The smoothed finite element methods (S-FEM) are a family of methods formulated through carefully designed combinations of the standard FEM and some of the techniques from the meshfree methods. Studies have proven that S-FEM models behave softer than the FEM counterparts using the same mesh structure, often produce more accurate solutions, higher convergence rates, and much less sensitivity to mesh distortion. They work well with triangular or tetrahedral mesh that can be automatically generated, and hence are ideal for automated computations and adaptive analyses. Some S-FEM models can also produce upper bound solution for force driving problems, which is an excellent unique complementary feature to FEM. Because of these attractive properties, S-FEM has been applied to numerous problems in the disciplines of material mechanics, biomechanics, fracture mechanics, plates and shells, dynamics, acoustics, heat transfer and fluid–structure interactions. This paper reviews the developments and applications of the S-FEM in the past ten years. We hope this review can shed light on further theoretical development of S-FEM and more complex practical applications in future.

Smoothed Finite Element Methods (S-FEM): An Overview and Recent Developments

The cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using three-node triangular elements was recently proposed to improve the performance of the discrete shear gap method (DSG3) for static and free vibration analyses of isotropic Mindlin plates. In this paper, the CS-FEM-DSG3 is further extended for static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators. In the piezoelectric composite plates, the electric potential is assumed to be a linear function through the thickness of each piezoelectric sublayer. A displacement and velocity feedback control algorithm is used for active control of the static deflection and the dynamic response of the plates through closed loop control with bonded or embedded distributed piezoelectric sensors and actuators. The accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of other available numerical results.

http://iopscience.iop.org/article/10.1088/0964-1726/22/9/095026/pdf

Static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators by the cell-based smoothed discrete shear gap method (CS-FEM-DSG3)

Geometrically nonlinear analysis of functionally graded plates using a cell-based smoothed three-node plate element (CS-MIN3) based on the C0-HSDT

Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCS-DSG3)

A three-node triangular element with continuous nodal stress

SUMMARY

This paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node-based smoothed FEM in combination with a primal–dual algorithm. An associated primal–dual form based on the von Mises yield criterion is adopted. The primal-dual algorithm together with a Newton-like iteration are then used to solve this associated primal–dual form to determine simultaneously both approximate upper and quasi-lower bounds of the plastic collapse limit and the shakedown limit. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to show the reliability, accuracy, and generality of the present formulation compared with other available methods. Copyright © 2011 John Wiley & Sons, Ltd.

T.N. Tran

Papers

Computation of limit and shakedown loads using a node‐based smoothed finite element method