Sampling-Based RBDO of Ship Hull Structures Considering Thermo-Elasto-Plastic Residual Deformation

We present a shape optimization method using a sampling-based RBDO method linked with a commercial finite element analysis (FEA) code ANSYS, which is applicable to residual deformation problems of the ship hull structure in welding process. The programming language ANSYS Parametric Design Language (APDL) and shell elements are used for the thermo-elasto-plastic analysis. The shape of the ship hull structure is modeled using the bicubic Ferguson patch and coordinate components of vertices, tangential vectors of boundary curves are selected as design variables. The sensitivity of probabilistic constraint is calculated from the probabilistic sensitivity analysis using the score function and Monte Carlo Simulation (MCS) on the surrogate model constructed by using the Dynamic Kriging (DKG) method. The sequential quadratic programming (SQP) algorithm is used for the optimization. In two numerical examples, the suggested optimization method is applied to practical residual deformation problems in welding ship hull structures, which proves the sampling-based RBDO can be successfully utilized for obtaining a reliable optimum design in highly nonlinear multi-physics problem of thermo-elasto-plasticity.     

Prediction of wave pattern and wave resistance of surface piercing bodies by a boundary element method

An iterative boundary element method, which was originally developed for both two‐ and three‐dimensional cavitating hydrofoils moving steadily under a free surface, is modified and extended to predict the wave pattern and wave resistance of surface piercing bodies, such as ship hulls and vertical struts. The iterative nonlinear method, which is based on the Green theorem, allows the separation of the surface piercing body problem and the free‐surface problem. The free‐surface problem is also separated into two parts; namely, left and right (with respect to x axis) free‐surface problems. Those all (three) problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The wetted surface of the body (ship hull or strut, including cavity surface if exists) and the left and right parts with respect to x axis of free surface are modelled with constant strength dipole and constant strength source panels. In order to prevent upstream waves, the source strengths from some distance in front of the body to the end of the truncated upstream boundary are enforced to be zero. No radiation condition is enforced for downstream and transverse boundaries. A transverse wave cut technique is used for the calculation of wave resistance. The method is first applied to a point source and a three‐dimensional submerged cavitating hydrofoil to validate the method and a Wigley hull and a vertical strut to compare the results with those of experiments. Copyright © 2007 John Wiley & Sons, Ltd.     

MPS-FEM方法模拟弹性船体在规则波中的运动

船舶在海洋中航行时经常会受波浪的作用,在波浪的作用下,船体可能会发生六自由度的运动.在船体运动幅度较小时,可以简单地将船体运动视为刚体运动.但当波浪环境较为剧烈、船体运动幅度较大时,船体可能会发生变形,此时船舶弹性的影响无法忽略.因此,研究弹性船体在波浪中的运动对船舶运动性能和航行安全具有重要的意义.移动粒子半隐式方法 MPS方法是一种基于拉格朗日方法表示的无网格粒子类方法,该方法在模拟具有自由面大变形特征的问题时具有其独特的优势.有限元方法 FEM作为一种传统的并且已被广泛应用的结构求解方法,具有很好的稳定性、准确性和鲁棒性.本文将MPS方法与FEM方法二者的优势结合,基于MPS-FEM耦合方法,使用自主开发的MPSFEM-SJTU流固耦合求解器,模拟刚性船体和弹性船体在规则波中的运动,并分析船体的弹性对船体运动响应的影响.首先模拟刚性船体在不同波长的规则波中的运动,研究规则波波长对船体运动响应的影响.接着分别模拟了刚性和弹性船体在规则波中的运动,结果表明,刚性船体的运动幅值大于弹性船体的运动幅值,而弹性船体船舯附近的压力大于刚性船体.     

Time series prediction of nonlinear ship structural responses in irregular seaways using a third-order Volterra model

To predict the nonlinear structural responses of a ship traveling through irregular waves, a third-order Volterra model was applied based on the given irregular data. A nonlinear wave–body interaction system was identified using the nonlinear autoregressive with exogenous input (NARX) technique, which is one of the most commonly used nonlinear system identification schemes. The harmonic probing method was applied to extract the first-, second- and third-order frequency response functions of the system. To achieve this, a given set of time history data of both the irregular wave excitation and the corresponding midship vertical bending moment for a certain sea state was fed into the three-layer perceptron neural network. The network parameters are determined based on the supervised training. Next, the harmonic probing method was applied to the identified system to extract the frequency response function of each order. While applying the harmonic probing method, the nonlinear activation function (i.e., the hyperbolic tangent function) was expanded into a Taylor series for harmonic component matching. After the frequency response functions were obtained, the structural responses of the ship under an arbitrary random wave excitation were easily calculated with rapidity using a third-order Volterra series. Additionally, the methodology was validated through the in-depth analysis of a nonlinear oscillator model for a weak quadratic and cubic stiffness term, whose analytic solutions are known. It was confirmed that the current method effectively predicts the nonlinear structural response of a large container carrier under arbitrary random wave excitation.     

