Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.

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.

A New Curve Fitting Method for Forming Limit Experimental Data

The forming limit curve （FLC） can be obtained by means of curve fitting the limit strain points of different strain paths. The theory of percent regression analysis is applied to the curve fitting of forming limit experimental data.Forecast intervals of FLC percentiles can be calculated. Thus reliability and confidence level can be considered. The theoretical method to get the limits of limit strain points distributing region is presented, and the FLC position can be adjusted according to practical requirement. Method for establishing FLC with high reliability using small samples is presented at the same time. This method can make full use of the current experimental data and the previous data.Compared with the traditional method that can only use current experimental data, fewer specimens are required in the present method to obtain the same precision and the result is more accurate with the same number of specimens.

CFD-Based Method of Determining Form Factor k for Different Ship Types and Different Drafts

The value of form factor k at different drafts is important in predicting full-scale total resistance and speed for different types of ships. In the ITTC community, most organizations predict form factor k using a low-speed model test. However, this method is problematic for ships with bulbous bows and transom. In this article, a Computational Fluid Dynamics(CFD)-based method is introduced to obtain k for different type of ships at different drafts, and a comparison is made between the CFD method and the model test. The results show that the CFD method produces reasonable k values. A grid generating method and turbulence model are briefly discussed in the context of obtaining a consistent k using CFD.

DEFORMATION ANALYSIS OF SHEET METAL SINGLE-POINT INCREMENTAL FORMING BY FINITE ELEMENT METHOD SIMULATION

Single-point incremental forming （SPIF） is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation analysis on forming process becomes an important and useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the forming tool. Using solid brick elements, the finite element method（FEM） model of truncated pyramid was established. Based on the theory of anisotropy and assumed strain formulation, the SPIF processes with different parameters were simulated. The resulted comparison between the simulations and the experiments shows that the FEM model is feasible and effective. Then, according to the simulated forming process, the deformation pattern of SPIF can be summarized as the combination of plane-stretching deformation and bending deformation. And the study about the process parameters＇ impact on deformation shows that the process parameter of interlayer spacing is a dominant factor on the deformation. Decreasing interlayer spacing, the strain of one step decreases and the formability of blank will be improved. With bigger interlayer spacing, the plastic deformation zone increases and the forming force will be bigger.

Theory and Method of Optimum Path Forming for Sheet Metal

Ideal forming results will be achieved if the sheet metal is formed along an optimum forming path. Such a path can be realized by multi-point forming technique. On the basis of the theory of the ideal forming path (or minimum plastic work path), the concept of an optimum forming path is proposed in this paper. The forming path can be described by the initial configuration, objective configuration and a series of intermediate configurations. According to the deformation theory and constitutive equation in ideal path forming, a finite element method to calculate the initial configuration is set up. The functional to determinate intermediate configurations is introduced and the numerical method to solve the configuration is presented. Based on the method presented in the paper, multi-step multi-point forming tests for sheet metal are designed. The test results demonstrate that when the sheet is deformed along an approximate optimum forming path, the maximum deformation curvature for the sphere objective shape and saddle objective shape are 11%∼40% and 15%∼50% greater than those of a sheet deformed along a common path respectively.

Meshfree Method Numerical Simulation of Sheet Metal Forming Process

Metal forming plays an important role in manufacturing industry and is widely applied in industries.The tradi- tional finite element method(FEM)numerical simulation is commonly used to predict metal forming process.Conventional finite element analysis of metal forming processes often breaks down due to severe mesh distortion,therefore time-consuming remeshing is necessary.Meshfree methods have been developed since 1977 and can avoid this problem.This new generation of computational methods reduces time-consuming model generation and refinement effort,and its shape function has higher order connectivity than FEM’s.In this paper the velocity shape functions are developed from a reproducing kernel approximation that satisfies consistency conditions and is used to analyze metal tension rigid viscoplastic deforming and Magnesium Alloy(MB 15)sheet superplastic ten- sion forming.A meshfree method metal forming modeling program is set up,the partition of unity method is used to compute the integrations in weak form equations and penalty method is used to impose the essential boundary condition exactly.Metal forming examples,such as sheet metal superplastic tension forming and metal rigid viscoplastic tension forming,are analyzed to demon- strate the performance of mesh free method.

