Adaptive selective ES-FEM limit analysis of cracked plane-strain structures

Nguyen‐Xuan, H.; Rabczuk, Timon

doi:10.1007/s11709-015-0317-7

Cited by 16 publications

(2 citation statements)

References 36 publications

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“…Similar to ES-FEM, the FS-FEM is more accurate than the standard FEM using the same T4 mesh for dynamic problems [39] and both linear and nonlinear problems [36]. Because of its excellent properties, S-FEM has been applied to a wide range of practical mechanics problems such as fracture mechanics and fatigue behavior [40][41][42][43], nonlinear material behavior analysis [35,38,[44][45][46][47][48], plates and shells [49][50][51][52], piezoelectric structures [43,[53][54][55], heat transfer and thermomechanical problems [56][57][58][59], vibration analysis and acoustics problems [39,58,[60][61][62], and fluid and structure interaction problems [63][64][65][66]. We refer the reader to [67,68] for recent in-depth reviews of S-FEM.…”

Section: Related Workmentioning

confidence: 99%

A Smoothed Finite Element‐Based Elasticity Model for Soft Bodies

Zhang

Zhou

Huang

et al. 2017

Mathematical Problems in Engineering

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One of the major challenges in mesh-based deformation simulation in computer graphics is to deal with mesh distortion. In this paper, we present a novel mesh-insensitive and softer method for simulating deformable solid bodies under the assumptions of linear elastic mechanics. A face-based strain smoothing method is adopted to alleviate mesh distortion instead of the traditional spatial adaptive smoothing method. Then, we propose a way to combine the strain smoothing method and the corotational method. With this approach, the amplitude and frequency of transient displacements are slightly affected by the distorted mesh. Realistic simulation results are generated under large rotation using a linear elasticity model without adding significant complexity or computational cost to the standard corotational FEM. Meanwhile, softening effect is a by-product of our method.

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Section: Related Workmentioning

confidence: 99%

A Smoothed Finite Element‐Based Elasticity Model for Soft Bodies

Zhang

Zhou

Huang

et al. 2017

Mathematical Problems in Engineering

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“…Then, Liu and his co-workers [22][23][24][25] applied this technique to standard FEM and proposed a class of smoothed finite element method (S-FEM). Typical S-FEM models include the cell-based S-FEM model (CS-FEM) [26], node-based S-FEM model (NS-FEM) [27,28], and edge-based S-FEM model (ES-FEM) [29][30][31][32]. Several papers demonstrate that the NS-FEM performs well in heat transfer analysis [33,34], fracture analysis [35], acoustic problems [36,37], axisymmetric shell structures [38], static and dynamic analysis [39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Circular Tunnels in Cohesive-Frictional Soil Using the Node-Based Smoothed Finite Element Method (NS-FEM)

Vo-Minh¹

2022

Theory and Practice of Tunnel Engineering

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In this chapter, the stability of a circular tunnel and dual circular tunnels in cohesive-frictional soils subjected to surcharge loading is investigated by using the node-based smoothed finite element method (NS-FEM). In the NS-FEM, the smoothing strain is calculated over smoothing domains associated with the elements’ nodes. The soil is assumed as a uniform Mohr-Coulomb material, and it obeys an associated flow rule. By using the second-order cone programming (SOCP) for solving the optimization problems, the ultimate load and failure mechanisms of the circular tunnel are considered. This chapter discusses the influence of the soil weight γD/c, the tunnel diameter ratio to its depth H/D, the vertical and horizontal spacing ratio (L/D, S/D) of two tunnels and soil internal friction angle ϕ on the stability numbers σs/c are calculated. The stability numbers obtained from the present approach are compared with the available literature for tunnels.

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