A Newton type iterative inverse method for heat-conduction problems

An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.     

A Newton type iterative method for heat-conduction inverse problems

An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.     

On a class of generalized nonlinear implicit quasivariational inclusions

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降落伞膜索非线性有限元模拟

用膜单元和索单元模拟降落伞织物绳索系统,基于完全拉格朗日格式的非线性有限元方法编程计算降落伞的结构动力学特性。采用增量与迭代混合方法改善非线性计算的收敛特性并结合HHT隐式时间推进方法减小整体迭代计算量。使用修正应力应变张量导数的方法模拟膜单元单向应力状态并针对膜单元和索单元分别进行了非线性有限元计算验证。最后针对C-9型降落伞建立三维有限元模型,根据设定流速对伞衣施加均匀压强载荷,将模拟展开的结果与使用相同模型、不同方法商业软件的文献进行对比,显示了隐式非线性有限元方法模拟降落伞膜索系统大变形动力学的能力。     

The auto-adjustable damping method for solving nonlinear equations

I.IntroductionTherearealotofnonlinearproblemsinengineering.Forexamples,theheattrallsfel'with'nonlinearradiation-convectionboundaryalldlimitedheatcapacity,thenonlinearhydrodynamicsandaerodynamics,thenonlillearstrtlcturaldynamicresponsesandtheIihe.Itisalmostimpossibletosolvethe11onlinearequationsbydirectmethodexceptfi)rsomespecialnonlinearequations.Thegeneralapproachislinearizingtheequationsandformingvariousiterationprocedures.Forthestronglynonlillearproblems,thesolutionobtainedintheitcrativep…     

Karman型正交异性矩形薄板非线性弯曲的统一求解方法

本文对Karman型四边支承正交异性薄板在5种不同边界条件下的几何非线性弯曲进行了统一分析。所设的位移函数均为梁振动函数。它们精确地满足边界条件，利用Galerkin方法和位移函数的正交属性，转换控制方程为非线性代数方程。用“稳定化双共轭梯度法”求解稀疏矩阵线性方程组以及“可调节参数的修正迭代法”求解非线性代数方程组，最后给出了相应的数值结果。     

处理一种非线性问题迭代法的计算机方法

本文依非线性问题的积分方程组,按迭代法得出一般迭代表达式.由此,任意次迭代解的所有待定系数可用计算机计算,使研究复杂的非路性问题成为可能.     

矩形板非线性蠕变损伤屈曲特性分析

基于Von Karman非线性板理论和Kachanov-Rabotnov损伤理论,建立了在横向和面内载荷共同作用下考虑蠕变损伤效应的矩形板的非线性控制平衡方程,采用有限差分法和时间增量算法对未知变量进行离散,对整个问题进行迭代求解,分析了几何非线性、荷载等因素对板非线性蠕变损伤特性的影响。     

METHOD OF GREEN＇S FUNCTION OF CORRUGATED SHELLS

By using the fundamental equations of axisymmetric shallow shells of revolution, the nonlinear bending of a shallow corrugated shell with taper under arbitrary load has been investigated. The nonlinear boundary value problem of the corrugated shell was reduced to the nonlinear integral equations by using the method of Green＇s function. To solve the integral equations, expansion method was used to obtain Green＇s function. Then the integral equations were reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton＇ s iterative method was utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, deflection at center was taken as control parameter. Corresponding loads were obtained by increasing deflection one by one. As a numerical example,elastic characteristic of shallow corrugated shells with spherical taper was studied.Calculation results show that characteristic of corrugated shells changes remarkably. The snapping instability which is analogous to shallow spherical shells occurs with increasing load if the taper is relatively large. The solution is close to the experimental results.     

Analytical formulas of solutions of geometrically nonlinear equations of axisymmetric plates and shallow shells

Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence of the iterative method, is used to prove the convergence of the analytical formulas of the exact solutions of the equations.     

NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEM

The nonlinear dynamic equations of a multibody system composed of ?exible beams are derived by using the Lagrange multiplier method. The nonlinear Euler beam theory with inclusion of axial deformation e?ect is employed and its deformation ?eld is …     

Analysis and calculation of the nonlinear stability of the rotational composite shell

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Algorithm for phase contrast X-ray tomography based on nonlinear phase retrieval

A new algorithm for phase contrast X-ray tomography under holographic measurement was proposed in this paper. The main idea of the algorithm was to solve the nonlinear phase retrieval problem using the Newton iterative method. The linear equations for the Newton directions were proved to be ill-posed and the regularized solutions were obtained by the conjugate gradient method. Some numerical experiments with computer simulated data were presented. The efficiency, feasibility and the numerical stability of the algorithm were illustrated by the numerical experiments. Compared with the results produced by the linearized phase retrieval algorithm, we can see that the new algorithm is not limited to be only efficient for the data measured in the near-field of the Fresnel region and thus it has a broader validity range.     

Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations

Two types of implicit algorithms have been improved for high order discontinuous Galerkin (DG) method to solve compressible Navier-Stokes (NS) equations on triangular grids. A block lower-upper symmetric Gauss-Seidel (BLU-SGS) approach is implemented as a nonlinear iterative scheme. And a modified LU-SGS (LLU-SGS) approach is suggested to reduce the memory requirements while retain the good convergence performance of the original LU-SGS approach. Both implicit schemes have the significant advantage that only the diagonal block matrix is stored. The resulting implicit high-order DG methods are applied, in combination with Hermite weighted essentially non-oscillatory (HWENO) limiters, to solve viscous flow problems. Numerical results demonstrate that the present implicit methods are able to achieve significant efficiency improvements over explicit counterparts and for viscous flows with shocks, and the HWENO limiters can be used to achieve the desired essentially non-oscillatory shock transition and the designed high-order accuracy simultaneously.     

Nonlinear evolution analysis of T-S disturbance wave at finite amplitude in nonparallel boundary layers

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微分求积方法对于桩基大变形分析的应用

本文基于大变形的理论,采用弧坐标首先建立了具有初始位移的桩基的非线性数学模型,一组强非线性的微分-积分方程,其中,地基的抗力采用了Winkeler模型;其次,引入变数变换将微分-积分方程转化为一组非线性微分方程,并用微分求积方法离散了方程组,得到一组离散化的非线性代数方程;最后用Newton-Raphson迭代方法对离散化方程进行了求解,得到了桩基变形前后的构形、弯矩和剪力.计算中选取了两种不同类型的初始位移,并考察了它们对桩基大变形力学行为的影响.     

多自由度柔性结构非线性随机振动响应分析方法

随机等效线性化方法是多自由度结构非线性随机振动分析的有效方法,然而柔性结构隐式的系统方程限制了该方法的应用.本文首先提出了把多自由度柔性结构隐式系统方程显式化的等效非线性系统建立方法,该方法结合模态分析,将系统几何非线性作用等效为模态坐标的高次多项式组合,把多自由度物理系统转化为容易求解的模态系统;在此基础上运用随机等效线性化技术建立柔性结构非线性随机振动响应分析方法.该方法通过引入虚拟激励原理,大幅提高了计算效率,使对多自由柔性结构的非线性随机振动响应分析成为可能.通过算例分析,本文分析结果和精确解与数值模拟解的比较结果表明,本文方法具有较好的计算精度和较高的计算效率,能够应用于实际柔性工程结构的随机振动响应分析.     

STUDY OF PARAMETRIC VIBRATION OF GYROSCOPIC CONTINUA BASED ON NONLINEAR NORMAL MODES AND A NUMERICAL ITERATIVE APPROACH

以脉动流输流管为例,利用非线性模态技术和一种数值迭代法研究陀螺连续体的非线性参数振动响应问题. 通过谐波平衡法将系统非线性非自治控制方程转化为拟自治方程,并在状态空间上利用不变流形法构造系统的非线性模态. 以对应自治系统的解为初值,采用一种数值迭代法来求解拟自治控制方程的模态系数,结果证明了该迭代法的快速收敛性. 在频域分析中得到了幅频响应和相空间上的不变流形,而在时域复模态分析中则发现了参激陀螺系统的正交相位差和行波振动现象.     

Projection 2 Goes Turbulent - and Fully Implicit

We describe and demonstrate both our newest projection method (fully implicit) for the incompressible Navier-Stokes equations via the finite element method and our newest turbulence model - a somewhat sophisticated nonlinear (cubic) eddy viscosity model that does not employ wall functions or normal distances to walls - the combination providing a method and a model that is each applicable in arbitrary geometry. We demonstrate both via a flow simulation past an automobile-like body at a Reynolds number of 4.3 million.     

A conservative semi‐implicit method for coupled surface–subsurface flows in regional scale

A semi‐implicit method for coupled surface–subsurface flows in regional scale is proposed and analyzed. The flow domain is assumed to have a small vertical scale as compared with the horizontal extents. Thus, after hydrostatic approximation, the simplified governing equations are derived from the Reynolds averaged Navier–Stokes equations for the surface flow and from the Darcy's law for the subsurface flow. A conservative free‐surface equation is derived from a vertical integral of the incompressibility condition and extends to the whole water column including both, the surface and the subsurface, wet domains. Numerically, the horizontal domain is covered by an unstructured orthogonal grid that may include subgrid specifications. Along the vertical direction a simple z‐layer discretization is adopted. Semi‐implicit finite difference equations for velocities and a finite volume approximation for the free‐surface equation are derived in such a fashion that, after simple manipulation, the resulting discrete free‐surface equation yields a single, well‐posed, mildly nonlinear system. This system is efficiently solved by a nested Newton‐type iterative method that yields simultaneously the pressure and a non‐negative fluid volume throughout the computational grid. The time‐step size is not restricted by stability conditions dictated by friction or surface wave speed. The resulting algorithm is simple, extremely efficient, and very accurate. Exact mass conservation is assured also in presence of wetting and drying dynamics, in pressurized flow conditions, and during free‐surface transition through the interface. A few examples illustrate the model applicability and demonstrate the effectiveness of the proposed algorithm. Copyright © 2015 John Wiley & Sons, Ltd.