Virtual Element Methods in Engineering Sciences
暫譯: 工程科學中的虛擬元素方法
Wriggers, Peter, Aldakheel, Fadi, Hudobivnik, Blaz
- 出版商: Springer
- 出版日期: 2024-10-29
- 售價: $7,180
- 貴賓價: 9.5 折 $6,821
- 語言: 英文
- 頁數: 452
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031392574
- ISBN-13: 9783031392573
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商品描述
This book provides a comprehensive treatment of the virtual element method (VEM) for engineering applications, focusing on its application in solid mechanics. Starting with a continuum mechanics background, the book establishes the necessary foundation for understanding the subsequent chapters. It then delves into the VEM's Ansatz functions and projection techniques, both for solids and the Poisson equation, which are fundamental to the method. The book explores the virtual element formulation for elasticity problems, offering insights into its advantages and capabilities. Moving beyond elasticity, the VEM is extended to problems in dynamics, enabling the analysis of dynamic systems with accuracy and efficiency. The book also covers the virtual element formulation for finite plasticity, providing a framework for simulating the behavior of materials undergoing plastic deformation. Furthermore, the VEM is applied to thermo-mechanical problems, where it allows for the investigation ofcoupled thermal and mechanical effects. The book dedicates a significant portion to the virtual elements for fracture processes, presenting techniques to model and analyze fractures in engineering structures. It also addresses contact problems, showcasing the VEM's effectiveness in dealing with contact phenomena. The virtual element method's versatility is further demonstrated through its application in homogenization, offering a means to understand the effective behavior of composite materials and heterogeneous structures. Finally, the book concludes with the virtual elements for beams and plates, exploring their application in these specific structural elements. Throughout the book, the authors emphasize the advantages of the virtual element method over traditional finite element discretization schemes, highlighting its accuracy, flexibility, and computational efficiency in various engineering contexts.
商品描述(中文翻譯)
本書全面探討虛擬元素法（Virtual Element Method, VEM）在工程應用中的應用，特別是其在固體力學中的應用。書中首先介紹連續介質力學的背景，為理解後續章節奠定必要的基礎。接著深入探討VEM的Ansatz函數和投影技術，這些對於固體及泊松方程（Poisson equation）來說都是該方法的基本要素。本書探討了彈性問題的虛擬元素公式，提供了其優勢和能力的見解。超越彈性，本書將VEM擴展到動力學問題，使得能夠準確且高效地分析動態系統。本書還涵蓋了有限塑性（finite plasticity）的虛擬元素公式，提供了一個模擬材料經歷塑性變形行為的框架。此外，VEM還應用於熱-機械問題，允許研究耦合的熱效應和機械效應。本書還專門討論了與斷裂過程相關的虛擬元素，展示了建模和分析工程結構中斷裂的技術。它還處理接觸問題，展示了VEM在處理接觸現象方面的有效性。虛擬元素法的多功能性進一步通過其在均質化（homogenization）中的應用得以展示，提供了一種理解複合材料和異質結構有效行為的方法。最後，本書以梁和板的虛擬元素作結，探討其在這些特定結構元素中的應用。在整本書中，作者強調虛擬元素法相較於傳統有限元素離散化方案的優勢，突顯其在各種工程背景下的準確性、靈活性和計算效率。
作者簡介
Professor Dr.-Ing. habil. P. Wriggers studied Civil Engineering at the University Hannover; he obtained his Dr.-Ing degree at the University of Hannover in 1980 on "Contact-impact problems." Since April 2022, he is Emeritus Professor at Leibniz Universität Hannover. Peter Wriggers is Member of the "Braunschweigische Wissenschaftliche Gesellschaft," the Academy of Science and Literature in Mainz, the German National Academy of Engineering "acatech" and the National Academy of Croatia. He was President of GAMM, President of GACM and Vice-President of IACM. Furthermore, he acts as Editor-in-Chief for the International Journal "Computational Mechanics" and "Computational Particle Mechanics." He was awarded the Fellowship of IACM and received the "Computational Mechanics Award" and the "IACM Award" of IACM, the "Euler Medal" of ECCOMAS as well as three honorary degrees from the Universities of Poznan, ENS Cachan and TU Darmstadt.