DEPENDENCE OF PREDICTION MODEL OF FORMING LIMIT STRAINS ON FORMING METHOD AND MECHANICAL PROPERTIES OF SHEET METALS

ＤＥＰＥＮＤＥＮＣＥＯＦＰＲＥＤＩＣＴＩＯＮＭＯＤＥＬＯＦＦＯＲＭＩＮＧＬＩＭＩＴＳＴＲＡＩＮＳＯＮＦＯＲＭＩＮＧＭＥＴＨＯＤＡＮＤＭＥＣＨＡＮＩＣＡＬＰＲＯＰＥＲＴＩＥＳＯＦＳＨＥＥＴＭＥＴＡＬＳ①ＺｈｏｕＷｅｉｘｉａｎＤｅｐａｒｔｍｅｎｔｏｆＡｅ...

COMPLEX INNER PRODUCT AVERAGING METHOD FOR CALCULATING NORMAL FORM OF ODE

This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.

Effect of Preparation Method on Surface Area and Crystalline Form of CeO_2-ZrO_2 Solid Solution

The CeO_2-ZrO_2 solid solutions were prepared by a reverse microemulsion method. The effect of preparation parameters on the surface area and crystalline form of the solid solutions were studied by the BET surface area and XRD analysis. The studies indicate that the separation of the microemulsion phase during the preparation procedure can decrease the specific surface area of sample, adding hydrogen peroxide in the matrix solution can increase the specific surface area and stability of sample. The surface area of sample calcined at 550 ℃ for 5 h is 149 m^2·g^(-1), and that calcined at 900 ℃ for 6 h is 88 m^2·g^(-1). The sample with tetragonal symmetry Ce_(0.5)Zr_(0.5)O_2 phase has a higher stability.

Forming Mechanism of Gaseous Defect in Ti-48Al-2Cr-2Nb Exhaust Valves Formed with Permanent Mold Centrifugal Casting Method

A method combining theoretical analysis with experiment is adopted and the flowing process of Ti-48A1-2Cr-2Nb alloy melt poured in a permanent mould during the centrifugal casting process has been analyzed. A mathematical model of the filling process is established and the forming mechanism of internal gaseous defect is summarized. The results of calculation show that the melt fills the mould with varying cross-section area and inclined angle. The filling speed of the cross-section is a function of filling time. The cross-section area is directly proportional to the filling speed and the inclined angle is inversely proportional to the filling speed at a given rotating speed of the platform. Both of them changes more obvious near the mould entrance. The gaseous defect can be formed in several ways and the centrifugal field has an important influence on the formation of the defect. In addition, the filling process in centrifugal field has been verified by wax experiments and the theoretical analysis are consistent with experimental results.

PREDICTION FOR FORMING LIMIT OF AL2024T3 SHEET BASED ON DAMAGE THEORY USING FINITE ELEMENT METHOD

This paper presents the application of anisotropic damage theory to the study of forming limit diagram of A12024T3 aluminum alloy sheet. In the prediction of limiting strains of the aluminum sheet structure, a finite element cell model has been constructed. The cell model consists of two phases, the aluminum alloy matrix and the intermetallic cluster. The material behavior of the aluminum alloy matrix is described with a fully coupled elasto-plastic damage constitutive equation. The intermetallic cluster is assumed to be elastic and brittle. By varying the stretching ratio, the limiting strains of the sheet under biaxial stretching have been predicted by using the necking criterion proposed. The prediction is in good agreement with the experimental findings. Moreover, the finite element cell model can provide information for understanding the microscopic damage mechanism of the aluminum alloy. Over-estimation of the limit strains may result if the effect of material damage is ignored in the sheet metal forming study.