Boundary mixed variational inequality in friction problem

IntroductionThestaticffichonProblemdiscussedinthespaperisakindofnonlinearunilateralboundalvaluePIDbleth.Itiswell-knownthatordinarylinearelliphcboundaryvalueProblemoftencormspondstOCertainlinearvariahonalequahon,theexistenceanduniquenessofitssolutioncanbeobtainedbyusingthein-MilgramtheoremorBabuskatheorem.HoweverthisunilateralboundalvallueProblemcormSPOndstoakindof"dxedvariahonalinequality['J.Sinceitcontainsthenonlinearindifferentialfunchonal,theusuallinearizationmethodsareuseless.Thereby…     

刚接与铰接混合连接杆系结构的几何非线性分析

本文提出用子结构原理解决具有刚接与铰接混合连接空间杆系结构的几何非线性分析,实现其非线性稳定性分析的载荷-位移全过程跟踪。该法无须单独推导刚接、铰接以及一端刚接一端铰接单元的弹性刚度矩阵和几何刚度矩阵,而可以直接由空间梁单元退化得到,而且可以将平面问题与空间问题、刚接与铰接混合连接体系进行统一处理,算例表明,本文方法对于杆系结构的统一和整体分析是有效的。     

Unsteady RANS method for surface ship boundary layer and wake and wave field

Results are reported of an unsteady Reynolds‐averaged Navier–Stokes (RANS) method for simulation of the boundary layer and wake and wave field for a surface ship advancing in regular head waves, but restrained from body motions. Second‐order finite differences are used for both spatial and temporal discretization and a Poisson equation projection method is used for velocity–pressure coupling. The exact kinematic free‐surface boundary condition is solved for the free‐surface elevation using a body‐fitted/free‐surface conforming grid updated in each time step. The simulations are for the model problem of a Wigley hull advancing in calm water and in regular head waves. Verification and validation procedures are followed, which include careful consideration of both simulation and experimental uncertainties. The steady flow results are comparable to other steady RANS methods in predicting resistance, boundary layer and wake, and free‐surface effects. The unsteady flow results cover a wide range of Froude number, wavelength, and amplitude for which first harmonic amplitude and phase force and moment experimental data are available for validation along with frequency domain, linear potential flow results for comparisons. The present results, which include the effects of turbulent flow and non‐linear interactions, are in good agreement with the data and overall show better capability than the potential flow results. The physics of the unsteady boundary layer and wake and wave field response are explained with regard to frequency of encounter and seakeeping theory. The results of the present study suggest applicability for additional complexities such as practical ship geometry, ship motion, and maneuvering in arbitrary ambient waves. Copyright © 2001 John Wiley & Sons, Ltd.     

Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients

The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.

     

Transmission boundary condition for mixed variable finite-difference method

All kinds of numerical methods based on the discretization of first-order velocity-stress hyperbolic system of elastic wave equations are named mixed variable finite-difference method in this paper, and the transmission boundary condition of artificial boundaries is studied here by the mixed variable finite-difference method. The transmission condition of complex geometrical boundaries of a transversely isotropic medium is presented based on the characteristic variables of wavefields propagating in the normal direction of the boundary. The boundary condition proposed in this paper is a local artificial boundary condition, with which the computation cost is very low. Elastic wave propagations in transversely isotropic medium are modelled by the staggered grid finite-difference method incorporated with the boundary condition presented. Numerical results and analysis of reflection coefficients show that the reflections of incoming waves by artificial boundaries are efficiently reduced.Supported by National Natural Science Foundation and Liaoning Province Science Foundation.     

