A Convergence Analysis of an H-Version Finite-Element Method with High-Order Elements for Two-Dimensional Elasto-Plasticity Problems

This communication shows how the smoothed finite element method (SFEM) very recently proposed by G. R. Liu [14] can be extended to elasto-plasticity. The SFEM results are in excellent agreement with the finite element (FEM) and analytical results. For the examples treated, the method is quite insensitive to mesh distortion and volumetric locking. Moreover, the SFEM yields more compliant load-displacement curves compared to the standard, displacement based FE method, as expected from the theoretical developments recently published in [4], [3] and [6].

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An effective high-order element for analysis of two-dimensional linear problem using SBFEM

Journal of Science and Technology in Civil Engineering (STCE) - NUCE ◽

10.31814/stce.nuce2021-15(3)-09 ◽

2021 ◽

Vol 15 (3) ◽

pp. 109-122

Author(s):

Nguyen Van Chung ◽

Nguyen Thanh Him ◽

Bui Quoc Khiem ◽

Pham Ngoc Tien

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Boundary Conditions ◽

Linear Problem ◽

High Order ◽

Surface Load ◽

Two Dimensional ◽

High Order Element ◽

Scaled Boundary Finite Element ◽

Element Method

The scaled boundary finite element method (SBFEM) is a semi-analytical method, whose versatility, accuracy, and efficiency are not only equal to, but potentially better than the finite element method and the boundary element method for certain problems. This paper investigates the possibility of using an efficient high-order polynomial element in the SBFEM to form the approximation in the circumferential direction. The governing equations are formulated from the classical linear elasticity theory via the SBFEM technique. The scaled boundary finite element equations are formulated within a general framework integrating the influence of the distributed body source, mixed boundary conditions, contributions the side face with either prescribed surface load or prescribed displacement. The position of scaling center is considered for modeling problem. The proposed method is evaluated by solving two-dimensional linear problem. A selected set of results is reported to demonstrate the accuracy and convergence of the proposed method for solving problems in general boundary conditions.

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Reduction of stress concentration around a hole in a uniaxially loaded plate

The Journal of Strain Analysis for Engineering Design ◽

10.1243/03093247v182135 ◽

1983 ◽

Vol 18 (2) ◽

pp. 135-141 ◽

Cited By ~ 22

Author(s):

U C Jindal

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Stress Concentration ◽

Circular Hole ◽

High Order ◽

Two Dimensional ◽

The Finite Element Method ◽

Loaded Plate ◽

Hole Geometry ◽

Element Method

The stress concentration around a circular hole in a plate can be reduced by up to 21 per cent by introducing auxiliary holes on either side of the original hole. But this approach of auxiliary holes creates two more regions of stress concentration in the plate. In the present study, the hole geometry has been modified to effect stress reductions as high as 22 per cent. The problem has been analysed numerically by the finite element method and experimentally by two-dimensional photoelasticity. It has been observed that by making the hole oblong in the direction of loading, a high order of reduction in stress concentration around the hole can be obtained.

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