The smoothed finite element method (S-FEM):A framework for the design of numerical models for desired solutions

作     者：Gui-Rong Liu 

作者机构：Department of Aerospace Engineering and Engineering MechanicsUniversity of CincinnatiCincinnati 45219USA 

出 版 物：《Frontiers of Structural and Civil Engineering》 (结构与土木工程前沿（英文版）)

年 卷 期：2019年第13卷第2期

页      面：456-477页

核心收录：

学科分类：1305[艺术学-设计学（可授艺术学、工学学位）] 08[工学] 0813[工学-建筑学] 0814[工学-土木工程] 

主　　题：computational method finite element method smoothed finite element method strain smoothing technique smoothing domain weakened weak form solid mechanics softening effect upper bound solution 

摘      要：The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects;2) upper-bound solutions;3) accurate solutions and higher convergence rates;4) insensitivity to mesh distortion;5) Jacobian?free;6) volumetric-locking-free;and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on Al-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.