Rapid Springback Compensation for Age Forming Based on Quasi Newton Method

Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improve greatly. To increase the springback compensate speed of designing age forming mold, process of calculating springback for a certain mold with finite element method is analyzed. Springback compensation is abstracted as finding a solution for a set of nonlinear functions and a springback compensation algorithm is presented on the basis of quasi Newton method. The accuracy of algorithm is verified by developing an ABAQUS secondary development program with MATLAB. Three rectangular integrated panels of dimensions 710 mmx750 mm integrated panels with intersected ribs of 10 mm are selected to perform case studies. The algorithm is used to compute mold contours for the panels with cylinder, sphere and saddle contours respectively and it takes 57%, 22% and 33% iterations as compared to that of displacement adjustment （DA） method. At the end of iterations, maximum deviations on the three panels are 0.618 4 mm, 0.624 1 mm and 0.342 0 mm that are smaller than the deviations determined by DA method （0.740 8 mm, 0.740 8 mm and 0.713 7 mm respectively）. In following experimental verification, mold contour for another integrated panel with 400 ram^380 mm size is designed by the algorithm. Then the panel is age formed in an autoclave and measured by a three dimensional digital measurement devise. Deviation between measuring results and the panel＇s design contour is less than 1 mm. Finally, the iterations with different mesh sizes （40 mm, 35 mm, 30 mm, 25 mm, 20 mm） in finite element models are compared and found no considerable difference. Another possible compensation method, Broyden-Fletcher-Shanmo method, is also presented based on the solving nonlinear fimctions idea. The Broyden-Fletcher-Shanmo method is employed to compute mold contour for the second panel. It only takes 50% iterations compared to that of DA. The proposed method can serve a faster mold contour compensation method for sheet metal forming.

Quasi Ellipsoid Gear Surface Reconstruction Based on Meshless Local Petrov-Galerkin Method and Transmission Characteristic

Special transmission 3D model simulation must be based on surface discretization and reconstruction, but special transmission usually has complicated tooth shape and movement, so present software can＇t provide technical support for special transmission 3D model simulation. Currently, theoretical calculation and experimental method are difficult to exactly solve special transmission contact analysis problem. How to reduce calculation and computer memories consume and meet calculation precision is key to resolve special transmission contact analysis problem. According to 3D model simulation and surface reconstruction of quasi ellipsoid gear is difficulty, this paper employes meshless local Petrov-Galerkin （MLPG） method. In order to reduce calculation and computer memories consume, we disperse tooth mesh into finite points--sparseness points cloud or grid mesh, and then we do interpolation reconstruction in some necessary place of the 3D surface model during analysis. Moving least square method （MLSM） is employed for tooth mesh interpolation reconstruction, there are some advantages to do interpolation by means of MLSM, such as high precision, good flexibility and no require of tooth mesh discretization into units. We input the quasi ellipsoid gear reconstruction model into simulation software, we complete tooth meshing simulation. Simulation transmission ratio during meshing period was obtained, compared with theoretical transmission ratio, the result inosculate preferably. The method using curve reconstruction realizes surface reconstruction, reduce simulation calculation enormously, so special gears simulation can be realized by minitype computer. The method provides a novel solution for special transmission 3D model simulation analysis and contact analysis.

Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

In the digital image correlation research of fatigue crack growth rate,the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor,thereby affecting the life prediction.This paper proposes a Gauss-Newton iteration method for solving the crack tip position.The conventional linear fitting method provides an iterative initial solution for this method,and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix.A noise-added artificial displacement field is used to verify the feasibility of the method,which shows that all parameters can be solved with satisfactory results.The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result,and the relative error between the two is only−0.621%;The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip,and the maximum relative error with the test plastic zone area is−11.29%.The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05%.The crack tip coordinates,stress intensity factors,and plastic zone contour changes in the loading and unloading phases are explored.The results show that the crack tip change during the loading process is faster than the change during the unloading process;the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process;under the same load,the theoretical plastic zone during the unloading process is higher than that during the loading process.

3D magnetotelluric inversions with unstructured finite-element and limited-memory quasi-Newton methods

Traditional 3D Magnetotelluric(MT) forward modeling and inversions are mostly based on structured meshes that have limited accuracy when modeling undulating surfaces and arbitrary structures. By contrast, unstructured-grid-based methods can model complex underground structures with high accuracy and overcome the defects of traditional methods, such as the high computational cost for improving model accuracy and the difficulty of inverting with topography. In this paper, we used the limited-memory quasi-Newton(L-BFGS) method with an unstructured finite-element grid to perform 3D MT inversions. This method avoids explicitly calculating Hessian matrices, which greatly reduces the memory requirements. After the first iteration, the approximate inverse Hessian matrix well approximates the true one, and the Newton step(set to 1) can meet the sufficient descent condition. Only one calculation of the objective function and its gradient are needed for each iteration, which greatly improves its computational efficiency. This approach is well-suited for large-scale 3D MT inversions. We have tested our algorithm on data with and without topography, and the results matched the real models well. We can recommend performing inversions based on an unstructured finite-element method and the L-BFGS method for situations with topography and complex underground structures.