Assessment of adaptive and heuristic time stepping for variably saturated flow

The performance of improved initial estimates and ‘heuristic’ and ‘adaptive’ techniques for time step control in the iterative solution of Richards equation is evaluated. The so‐called heuristic technique uses the convergence behaviour of the iterative scheme to estimate the next time step whereas the adaptive technique regulates the time step on the basis of an approximation of the local time truncation error. The sample problems used to assess these various schemes are characterized by nonuniform (in time) boundary conditions, sharp gradients in the infiltration fronts, and discontinuous derivatives in the soil hydraulic properties. It is found that higher order initial solution estimates improve the convergence of the iterative scheme for both the heuristic and adaptive techniques, with greater overall performance gains for the heuristic scheme, as could be expected. It is also found that the heuristic technique outperforms the adaptive method under strongly nonlinear conditions. Previously reported observations suggesting that adaptive techniques perform best when accuracy requirements on the numerical solution are very stringent are confirmed. Overall both heuristic and adaptive techniques have their limitations, and a more general or mixed time stepping strategy combining truncation error and convergence criteria is recommended for complex problems. Copyright © 2006 John Wiley & Sons, Ltd.     

用瑞利-李兹法求解瞬时非稳态滑动轴承油膜力的新算法

提出了一个利用瑞利一李兹方法求解Reynolds边界条件下非稳态滑动轴承油膜力的近似算法,充分利用油膜力分布的特性,用双曲余弦函数来表示油膜力的轴向压力分布,而用多项式函数插值法来求解油膜力的周向压力分布,并同时计算出油膜力的破裂边界。算例表明本算法达到了相当高的精度,可用于转子系统的非线性数值分析,能大大降低数值求解瞬态油膜力的计算时间。     

Numerical simulation of fully nonlinear irregular wave tank in three dimension

A fully nonlinear irregular wave tank has been developed using a three‐dimensional higher‐order boundary element method (HOBEM) in the time domain. The Laplace equation is solved at each time step by an integral equation method. Based on image theory, a new Green function is applied in the whole fluid domain so that only the incident surface and free surface are discretized for the integral equation. The fully nonlinear free surface boundary conditions are integrated with time to update the wave profile and boundary values on it by a semi‐mixed Eulerian–Lagrangian time marching scheme. The incident waves are generated by feeding analytic forms on the input boundary and a ramp function is introduced at the start of simulation to avoid the initial transient disturbance. The outgoing waves are sufficiently dissipated by using a spatially varying artificial damping on the free surface before they reach the downstream boundary. Numerous numerical simulations of linear and nonlinear waves are performed and the simulated results are compared with the theoretical input waves. Copyright © 2006 John Wiley & Sons, Ltd.     

A fully non‐linear model for three‐dimensional overturning waves over an arbitrary bottom

An accurate three‐dimensional numerical model, applicable to strongly non‐linear waves, is proposed. The model solves fully non‐linear potential flow equations with a free surface using a higher‐order three‐dimensional boundary element method (BEM) and a mixed Eulerian–Lagrangian time updating, based on second‐order explicit Taylor series expansions with adaptive time steps. The model is applicable to non‐linear wave transformations from deep to shallow water over complex bottom topography up to overturning and breaking. Arbitrary waves can be generated in the model, and reflective or absorbing boundary conditions specified on lateral boundaries. In the BEM, boundary geometry and field variables are represented by 16‐node cubic ‘sliding’ quadrilateral elements, providing local inter‐element continuity of the first and second derivatives. Accurate and efficient numerical integrations are developed for these elements. Discretized boundary conditions at intersections (corner/edges) between the free surface or the bottom and lateral boundaries are well‐posed in all cases of mixed boundary conditions. Higher‐order tangential derivatives, required for the time updating, are calculated in a local curvilinear co‐ordinate system, using 25‐node ‘sliding’ fourth‐order quadrilateral elements. Very high accuracy is achieved in the model for mass and energy conservation. No smoothing of the solution is required, but regridding to a higher resolution can be specified at any time over selected areas of the free surface. Applications are presented for the propagation of numerically exact solitary waves. Model properties of accuracy and convergence with a refined spatio‐temporal discretization are assessed by propagating such a wave over constant depth. The shoaling of solitary waves up to overturning is then calculated over a 1:15 plane slope, and results show good agreement with a two‐dimensional solution proposed earlier. Finally, three‐dimensional overturning waves are generated over a 1:15 sloping bottom having a ridge in the middle, thus focusing wave energy. The node regridding method is used to refine the discretization around the overturning wave. Convergence of the solution with grid size is also verified for this case. Copyright © 2001 John Wiley & Sons, Ltd.     

