A modified PODI-RBF method to improve the accuracy of local solutions for real-time finite element simulations of indenter contact problems

IF 4 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Advances in Engineering Software Pub Date : 2024-11-04 DOI:10.1016/j.advengsoft.2024.103806

Hyeon-Gyeong Lee, Hyun-Gyu Kim

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Abstract

In this paper, a novel method is proposed to improve the accuracy of local solutions of the PODI-RBF method for real-time finite element (FE) simulations of indenter contact problems. In the offline stage, proper orthogonal decomposition (POD) basis vectors and coefficients are extracted from solution snapshots collected from full-order FE simulations of indenter contact problems with training contact locations and indentation depths. In the online stage, RBF interpolation is used to estimate POD basis vectors and coefficients for a new contact loading. Although the POD with interpolation (PODI) method using RBFs is very useful for obtaining FE solutions of indenter contact problems in real time, local solutions near a new contact location are less accurate when a new contact location is not close to the training contact locations. To improve the accuracy of local solutions near a new contact location, the first POD basis vector is replaced by the shifted first POD basis vector for the closest training contact location to the new contact location. Numerical results show that the modified PODI-RBF method is efficient and effective to achieve real-time FE simulations of indenter contact problems while improving the accuracy of local solutions near contact locations.

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改进 PODI-RBF 方法，提高压头接触问题实时有限元模拟局部解的精度

本文提出了一种新方法，以提高用于压头接触问题实时有限元（FE）模拟的 PODI-RBF 方法局部解的精度。在离线阶段，适当的正交分解（POD）基向量和系数是从训练接触位置和压痕深度的压头接触问题全阶有限元模拟的解快照中提取的。在联机阶段，使用 RBF 插值估计新接触载荷的 POD 基向量和系数。虽然使用 RBF 的插值 POD（PODI）方法对于实时获得压头接触问题的有限元求解非常有用，但当新接触位置与训练接触位置不相近时，新接触位置附近的局部求解精度较低。为了提高新接触位置附近局部解的精确度，第一 POD 基向量由与新接触位置最近的训练接触位置的移位第一 POD 基向量代替。数值结果表明，改进后的 PODI-RBF 方法能高效实现压头接触问题的实时有限元模拟，同时提高接触位置附近局部解的精度。

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来源期刊

Advances in Engineering Software 工程技术-计算机：跨学科应用

CiteScore

7.70

自引率

4.20%

发文量

169

审稿时长

37 days

期刊介绍： The objective of this journal is to communicate recent and projected advances in computer-based engineering techniques. The fields covered include mechanical, aerospace, civil and environmental engineering, with an emphasis on research and development leading to practical problem-solving. The scope of the journal includes: • Innovative computational strategies and numerical algorithms for large-scale engineering problems • Analysis and simulation techniques and systems • Model and mesh generation • Control of the accuracy, stability and efficiency of computational process • Exploitation of new computing environments (eg distributed hetergeneous and collaborative computing) • Advanced visualization techniques, virtual environments and prototyping • Applications of AI, knowledge-based systems, computational intelligence, including fuzzy logic, neural networks and evolutionary computations • Application of object-oriented technology to engineering problems • Intelligent human computer interfaces • Design automation, multidisciplinary design and optimization • CAD, CAE and integrated process and product development systems • Quality and reliability.