提高板材成形效率的坐标网分析法

摘要

本篇文章是采用一种新推出的方法来对提高板材的成形效率进行分析,这种方法就是坐标网分析法。这种方法就是研究扭曲单体，即通过适当的研究规范，建立补片，包括修正后的单体。每一片都被扩展到一个三维的表面从而获得一个连续坐标的信息。在构造表面时，应包括每一个片，NURBS(非均匀有理B样条)表面被用来描述一个三维自由表面。以被构造表面为基础，每一个节点一般被安排成一个非常接近正方形的单体元素。计算状态函数是从它原始的网格系统映射到新的网格之内，从而对成形进行下一阶段的分析或更进一步的分析。按网格方法的分析结果与没有坐标网方法直接成行的分析结果相比较来确定哪一种方法是更有效的。(毕业设计)
© 2003 Elsevier B.V. 版权所有.

关键词：坐标网；变形单体；NURBS；有限元分析

1. 概述

随着计算机技术和数字技术的结合和快速发展，用数字模拟进行板材成形加工达到空前的繁荣。数字分析对复杂几何图形的板材成形和多级成形都可以做到。对于一个复杂的几何模型来说，尽管局部严重变形将会导致计算时间的增加和数据分析的减少。从而使分析结果更加不准确。几何网格的扭曲和严重变形对板材成形的质量有很大影响,特别是对于多级成形。当上一级成形的分析结果用于下一级成形分析时，几何网格的扭曲和变形对分析结果影响更大。这种被扭曲网格的错误表象可以通过整体的或自适应重啮合技术的网格系统的重建来避免。在模拟期间，减少单体扭曲，自适应重啮合技术被认为是一种有效的方法。但是，它仍然需要大量的计算，并且在单体的细分中也受到限制。

Abstract

This paper newly proposes a mesh regularization method for the enhancement of the efficiency in sheet metal forming analysis. The regularization method searches for distorted elements with appropriate searching criteria and constructs patches including the elements to
be modified. Each patch is then extended to a three-dimensional surface in order to obtain the information of the continuous coordinates. In constructing the surface enclosing each patch, NURBS (non-uniform rational B-spline) surface is employed to describe a three-dimensional free surface. On the basis of the constructed surface, each node is properly arranged to form unit elements as close as to a square. The state variables calculated from its original mesh geometry are mapped into the new mesh geometry for the next stage or incremental step
of a forming analysis. The analysis results with the proposed method are compared to the results from the direct forming analysis without mesh regularization in order to confirm the validity of the method.
© 2003 Elsevier B.V. All rights reserved.

Keywords: Mesh regularization; Distorted element; NURBS; Patch; Finite element analysis

1.  Introduction

Numerical  simulation  of  sheet  metal  forming  processes enjoys its prosperity with a burst of development of the com- puters and the related numerical techniques. The numerical analysis has extended its capabilities for sheet metal forming of complicated geometry models and multi-stage forming. In the case of a complicated geometry model, however, severe local deformation occurs to induce the increase of the com- puting time and deteriorate the convergence of the analysis. Distortion and severe deformation of the mesh geometry has an effect on the quality of forming analysis results especially in the case of multi-stage forming analysis when the mesh geometry formed by the forming analysis at the first stage is used for the forming analysis at the next stage. This ill behavior of the distorted mesh can be avoided by the recon- struction of the mesh system such as the total or the adaptive remeshing  techniques.  The  adaptive  remeshing  technique is known to be an efficient method to reduce distortion of element  during  the  simulation,  but  it  still  needs  tremen- dous  computing  and  puts  restrictions  among  subdivided elements.

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