One Step Positive Approach for Sheet Metal Forming Simulation Based on Quasi-conjugate-gradient Method

In one step inverse finite element approach, an initial blank shape is normally predicted from the final deformed shape. The final deformed shape needs to be trimmed into a final part after stamping, the trimmed area, therefore, needs to be compensated manually before using one step inverse approach, which causes low efficiency and in consistency with the real situation. To solve this problem, one step positive approach is proposed to simulate the sheet metal stamping process. Firstly the spatial initial solution of one step positive method is preliminarily obtained by using the mapping relationship and area coordinates, then based on the deformation theory the iterative solving is carried out in three-dimensional coordinate system by using quasi-conjugate-gradient method. During iterative process the contact judgment method is introduced to ensure that the nodes on the spatial initial solution are not separated from die surface. The predicted results of sheet metal forming process that include the shape and thickness of the stamped part can be obtained after the iterative solving process. The validity of the proposed approach is verified by comparing the predicted results obtained through the proposed approach with those obtained through the module of one step inverse approach in Autoform and the real stamped part. In one step positive method, the stamped shape of regular sheet can be calculated fast and effectively. During the iterative solution, the quasi-conjugate-gradient method is proposed to take the place of solving system of equations, and it can improve the stability and precision of the algorithm.

A numerical method for one-dimensional nonlinear sine-Gordon equation using multiquadric quasi-interpolation

In this paper, we use a univariate multiquadric quasi-interpolation scheme to solve the one-dimensional nonlinear sine-Gordon equation that is related to many physical phenomena. We obtain a numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative and a difference scheme to approximate the temporal derivative. The advantage of the obtained scheme is that the algorithm is very simple so that it is very easy to implement. The results of numerical experiments are presented and compared with analytical solutions to confirm the good accuracy of the presented scheme.

FPGA-based Acceleration of Davidon-Fletcher-Powell Quasi-Newton Optimization Method

Quasi-Newton methods are the most widely used methods to find local maxima and minima of functions in various engineering practices. However, they involve a large amount of matrix and vector operations, which are computationally intensive and require a long processing time. Recently, with the increasing density and arithmetic cores, field programmable gate array(FPGA) has become an attractive alternative to the acceleration of scientific computation. This paper aims to accelerate Davidon-Fletcher-Powell quasi-Newton(DFP-QN) method by proposing a customized and pipelined hardware implementation on FPGAs. Experimental results demonstrate that compared with a software implementation, a speed-up of up to 17 times can be achieved by the proposed hardware implementation.

GLOBAL COVERGENCE OF THE NON-QUASI-NEWTON METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEMS

In this paper, the non-quasi-Newton＇s family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton＇s family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.

Improving Wilson-θ and Newmark-β Methods for Quasi-Periodic Solutions of Nonlinear Dynamical Systems

Quasi-periodic responses can appear in a wide variety of nonlinear dynamical systems. To the best of our knowledge, it has been a tough job for years to solve quasi-periodic solutions, even by numerical algorithms. Here in this paper, we will present effective and accurate algorithms for quasi-periodic solutions by improving Wilson-θ and Newmark-β methods, respectively. In both the two methods, routinely, the considered equations are rearranged in the form of incremental equilibrium equations with the coefficient matrixes being updated in each time step. In this study, the two methods are improved via a predictor-corrector algorithm without updating the coefficient matrixes, in which the predicted solution at one time point can be corrected to the true one at the next. Numerical examples show that, both the improved Wilson-θ and Newmark-β methods can provide much more accurate quasi-periodic solutions with a smaller amount of computational resources. With a simple way to adjust the convergence of the iterations, the improved methods can even solve some quasi-periodic systems effectively, for which the original methods cease to be valid.

Overlapping Nonmatching Grid Method for the Ergodic Control Quasi Variational Inequalities

In this paper, we provide a maximum norm analysis of an overlapping Schwarz method on nonmatching grids for a quasi-variational inequalities related to ergodic control problems studied by M. Boulbrachene [1], where the “discount factor” (i.e., the zero order term) is set to 0, we use an overlapping Schwarz method on nonmatching grid which consists in decomposing the domain in two sub domains, where the discrete alternating Schwarz sequences in sub domains converge to the solution of the ergodic control IQV for the zero order term. For and under a discrete maximum principle we show that the discretization on each sub domain converges quasi-optimally in the norm to 0.

