值计算,结果表明,数值计算结果与试验结果吻合较好,试验工况下分布在加强筋上均布轮印载荷为接触面上均布轮印载荷的1.279倍。研究了加筋板面板初始缺陷、加强筋高度以及加筋板面板厚度对轮印载荷分布的影响。数值结果表明:考虑面板初始缺陷、降低面板厚度和增加加强筋的高度使轮印载荷分配到加强筋上的比例增大,但在相对刚度变化相同的情况下,降低面板厚度和增加加强筋高度对轮印载荷分布的影响不同。     

Free vibration analysis of antisymmetric laminated rectangular plates with distributed patch mass using third-order shear deformation theory

A free vibration analysis of laminated composite plates carrying a distributed patch mass is analyzed and presented in this paper. The Hamilton's Principle, using third-order shear deformation theory, is applied to simply supported rectangular plates. The displacement of the plate is postulated by a double Fourier series. The effects of size and location of the distributed patch mass on the response of the plate are also presented. A thorough comparison with well known published results is presented for the case of free vibration of unloaded plates and good agreement is observed.     

Analysis of stiffened shell for ships and ocean structures by finite element method

Static analysis of stiffened shells has been carried out using an eight-noded isoparametric element for the shell and a three-noded curved beam element for the stiffener. A same displacement function is used for the shell and the stiffener elements. A modified technique has been followed to analyse the shell, which is an improvement over the degenerated shell concept. The stiffness matrix of the curved beam element is generated irrespective of its position and orientation within the shell element. The stiffness matrix of the stiffener is then transferred to all the nodes of the shell element. Numerical examples of stiffened shells with concentric and eccentric stiffeners have been analysed and the results presented together with those available in published literature.     

Pseudo-Static Elasto-Plastic Cyclic Creep Model and Cyclic Stability of Offshore Soft Foundation

The accumulative shear deformation of soft clays under cyclic loads is considered as pseudo-staticcreep.A pseudo-static elasto-plastic cyclic creep model is developed based on the visco-elasto-plastic theory.Theparameters in the model are determined by cyclic triaxial soil tests.A method for analyzing the stability of offshoresoft foundation under wave loads is given by combining the model with pseudo-static creep analysis.An exampleis analyzed by the method.The results show that the horizontal and vertical stability of foundations under waveloads can be analyzed by it and the analytical results are qualitatively consistent with the observed failure modes ofshallow foundations.     

Acoustic radiation from shear deformable ring-stiffened laminated composite cylindrical shell submerged in flowing fluid

Acoustic radiation from a point driven, infinite, periodically ring-stiffened, laminated composite cylindrical shell submerged in flowing fluid is investigated theoretically. Both the effects of in-plane and out-of-plane vibrations of the ring-stiffeners and the effects of fluid convection on far field acoustic radiation behaviors are concerned. The equations of motion of the laminated composite cylindrical shell is presented on the basis of the first order shear deformation theory. Fourier transform and Poisson summation formula are used to transform the equations into a set of infinite algebraic equations expressed in the wavenumber domain. After truncation, the response of the laminated composite cylindrical shell is solved, and the stationary phase approximate is employed to find the expression for the far field sound pressure. Convergence analysis of the numerical solutions is conducted. The theoretical model and numerical method proposed in this paper are validated by comparison with those presented in available literature. Finally, numerical results are presented to demonstrate the effects of various parameters such as the size and spacing of the ring-stiffener, the thickness and the radius of the cylindrical shell, the lamination angle and the lamination scheme of the composite materials as well as the Mach number on the far field sound pressure.     

海洋平台板架结构简化评估对比研究

在海洋浮体平台设计初期,为了快速评估设计方案的结构强度水平,需要研究高效的简化方法。本文基于正交异性板理论,综合了平面应力和横向弯曲两种承载方式,改进了板架结构的正交简化评估方法。改进方法克服了原来只针对单一载荷型式的局限性,可以满足组合载荷状态下板架参数的等效变换。为了验证改进方法的适用性和精度水平,分别采用常规方法和改进方法,针对某案例平台的局部板架结构和整体结构开展了强度评估。评估结果的对比分析表明,采用改进方法得到的结构区域应力水平误差在15%以内,满足初始阶段总强度评估的精度要求?     

Design similar scale model of a 10,000 TEU container ship through combined ultimate longitudinal bending and torsion analysis

This paper firstly figures out a similar scale model regarding ultimate strength experiment of a typical ultra large container ship (ULCS) through combined ultimate longitudinal bending and torsion analysis, in which the similarity theory is proposed to design the scale model for reflecting the progressive collapse behaviors of true ships in ultimate strength model test. The present study presents the similarity between scale model and true ship in cross-section considering the height of neutral axis, the section modulus, the inertia moment about neutral axis and the polar inertia moment should fit the geometrical similarity theory, and in strength considering buckling strength and shear ultimate strength of plates and stiffened panels should fit the strength similarity theory. Numerical investigations are conducted on the ultimate strength of a 10,000 TEU container ship and the similar scale model under pure hogging bending, pure torsion and combined bending and torsion, respectively. The nonlinear finite element method (NFEM) is adopted considering the effects of initial deformations and both material and geometric nonlinearities. Finally, the numerical results are compared with each other and discussed showing a good agreement in both elastic and inelastic range during the progressive collapse behaviors, which means the similar scale model can represent the true ship regarding ultimate strength test. And the similarity theory is verified quite stable after the uncertainty analysis.