The Refinement Algorithm of Blank Outline Based on One-Step Inverse Analysis

2016 ◽  
Vol 725 ◽  
pp. 517-522
Author(s):  
Jia Kai Zhou ◽  
Yi Dong Bao ◽  
Wan Lin Zhou ◽  
Jing Cui ◽  
Hui Ting Wang
Keyword(s):  
Inverse Analysis ◽  
Computation Time ◽  
Initial Configuration ◽  
Final Configuration ◽  
Characteristic Lines ◽  
Rounded Corner ◽  
Part Surface ◽  
One Step ◽  
Blank Shape ◽  
Refinement Algorithm

Blank dimensions and outlines can be obtained in one-step inverse analysis. Applying more accurate mesh will achieve more precise outlines while usually lead to the increase of computation time. To ensure operation efficiency, this paper proposes a new blank outline refinement algorithm based on one-step inverse analysis. Firstly, the initial configuration is obtained from the final configuration by one-step inverse analysis. Secondly, all outline nodes is projected to the nearest element in the final configuration. Thirdly, according to the position of projected nodes in the element, the coordinate of outline nodes in the initial configuration is achieved through mapping. Finally the number of outline nodes is increased in rounded corners, the coordinate of added nodes are calculated through interpolation. At last all outlines corresponding to characteristic lines of part surface are acquired. Using A-pillar as an example, outlines are calculated by the refinement algorithm and commercial software. It proves that under the same mesh quality, outlines obtained by refinement algorithm become more accurate and smooth, especially in rounded corner. The results can contribute to judge the rationality of blank shape and improve the final part forming property. This algorithm refines the accuracy of outlines and ensures the efficiency of one-step inverse analysis.

A New Algorithm of the Boundary Restraining Force for One-Step Inverse Analysis

2016 ◽  
Vol 725 ◽  
pp. 511-516
Author(s):  
Yi Dong Bao ◽  
Xue Jiao Qin ◽  
Jing Cui ◽  
Hui Ting Wang
Keyword(s):  
Adaptive Algorithm ◽  
Distributed Algorithm ◽  
Inverse Analysis ◽  
The Self ◽  
Experimental Results ◽  
Blank Holder ◽  
One Step ◽  
Blank Shape ◽  
Restraining Force ◽  
Self Adaptive

In one-step inverse analysis, the restraining force produced by blank holder and draw bead need to be replaced equivalently by the nodal force to obtain a rational blank shape. But the distribution of the equivalent restraining force should not be uniform. A self-adaptive algorithm of the equivalent restraining force is presented in this paper. By comparing the initial configration contour line of the part obtained from three different methods (self-adaptive algorithm, uniformly distributed algorithm and a commercial software Fastform) with experimental results, the self-adaptive algorithm is proved to be accurate and convenient.

FAST SPRINGBACK SIMULATION OF BENDING FORMING BASED ON ONE-STEP INVERSE ANALYSIS

2008 ◽  
Vol 22 (31n32) ◽  
pp. 6057-6063
Author(s):  
YI-DONG BAO ◽  
WEN-LIANG CHEN ◽  
HONG WU
Keyword(s):  
Sheet Metal Forming ◽  
Metal Forming ◽  
Inverse Analysis ◽  
Simulation Method ◽  
Spring Back ◽  
Deformation Path ◽  
Bending Process ◽  
One Step ◽  
Implicit Solver ◽  
The One

A simplified one-step inverse analysis of sheet metal forming is a suitable tool to simulate the bending forming since the deformation path of bending forming is an approximately proportion one. A fast spring-back simulation method based on one-step analysis is proposed. First, the one-step inverse analysis is applied to obtain the stress distribution at the final stage of bending. Then, the unloading to get a spring back is simulated by LS-DYNA implicit solver. These processes are applied to the unconstrained cylindrical bending and the truck member rail. The spring-back and member rail widths at the several key sections are compared with experimental ones. It is well demonstrated that the proposed method is an effective way to predict the spring-back by unloading after bending process.

Accurate Prediction Approach of 3D Trimming Line for Auto Panel Part

2013 ◽  
Vol 535-536 ◽  
pp. 235-238 ◽  
Author(s):  
Yi Dong Bao ◽  
Yang Sang ◽  
Hou Min Wang
Keyword(s):  
Inverse Analysis ◽  
Layer By Layer ◽  
Adjacent Element ◽  
Analysis Theory ◽  
Comparison Results ◽  
Distorted Mesh ◽  
One Step ◽  
Experimental Values ◽  
Prediction Approach ◽  
Auto Panel

It is difficult to obtain 3D trimming line using traditional prediction methods for auto panel parts. An initial geometrical development method with element layer is proposed based on one step inverse analysis theory for this problem. The flange mesh can be unfold onto the die surface layer by layer according to nodal adjacent element relation, then the above development mesh is smoothed by mesh smoothing method with sliding constraint surface in order to delete overlap and distorted mesh, the 3D initial mesh can be obtained for one step inverse analysis method. The accurate 3D trimming line of auto panel part can be achieved by plasticity iteration of one step inverse analysis. A typical real part of 3D trimming line prediction is selected to prove this method, the comparison results between the simulated and experimental values show that this method has enough precision and can handle complex parts, satisfies the engineering practical demands.

