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

• Published in: Frontiers of Structural and Civil Engineering Vol. 13; no. 2; pp. 456 - 477
• Main Author: Liu, Gui-Rong
• Format: Journal Article
• Language: English
• Published: Beijing Higher Education Press 01.04.2019; Springer Nature B.V
• Subjects: Automation; Cities; Civil Engineering; Computer simulation; Countries; Design; Domains; Engineering; Finite element analysis; Finite element method; Formulations; Locking; Mathematical models; Meshless methods; Nonlinear programming; Properties (attributes); Regions; Review; Upper bounds; smoothing domain; solid mechanics; softening effect; finite element method; smoothed finite element method; strain smoothing technique; upper bound solution; computational method; weakened weak form
• ISSN: 2095-2430; 2095-2449
• DOI: 10.1007/s11709-019-0519-5

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 AI-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 on-demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.