Professor Dr.-Ing. habil. F. Aldakheel is since April 2023 professor for high performance computing at Leibniz Universität Hannover. After studying engineering in Aleppo, he initially worked at Alfurat University in Syria before moving to the Institute of Applied Mechanics at the University of Stuttgart for the master and Ph.D. studies and then the postdoc period. There he was course director for the international master's programme "Computational Mechanics of Materials and Structures" (COMMAS) as well as local director for the excellence programme "Erasmus Mundus Master of Science in Computational Mechanics". Most recently, he was Chief-Engineer/Group-Leader at the Institute for Continuum Mechanics at Leibniz Universität Hannover and Associate Professor (Honorary) at the Zienkiewicz Centre for Computational Engineering at Swansea University, UK. He has been awarded numerous awards, among them the Richard-von-Mises Prize of GAMM (Association of Applied Mathematics and Mechanics). His research interests are related tothe modeling of material behaviors, variational principles, computational solid mechanics, structural mechanics, finite and virtual element methods, multiphysics and multi-scales problems, machine learning, energy transition and experimental validation.
Dr. Blaz Hudobivnik studied Civil Engineering at the University of Ljubljana. He was awarded his Doctoral degree in 2016 under the supervision of Prof. Joze Korelc. He worked as Young researcher/Researcher between 2011 and October 2016 at the University of Ljubljana and after that he was employed as Postdoctoral researcher until April 2023 at the Institute of Continuum Mechanics at the Leibniz Universität Hannover. Since April 2023 he is employed in industry as simulation expert in mechanical design of batteries. His primary research fields are efficient implementation of nonlinear coupled problems, the development of the virtual element method and its application to a wide range of engineering problems. This includes 2D and 3D applications for linear and nonlinear materials, for static and dynamic solids, plate and contact problems, coupled problems (thermo-hydro-mechanics), phase field methods, multi-scale and optimization problems. Alongside research, he advises other institute members in numerical implementations due to his expert knowledge of the Software-Tool AceGen/AceFEM, developed by his doctoral advisor Prof. Korelc.
作者簡介(中文翻譯)
教授 Dr.-Ing. habil. P. Wriggers 於漢諾威大學學習土木工程；他於1980年在漢諾威大學獲得博士學位，研究主題為「接觸衝擊問題」。自2022年4月起，他成為漢諾威萊布尼茨大學的名譽教授。彼得·維格斯（Peter Wriggers）是「布倫瑞克科學學會」的成員，還是美因茲科學與文學學院、德國國家工程學院「acatech」及克羅地亞國家學院的成員。他曾擔任 GAMM 的會長、GACM 的會長及 IACM 的副會長。此外，他還擔任國際期刊《計算力學》（Computational Mechanics）和《計算粒子力學》（Computational Particle Mechanics）的主編。他獲得了 IACM 的研究員榮譽，並獲得了 IACM 的「計算力學獎」和「IACM 獎」，以及 ECCOMAS 的「歐拉獎」和波茲南大學、ENS Cachan 和達姆施塔特工業大學的三個榮譽學位。
教授 Dr.-Ing. habil. F. Aldakheel 自2023年4月起擔任漢諾威萊布尼茨大學的高效能計算教授。在阿勒頗學習工程學後，他最初在敘利亞的阿爾富拉特大學工作，然後轉到斯圖加特大學的應用力學研究所進行碩士和博士研究，隨後進行博士後研究。在那裡，他擔任國際碩士課程「材料與結構的計算力學」（COMMAS）的課程主任，以及卓越計劃「Erasmus Mundus 計算力學碩士」的地方主任。最近，他在漢諾威萊布尼茨大學的連續介質力學研究所擔任首席工程師/小組領導，並在英國斯旺西大學的 Zienkiewicz 計算工程中心擔任副教授（榮譽）。他獲得了多項獎項，其中包括 GAMM（應用數學與力學協會）的理查德·馮·米塞斯獎。他的研究興趣與材料行為建模、變分原理、計算固體力學、結構力學、有限元和虛擬元素方法、多物理場和多尺度問題、機器學習、能源轉型及實驗驗證有關。
Dr. Blaz Hudobivnik 於盧布爾雅那大學學習土木工程。他於2016年在 Joze Korelc 教授的指導下獲得博士學位。在2011年至2016年10月期間，他在盧布爾雅那大學擔任青年研究員/研究員，之後在漢諾威萊布尼茨大學的連續介質力學研究所擔任博士後研究員，直到2023年4月。自2023年4月起，他在業界擔任電池機械設計的模擬專家。他的主要研究領域包括非線性耦合問題的高效實現、虛擬元素方法的開發及其在各種工程問題中的應用。這包括線性和非線性材料的2D和3D應用、靜態和動態固體、板和接觸問題、耦合問題（熱-水-力學）、相場方法、多尺度和優化問題。除了研究外，他還因其對其博士導師 Prof. Korelc 開發的軟體工具 AceGen/AceFEM 的專業知識，向其他研究所成員提供數值實現的建議。