精化8—20节点块体元的综合一致质量阵及几种质量阵构成方法的讨论

针对精化８－２０节点块体元构造了几种不同类型的质量阵，通过对几种支撑条件下的梁进行的振动特性分析，对其进行了比较研究，提出了构造精化８－２０节点块体元质量阵的新途径—综合一致质量阵法。结果表明，这种综合一致质量阵方法是几种质量阵形成方法中对提高动力分析精度最为有效的方法。     

Large deformation solution of stiffened plates by a mixed finite element method

In the present paper, a finite element mixed variational functional and the iterative equations of the eccentric orthogonal stiffened plates are developed in accordance with nonlinear elasticity. By using an important technique the coupling coefficients of the two-dimensional coupling matrix are resolved into the known input data in the programming which is a three-dimensional coefficient matrix. The nonlinear equations are transformed into the instantaneous linear equations; and by using the conjugate gradient method the linear equations are solved. As a result, therefore, the calculation is enormously simplified, the precision manifested, and a satisfactory result obtained.     

港口非线性波浪耦合计算模型研究

建立了外域用差分法求解高阶Boussinesq方程、内域用边界元法求解Laplace方程的二维船 非线性波浪力时域计算的耦合模型. 研究了该类耦合模型的匹配条件、耦合求解过程和内域、 外域公共区域长度的确定. 该耦合模型计算结果与只用边界元求解Laplace方程模型的计算 结果和实验结果对比表明,该耦合模型不仅计算精度高,而且计算效率快,适用于研究较大 区域内波浪对物体的非线性作用.     

船体水下近距非接触爆炸损伤计算之两步迭代法

船体水下近距非接触爆炸产生的破口计算过程复杂,涉及船体板架、武器装药和爆距方位等诸多因素,工程实践中通常应用经验公式求解。基于舰船遭受定向型战斗部攻击、毁伤面近似垂直于毁伤轴和爆炸过程瞬时发生满足近似能量守恒基本条件,根据爆炸冲击波初始动能与爆炸作用区域结构塑性变形能等量传递的假设,给出了计算方法。考虑了附着加强筋的船体壳板等效厚度对抵御冲击波毁伤的影响,运用爆炸冲击波作用下船体壳板产生的极限应变超过板材动态极限应变导致壳板开裂这一基本原理,设计了两步迭代法计算流程,给出了简捷易用的迭代计算表格。针对4种典型装药当量冲击波作用下,5～20 m长度舱段,11 m以内爆炸距离,6和8 mm这2种典型厚度船体壳板遭受爆炸冲击受损情况进行了768组数据计算。引入平面拟合方程,通过判断截平面相似度分析,给出了计算方法的适用性判据,探讨了计算参数的适用范围,以保证两步迭代法能够客观反映水下近距非接触爆炸的实际破坏效果。结合经验公式计算结果和破损舰船受损实测数据,对该方法进行了检验,实践表明：两步迭代法易于工程实践且具有较好的准确性。     

On the discontinuous Galerkin computation of N‐waves focusing

Sonic boom focusing phenomenon can be predicted using the solution to the nonlinear Tricomi equation which is a hybrid (hyperbolic‐elliptic) second‐order partial differential equation. In this paper, the hyperbolic conservation law form is derived, which is valid in the entire domain. In this manner, the presence of two regions where the equation behaves differently (hyperbolic in the upper and elliptic in the lower half‐plane) is avoided. On the upper boundary, a new mixed boundary condition for the acoustic pressure is employed. The discretization is carried out using a discontinuous Galerkin (DG) method combined with a Runge–Kutta total‐variation diminishing scheme. The results show the accuracy of DG methods to solve problems involving sharp gradients and discontinuities. Comparisons with analytical results for the linear case, and other numerical results using classical explicit and compact finite difference schemes and weighted essentially non‐oscillatory schemes are included. Copyright © 2010 John Wiley & Sons, Ltd.     

Generalized mixed finite element method for 3D elasticity problems

Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.     

Wave Interactions in Nonlinear Elastic Strings

We study a system modeling the dynamics of a nonlinear elastic string. This is a 6 × 6 system of hyperbolic conservation laws, which is degenerate in that two wave families have multiplicity two. We construct the wave curves for this problem and solve the Riemann problem. We then give a detailed analysis of elementary wave interactions, leading to a Glimm theorem, and describe features of the system when the total variation is large. There are complicated wave patterns, including infinitely many interactions in finite time, and both three- and four-resonances may be present.