Broyden方法的收敛条件

讨论了求解非线性方程组的 Broyden方法在弱 Lipschitz条件下的半局部收敛性 ,并给出了‖ B-10 F(xk+ 1)‖‖ B-10 F(xk)‖ 的估计 .由于 Kantorovich型条件和弱 Smale型条件都是弱 Lipschitz型条件的特例 ,所以本文的结论以 Kantorovich型条件和 Smale型条件下的结论为其特例 .

宽扁肥大船型波激振动响应研究

宽扁肥大船型由于其较“柔”的结构特性极易引起高频持续的波激振动响应,同时显著提高了应力幅值水平及循环次数,极大影响了船体结构安全性与可靠性。采用非线性水弹性时域计算方法以及模型试验方法对某艘宽扁肥大船型的波激振动响应特性进行分析;验证了该理论预报方法的有效性及可靠性,并讨论了其高阶波激振动响应对总载荷水平的贡献程度,表明在某些遭遇频率下其波激振动响应较大。在宽扁肥大船结构设计及审核阶段,必须考虑其波激振动成分的影响。

Numerical simulation of the effect of coupling support of bolt-mesh-anchor in deep tunnel

The mechanical effects of bolt-mesh-anchor coupling support in deep tunnels were studied by using a numerical method, based on deep tunnel coupling supporting techniques and non-linear deformation mechanical theory of rock mass at great depths.It is shown that the potential of a rigid bolt support can be efficiently activated through the coupling effect between a bolt-net support and the surrounding rock.It is found that the accumulated plastic energy in the surrounding rock can be sufficiently transformed by the coupling effect of a bolt-mesh-tray support.The strength of the surrounding rock mass can be mobilized to control the deforma-tion of the surrounding rock by a pre-stress and time-space effect of the anchor support.The high stress transformation effect can be realized by the mechanical coupling effect of the bolt-mesh-anchor support, whereby the force of the support and deformation of the surrounding rock tends to become uniform, leading to a sustained stability of the tunnel.

A Modified Logvinovich Model For Hydrodynamic Loads on an Asymmetric Wedge Entering Water with a Roll Motion

The water entry problem of an asymmetric wedge with roll motion was analyzed by the method of a modified Logvinovich model (MLM). The MLM is a kind of analytical model based on the Wagner method, which linearizes the free surface condition and body boundary condition. The difference is that the MLM applies a nonlinear Bernoulli equation to obtain pressure distribution, which has been proven to be helpful to enhance the accuracy of hydrodynamic loads. The Wagner condition in this paper was generalized to solve the problem of the water entry of a wedge body with rotational velocity. The comparison of wet width between the MLM and a fully nonlinear numerical approach was given, and they agree well with each other. The effect of angular velocity on the hydrodynamic loads of a wedge body was investigated.

Solving the Sod Shock Tube Problem Using Localized Differential Quadrature (LDQ) Method

The localized differential quadrature (LDQ) method is a numerical technique with high accuracy for solving most kinds of nonlinear problems in engineering and can overcome the difficulties of other methods (such as difference method) to numerically evaluate the derivatives of the functions.Its high efficiency and accuracy attract many engineers to apply the method to solve most of the numerical problems in engineering.However,difficulties can still be found in some particular problems.In the following study,the LDQ was applied to solve the Sod shock tube problem.This problem is a very particular kind of problem,which challenges many common numerical methods.Three different examples were given for testing the robustness and accuracy of the LDQ.In the first example,in which common initial conditions and solving methods were given,the numerical oscillations could be found dramatically;in the second example,the initial conditions were adjusted appropriately and the numerical oscillations were less dramatic than that in the first example;in the third example,the momentum equation of the Sod shock tube problem was corrected by adding artificial viscosity,causing the numerical oscillations to nearly disappear in the process of calculation.The numerical results presented demonstrate the detailed difficulties encountered in the calculations,which need to be improved in future work.However,in summary,the localized differential quadrature is shown to be a trustworthy method for solving most of the nonlinear problems in engineering.

Numerical Investigations on Transient Behaviours of Two 3-D Freely Floating Structures by Using a Fully Nonlinear Method

Two floating structures in close proximity are very commonly seen in offshore engineering. They are often subjected to steep waves and, therefore, the transient effects on their hydrodynamic features are of great concem. This paper uses the quasi arbitrary Lagrangian Eulerian finite element method （QALE-FEM）, based on the fully nonlinear potential theory （FNPT）, to numerically investigate the interaction between two 3-D floating structures, which undergo motions with 6 degrees of freedom （DOFs）, and are subjected to waves with different incident angles. The transient behaviours of floating structures, the effect of the accompanied structures, and the nonlinearity on the motion of and the wave loads on the structures are the main focuses of the study. The investigation reveals an important transient effects causing considerably larger structure motion than that in steady state. The results also indicate that the accompanied structure in close proximity enhances the interaction between different motion modes and results in stronger nonlinearity causing 2hal-order component to be of similar significance to the fundamental one.