A SURFACE DEFECT PREDICTION METHOD FOR METAL FORMING PROBLEM

ＡＳＵＲＦＡＣＥＤＥＦＥＣＴＰＲＥＤＩＣＴＩＯＮＭＥＴＨＯＤＦＯＲＭＥＴＡＬＦＯＲＭＩＮＧＰＲＯＢＬＥＭ￥Ｐｅｎｇ，Ｙｉｎｇｈｏｎｇ；Ｒｕａｎ，Ｘｕｅｙｕ（ＳｈａｎｇｈａｉＲｅｓｅａｒｃｈＩｎｓｔｉｔｕｔｅｏｆＴｏｏｌ＆ＤｉｅＴｅｃｈｎｏｌｏｇｙ，Ｓ...

Application research on metal rheological forming of reproducing kernel partial method

The meshless method is a new numerical technology presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.The process of cylinder compression was analyzed by using rigid-plastic meshless variational principle and programming reproducing kernel partial method(RKPM),the influence of node number,weight functions and size factor on the solution was discussed and the suitable range of size factor was obtained.Compared with the finite element method(FEM),the feasibility and validity of the method were verified,which proves a good supplement of FEM in this field and provides a good guidance for the application of meshless in actual engineering.

Application in metal rheological forming of element-free Galerkin method

The element-free method is a new numerical technique presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.The element-free Galerkin method(EFGM) was applied for the solution to plastic large deformation.The simulation of metal rheological forming was successfully done by programming and its results were visualized by using the plotting and data analyses software Tecplot.Then plastic strain under different stages during rheological forming and the three principal stresses at the last deformation were obtained.The example shows the feasibility of EFGM used for metal rheological forming and provides a new method for numerical simulation of rheological forming of complex parts.

MESHFREE METHOD BASED ON POINT COLLOCATION FOR METAL FORMING SIMULATION

A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of metal ring compression. The point collocation method is a true meshfree method without the employment of a background mesh. It is shown that, in a point collocation approach, the remesh problem because of the mesh distortion in FEM （finite element method） and the low efficiency in Galerkin-based meshfree method are avoided. The corrected kernel functions are introduced to the stabilization of free-surface boundary conditions. The solution of symmetric ring compression problem is compared with a conventional finite element solution, and reasonable results have been obtained.

RESIDUAL A POSTERIORI ERROR ESTIMATE TWO-GRID METHODS FOR THE STEADY (NAVIER-STOKES) EQUATION WITH STREAM FUNCTION FORM

Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.

EFFECT OF BURNING METHOD ON THE FORMING PROCESSES OF PORTLAND CEMENT CLINKER

The forming temperature of Clinker melt underdifferent burning conditions has been studied by appearance examination and thermal shrinker determination, and the viscosity of melt has been discussed by studying the coordination number of Al^(3+) and Fe^(3+) in cement clinker burned by different method with x^- ray fluorescence analysis and Moss- bauer spectroscopy. The results show that the clin- ker melt under rapid burning may come into exis- tence at lower temperature and It's viscosity is lower. So the forming processes of clinker may be different at rapid burning from ordinary burning. They are probably an important factor to promote the formation of clinker burned at lower temperature with rapid burning method.

Model-element Analytic Method for Plastic Forming of Material

MEM(model element method) is proposed to resolve the present difficulties and problems in CAE about plastic forming of material.There are four advantages when MEM is integrated with FEM(finite element method) and UBM(upper boundary element method).First,it can make full use of their own advantages and overcome their own disadvantages;second,it can analyse material plastic fluid expediently;third,it can optimize design;finally,it can improve technological content and application effect of CAE software.Based on introducing the principle of MEM briefly,features and applications of MEM are pointed out.In conclusion,a new analysis method for plastic forming comes forth.

ADJOINT OPERATOR METHOD AND NORMAL FORMS OF HIGHER ORDER FOR NONLINEAR DYNAMICAL SYSTEM

Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotent linear part and Z(2)-asymmetry are computed. According to normal forms obtained, universal unfoldings for some degenerate bifurcation cases of codimension 3 and simple global characterizations, are studied.