PROPERTIES OF SELF-REPLICATING CELLULAR AUTOMATA SYSTEMS DISCOVERED USING GENETIC PROGRAMMING

2007 ◽  
Vol 10 (supp01) ◽  
pp. 61-84 ◽  
Author(s):  
ZHIJIAN PAN ◽  
JAMES REGGIA ◽  
DONGHONG GAO
Keyword(s):  
Cellular Automata ◽  
Genetic Programming ◽  
A Priori ◽  
Computation Time ◽  
Initial Configuration ◽  
Number Of Components ◽  
Arbitrary Structure ◽  
Wide Range ◽  
State Changes ◽  
Self Replication

We recently formulated an approach to representing structures in cellular automata (CA) spaces, and the rules that govern cell state changes, that is amenable to manipulation by genetic programming (GP). Using this approach, it is possible to efficiently generate self-replicating configurations for fairly arbitrary initial structures. Here, we investigate the properties of self-replicating systems produced using GP in this fashion as the initial configuration's size, shape, symmetry, allowable states, and other factors are systematically varied. We find that the number of GP generations, computation time, and number of resulting rules required by an arbitrary structure to self-replicate are positively and jointly correlated with the number of components, configuration shape, and allowable states in the initial configuration, but inversely correlated with the presence of repeated components, repeated sub-structures, and/or symmetric sub-structures. We conclude that GP can be used as a "replicator factory" to produce a wide range of self-replicating CA configurations, and that the properties of the resulting replicators can be predicted in part a priori. The rules controlling self-replication that are created by GP generally differ from those created manually in past CA studies.

Motion Planning of a Group of Agents Using the Homotopy Approach

2007 ◽  
Author(s):  
Mayank Lal ◽  
Suhada Jayasuriya ◽  
Swaminathan Sethuraman
Keyword(s):  
Motion Planning ◽  
Mobile Agents ◽  
Single Agent ◽  
Initial Configuration ◽  
Potential Fields ◽  
Polynomial Space ◽  
Time Varying ◽  
Multiple Roots ◽  
Final Configuration ◽  
Discriminant Variety

In this paper motion planning of a group of agents is done to move the group from an initial configuration to a final configuration through obstacles in 2-D. Also we introduce a new homotopy approach which uses potential fields to find paths in polynomial space. We use the homotopy approach for changing the group shape of the mobile agents and at the same time treat the group as a single agent by finding a bounding disc for it to plan the motion of the group through obstacles. A time varying polynomial is constructed, the roots of which represent the current positions of the mobile agents in a frame attached to the bounding disc. The real and imaginary parts of the roots of this polynomial represent the x and y coordinates of the mobile agents in this frame. This polynomial is constructed such that it avoids the discriminant variety or the set of polynomials having multiple roots. This is equivalent to saying that the mobile agents do not collide with each other at all times. The bounding disc is then used to plan the motion of the agents through obstacles such that the group avoids the obstacles at all times.

The Application on Initial Design of Auto Panel Based on One-Step FEM

2008 ◽  
Vol 575-578 ◽  
pp. 237-242
Author(s):  
Zhao Hu Deng ◽  
Yu Ping Huang ◽  
Yan Qin Zhang ◽  
Feng Ruan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Product Design ◽  
Early Stage ◽  
Incremental Method ◽  
One Step ◽  
Blank Shape ◽  
Formed Part ◽  
Auto Panel ◽  
Element Method

At the early stage of product design, the information about mould, blank and boundary condition are not definite. It is difficult to calculate with incremental method. For solving this problem, one-step finite element method(FEM) was put forward in recent years. It starts from product shape, takes it as the middle plane of formed part, disperses it and determines the location of nodes in initial blank at certain boundary conditions with finite element method. Then the corresponding blank shape can be obtained by one-step FEM. In this paper it is discussed that the basic theory of one-step FEM and the research of the key technology. And it is simulated the pressing of auto panel with one-step FEM. It is put forward that the final part should consider the effect of the technology. Through comparing one-step FEM with incremental method, it is showed that one-step FEM could calculate rapidly and had some credibility. It was suitable to evaluate the formability at the early stage of product design.

