%A Gui-Rong Liu %T The smoothed finite element method (S-FEM): A framework for the design of numerical models for desired solutions %0 Journal Article %D 2019 %J Front. Struct. Civ. Eng. %J Frontiers of Structural and Civil Engineering %@ 2095-2430 %R 10.1007/s11709-019-0519-5 %P 456-477 %V 13 %N 2 %U {https://journal.hep.com.cn/fsce/EN/10.1007/s11709-019-0519-5 %8 2019-03-12 %X

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.