Elastic-plastic analysis for pile-anchor supporting system of deep foundation pit

By using numerical analysis methods to simulate the deep excavation,a lot of analyses are established on the basis of two-dimensional plane strain,ignoring the fact that foundation pit possesses three dimensions. For soil constitutive relation,people always take linear and nonlinear model,without considering the plastic behavior of soil. Using plastic-elastic hardening model to simulate constitutive relation of soil characteristics,the authors carried out mechanical analysis for pit excavation and support. The results show that the analysis for the stress state of pile anchor system is an effective way which provides theoretical basis for calculation of soil displacement.

Numerical modeling airflow in soil with impact of groundwater

In order to simulate the airflow in anhydrous case and the water-air flow in groundwater case, a numerical model of airflow in soil was developed. For the nonlinearity of the governing partial differential equation, the corresponding discretization and linearization methods were given. Due to the mass transfer between air-phase and water-phase, phase states of the model elements were constantly changing. Thus, parameters of the model were divided into primary ones and secondary ones, and the primary variables changing with phase states and the secondary variables can be obtained by their functional relationship with the primary variables. Additionally, the special definite condition of this numerical model was illustrated. Two examples were given to simulate the airflow in soil whether there was groundwater or not, and the effectiveness of the numerical model is verified by comparing the results of simulation with that of exoeriment.

A numerical study on matching relationships of gravity waves in nonlinear interactions

Applying a fully nonlinear numerical scheme with second-order temporal and spatial precision,nonlinear interactions of gravity waves are simulated and the matching relationships of the wavelengths and frequencies of the interacting waves are discussed.In resonant interactions,the wavelengths of the excited wave are in good agreement with the values derived from sum or difference resonant conditions,and the frequencies of the three waves also satisfy the matching condition.Since the interacting waves obey the resonant conditions,resonant interactions have a reversible feature that for a resonant wave triad,any two waves are selected to be the initial perturbations,and the third wave can then be excited through sum or difference resonant interaction.The numerical results for nonresonant triads show that in nonresonant interactions,the wave vectors tend to approximately match in a single direction,generally in the horizontal direction.The frequency of the excited wave is close to the matching value,and the degree of mismatching of frequencies may depend on the combined effect of both the wavenumber and frequency mismatches that should benefit energy exchange to the greatest extent.The matching and mismatching relationships in nonresonant interactions differ from the results of weak interaction theory that the wave vectors are required to satisfy the resonant matching condition but the frequencies are permitted to mismatch and oscillate with amplitude of half the mismatching frequency.Nonresonant excitation has an irreversible characteristic,which is different from what is found for the resonant interaction.For specified initial primary and secondary waves,it is difficult to predict the values of the mismatching wavenumber and frequency for the excited wave owing to the complexity.

Short-Time Linear Response with Reduced-Rank Tangent Map

The recently developed short-time linear response algorithm,which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation,yields high precision of the response prediction.However,the computation of the short-time linear response formula with the full rank tangent map can be expensive.Here,a numerical method to potentially overcome the increasing numerical complexity for large scale models with many variables by using the reduced-rank tangent map in the computation is proposed.The conditions for which the short-time linear response approximation with the reduced-rank tangent map is valid are established,and two practical situations are examined,where the response to small external perturbations is predicted for nonlinear chaotic forced-dissipative systems with different dynamical properties.

On the Numerical Solution to a Nonlinear Wave Equation Associated with the First Painlev Equation:an Operator-Splitting Approach

The main goal of this article is to discuss the numerical solution to a nonlinear wave equation associated with the first of the celebrated Painlevd transcendent ordinary differential equations. In order to solve numerically the above equation, whose solutions blow up in finite time, the authors advocate a numerical methodology based on the Strang＇s symmetrized operator-splitting scheme. With this approach, one can decouple nonlinearity and differential operators, leading to the alternate solution at every time step of the equation as follows： （i） The first Painlevd ordinary differential equation, （ii） a linear wave equation with a constant coefficient. Assuming that the space dimension is two, the authors consider a fully discrete variant of the above scheme, where the space-time discretization of the linear wave equation sub-steps is achieved via a Galerkin/finite element space approximation combined with a second order accurate centered time discretization scheme. To handle the nonlinear sub-steps, a second order accurate centered explicit time discretization scheme with adaptively variable time step is used, in order to follow accurately the fast dynamic of the solution before it blows up. The results of numerical experiments are presented for different coefficients and boundary conditions. They show that the above methodology is robust and describes fairly accurately the evolution of a rather ＂violent＂ phenomenon.