Optimization of Initial Blank Shape to Minimize Defects in an A Pillar Inner Panel Using Finite Element Method

2012 ◽  
Vol 538-541 ◽  
pp. 1045-1048
Author(s):  
L.M. Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Model ◽  
Material Flow ◽  
Numerical Results ◽  
Fe Method ◽  
The Real ◽  
Final Configuration ◽  
Stamping Process ◽  
Blank Shape

Wrinkling and cracking are two major problems of the automobile inner panel. In this study, the stamping process of an A pillar inner panel is studied with the finite element (FE) method, aimed at avoiding drawbacks due to wrinkling and cracking. The established numerical model is proved accurate by comparing the numerical final configuration to the real part. Then the material flow of the blank is analyzed. It is concluded that blocking of material flow is the main reason for those two pathologies. Thus, a gap design is suggested to minimize the concerned defects. According to the numerical results, after optimizing, the inner panel is free from formability problems.

Blank Shape Design Based on Inverse Finite Element Method Using Ideal Forming Theory and a Modified Kinematics Formulation

Volume 3 ◽  
2004 ◽  
Author(s):  
Mohammad Habibi Parsa ◽  
Payam Pournia
Keyword(s):  
Deformation Gradient ◽  
Design Procedure ◽  
Deformation Gradient Tensor ◽  
Specific Product ◽  
Initial Blank ◽  
Blank Design ◽  
Material Element ◽  
One Step ◽  
Blank Shape ◽  
The Ideal

For stamping of sheet metals and converting them to specific product shapes without failure, the initial blanks should be correctly designed. Otherwise, final products will not be sound. So initial blank design is a critical step in stamping design procedure. In the present paper for calculating the total deformation gradient and its relation to each step’s deformation gradient tensor (F), a modified kinematics formulation will be introduced. This formulation has been used in connection with the ideal forming theory for predicting the initial blank shape of the specified products with defined blank thickness. In the ideal forming theory, each material element is prescribed to deform in a minimum plastic work path and ideal process is obtained when the deformations are most evenly distributed in the final products. The later has been assumed for developing a FEM code to predict the blank shape and size in one step, which has been applied for three different kinds of stampings, cylindrical, square and clover shape cups. The results show the capability of the new algorithm in designing the initial blank shape for stamping products.

The implementation of extrapolation with smoothing technique in solving stiff ordinary differential equations

2020 ◽  
Vol 11 (4) ◽  
pp. 567-578
Author(s):  
Noorhelyna Razali ◽  
Alias Jedi ◽  
Nuryazmin Ahmat Zainuri
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Computation Time ◽  
Order Reduction ◽  
Smoothing Technique ◽  
Content Type ◽  
Stiff Ordinary Differential Equations ◽  
One Step ◽  
The One ◽  
Symmetric Method

PurposeExtrapolation is a process used to accelerate the convergence of a sequence of approximations to the true value. Different stepsizes are used to obtain approximate solutions, which are combined to increase the order of the approximation by eliminating leading error terms. The smoothing technique is also applied to suppress order reduction and to dampen the oscillatory component in the numerical solution when solving stiff problems. The extrapolation and smoothing technique can be applied in either active, passive or the combination of both active and passive modes. In this paper, the authors investigate the best strategy of implementing extrapolation and smoothing technique and use this strategy to solve stiff ordinary differential equations. Based on the experiment, the authors suggest using passive smoothing in order to reduce the computation time.Design/methodology/approachThe two-step smoothing is a composition of four steps of the symmetric method with different weights. It is used as the final two steps when combined with many steps of the symmetric method. The aim is to preserve symmetry and provide damping for stiff problem and to be more robust than the one-step smoothing. The two-step smoothing is L-stable. The new method is then applied with extrapolation process in passive and active modes to investigate the most efficient and accurate method of implementation.FindingsIn this paper, the authors constructed the two-step smoothing to be more robust than the one-step smoothing. The two-step smoothing is constructed to achieve as high order as possible and able to restore the classical order of particular method compared to the one-step active smoothing that is only able to achieve order-1 condition. The two-step smoothing for ITR is also superior in solving stiff case since it has the super-convergent order-4 behavior. In our experiments with extrapolation, it is proven that the two-step smoothing is more accurate and more efficient than the one-step smoothing, namely 1ASAX. It is also observed that the method with smoothing is comparable if not superior to the existing base method in certain cases. Based on the experiment, the authors would suggest using passive smoothing if the aim is to reduce computation time. It is of interest to conduct more experiment to validate the accuracy and efficiency of the smoothing formula with and without extrapolation.Originality/valueThe implementation of extrapolation on two-step symmetric Runge–Kutta method has not been tested on variety of other test problems yet. The two-step symmetrization is an extension of the one-step symmetrization and has not been constructed by other researchers yet. The method is constructed such that it preserves the asymptotic error expansion in even powers of stepsize, and when used with extrapolation the order might increase by 2 at a time. The method is also L-stable and eliminates the order reduction phenomenon when solving stiff ODEs. It is also of interest to observe other ways of implementing extrapolation using other sequences or with interpolation.

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