Effect of boundary conditions on shakedown analysis of heterogeneous materials  

作　　者：Xiuchen GONG Yinghao NIE Gengdong CHENG Kai LI 

机构地区：[1]State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,International Research Center for Computational Mechanics,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116023,Liaoning Province,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2024年第1期39-68,共30页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Nos. 52075070 and12302254);the Dalian City Supports Innovation and Entrepreneurship Projects for High-Level Talents (No. 2021RD16);the Liaoning Revitalization Talents Program (No. XLYC2002108)。

摘　　要：The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force(NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions(DBCs), uniform traction boundary conditions(TBCs), and periodic boundary conditions(PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit(EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under TBCs.Conversely, utilizing PBCs to construct an SSF for the shakedown analysis lea

关 键 词：heterogeneous material self-equilibrium stress field(SSF) shakedown analysis effect of boundary conditions 

分 类 号：O344.5[理学—固体力学]