基于变分节块法六角形Quasi-diffusion程序开发及验证

传统扩散理论在中子各向异性强的堆芯计算中具有较低的精度,Quasi-diffusion方程相比于传统扩散方程引入更少的近似,通过艾丁顿因子描述传统扩散理论不能反映的中子流各向异性特点。国内外对六角形几何三维Quasi-diffusion方程研究有所不足。针对艾丁顿因子计算的非线性特点,本文基于“两步法”的思想,将艾丁顿因子看作是一个特殊的少群参数,采用中子能谱适应性更好的蒙特卡罗程序SERPENT计算,并对传统扩散变分节块法进行拓展,开发了六角形组件堆芯计算程序VNMQD。采用3D VVER1000基准题、RBWR单组件问题、3D BN600简化模型对程序进行了验证,结果表明:VNMQD程序开发正确,对于非均匀性较强的堆芯,VNMQD比传统扩散方法计算精度更高、计算效率接近,实现了计算精度和计算效率的平衡。

Adaptive Quasi-PID Control Method for Switching Power Amplifiers

Quasi-PID control method that is able to effectively inhibit the inherent tracking error of PI control method is proposed on the basis of a rounded theoretical analysis of a model of switching power amplifiers (SPAs). To avoid the harmful impacts of the circuit parameter variations and the random disturbances on quasi-PID control method, a single neuron is introduced to endow it with self-adaptability. Quasi-PID control method and the single neuron combine with each other perfectly, and their formation is named as single-neuron adaptive quasi-PID control method. Simulation and experimental results show that single-neuron adaptive quasi-PID control method can accurately track both the predictable and the unpredictable waveforms. Quantitative analysis demonstrates that the accuracy of single-neuron adaptive quasi-PID control method is comparable to that of linear power amplifiers (LPAs) and so can fulfill the requirements of some high-accuracy applications, such as protective relay test. Such accuracy is very difficult to be achieved by many modern control methods for converter controls. Compared with other modern control methods, the programming realization of single-neuron adaptive quasi-PID control method is more suitable for real-time applications and realization on low-end microprocessors for its simple structure and lower computational complexity.

QUASI-CRITICAL PATH METHOD FOR CONTROLLING THE START-TIME OF ACTIVITY

A new idea of Quasi-Critical Path has been defined in terms of the thoughtof Critical Path for the network method.The paper studies the time control problem of anetwork with forced start-time activity by both the optimal criterion of minimal reducedtime and the concept of Quasi-Critical Degree of activity,and proposes a feasible heuristicalgorithm.Another simpler algorithm is also presented,which can be realized inmicrocomputer.

Quasi-Newton Method for Optimal Blank Allowance Balancing

A balancing technique for casting or forging parts to be machined is presented in this paper.It allows an optimal part setup to make sure that no shortage of material(undercut)will occur during machining.Particularly in the heavy part in- dustry,where the resulting casting size and shape may deviate from expectations,the balancing process discovers whether or not the design model is totally enclosed in the actual part to be machined.The alignment is an iterative process involving nonlinear con- strained optimization,which forces data points to lie outside the nominal model under a specific order of priority.Newton methods for non-linear numerical minimization are rarely applied to this problem because of the high cost of computing.In this paper, Newton methods are applied to the balancing of blank part.The aforesaid algorithm is demonstrated in term of a marine propeller blade,and result shows that The Newton methods are more efficient and accurate than those implemented in past research and have distinct advantages compared to the registration methods widely used today.

OPTIMAL MOTION PLANNING FOR A RIGID SPACECRAFT WITH TWO MOMENTUM WHEELS USING QUASI-NEWTON METHOD

An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.

An Improved Quasi-Newton Method for Unconstrained Optimization

We present an improved method. If we assume that the objective function is twice continuously differentiable and uniformly convex, we discuss global and superlinear convergence of the improved quasi-Newton method.

NONLINEAR QUASI-CONFORMING FINITE ELEMENT METHOD

The nonlinear quasi-conforming FEM is presented based on the basic concept of the quasi- -conforming finite element. First, the incremental principle of stationary potential energy is discussed, Then, the formulation process of the nonlinear quasi-conforming FEM is given. Lastly, two computational examples of shells are given.

A Modified Quasi-Static Method for CALM System Analysis

The quasi-static analysis method introduced by API RP 2P is well known and accepted as a very useful mooring analysis method. In the early design stage, this method is widely used for preliminary analysis and mooring parameter selection. However, the quasi-static method of API RP 2P is developed for single-floating-body condition, i. e., only one floating body is considered in the computation procedure. Difficulties arise when it is used for the analysis of a CALM system, which is comprised of two floating bodies (tanker and buoy). This paper presents an analysis procedure for a two-floating-body system based on the quasi-static procedure of API RP 2P with some modifications reflecting special characteristics of the CALM system. Finally, the analysis results of a CALM system are given to illustrate the use of this procedure.

QUASI-PRINCIPAL AXIS METHOD IN FINITE DEFORMATION

A quasi-quasi-principal axis frame means a unit orthogonal frame in which the shear strains are small. As an extension of Hill's principal axis method we establish the approximate representations for various strains. the.finite rotation tensor, spins, strain rates. conjugate stresses and their rates with respect to quasi-principal axes. The quasiprincipal axis method may function as a new basis of numerically analyzing finite deformation problems.

A new stabilized method for quasi-Newtonian flows

For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, （bi）linear/（bi）linear and （bi）linear/constant element, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate velocity in the W 1,r（Ω） norm and that of the pressure in the L r＇ （Ω） （1/r ＋ 1/r＇ = 1）. The power law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results.