金屬體積成形過程的無網(wǎng)格RPIM方法分析

摘 要:建立了基于無網(wǎng)格徑向點(diǎn)插值RPIM法的二維體積成形動(dòng)態(tài)顯式計(jì)算模型.采用具有Delta函數(shù)性質(zhì)的RPIM形函數(shù)構(gòu)造位移域，因此可以很方便地施加本質(zhì)邊界條件.基于防御節(jié)點(diǎn)法給出了二維接觸碰撞問題的接觸力計(jì)算方法，避免罰函數(shù)法罰因子選擇問題，以及拉格朗日乘子法不適合顯式算法的問題.采用完全拉格朗日格式和彈塑性本構(gòu)關(guān)系解決金屬體積成形過程所涉及的幾何非線性和材料非線性問題，并通過將工件變形分解為偏量部分和體積部分，有效消除金屬體積成形中的體積自鎖現(xiàn)象.數(shù)值算例表明，該算法可方便準(zhǔn)確處理大變形畸變問題，是模擬金屬體積成形過程的一種有效方法.

關(guān)鍵詞:金屬體積成形;徑向點(diǎn)插值法;接觸;體積自鎖

中圖分類號(hào):TG301 文獻(xiàn)標(biāo)識(shí)碼:A

Numerical Simulation of Bulk Forming Processes

by Radial Point Interpolation Method (RPIM)

ZHENG Gang，WU Suzhen，LI Guangyao，CUI Xiangyang

(State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body， Hunan Univ， Changsha， Hunan 410082， China)

Abstract:The total Lagrangian formulation and implementation of radial point interpolation method (RPIM) was presented for the simulation of 2D bulk forming processes. In the present method， the displacement field function was approximated by using RPIM shape functions possessing Kronecker delta function property， whichcan facilitates the enforcement of essential boundary conditions. A simple contact searching algorithm was used to compute the contact force between the tools and the workpiece in the metal forming analysis and to solve the problems of the penalty method and Lagrangian multiplier method. In order to remedy the volumetric locking， the internal nodal forces of the workpiece were split into deviatoric part and volumetric part. The geometrical nonlinearities and material nonlinearities for the dynamic solution were treated by using the total Lagrangian description and an elasticplastic constitutive law. In order to remedy the volumetric locking， the workpiece was deformed into two parts， deviatoric part and volumetric part. The numerical examples show that RPIM is more efficient in dealing with large deformation problems such as bulk forming with severe distortion.

Key words: bulk forming; radial point interpolation method; contact; volumetric locking