• Structural Engineering and Mechanics
• /
• 제30권1호
• /
• pp.119-129
• /
• 2008

A small strain and elastoplastic formulation of Polygonal Element Method (PEM) is developed for efficient analysis of elastoplastic solids. In this work, the polygonal elements are constructed based on traditional triangular finite meshes. The construction method of polygonal mesh can directly utilize the sophisticated triangularization algorithm and reduce the difficulty in generating polygonal elements. The Wachspress rational finite element basis function is used to construct the approximations of polygonal elements. The incremental variational form and a von Mises type model are used for non-linear elastoplastic analysis. Several small strain elastoplastic numerical examples are presented to verify the advantages and the accuracy of the numerical formulation.

• Structural Engineering and Mechanics
• /
• 제86권3호
• /
• pp.311-324
• /
• 2023

Herein, we present effective polygonal finite elements to which the strain-smoothed element (SSE) method is applied. Recently, the SSE method has been developed for conventional triangular and quadrilateral finite elements; furthermore, it has been shown to improve the performance of finite elements. Polygonal elements enable various applications through flexible mesh handling; however, further development is still required to use them more effectively in engineering practice. In this study, piecewise linear shape functions are adopted, the SSE method is applied through the triangulation of polygonal elements, and a smoothed strain field is constructed within the element. The strain-smoothed polygonal elements pass basic tests and show improved convergence behaviors in various numerical problems.

• Structural Engineering and Mechanics
• /
• 제62권1호
• /
• pp.11-20
• /
• 2017

The base force element method (BFEM) is a new finite element method. In this paper, a degenerated 4-mid-node plane element from concave polygonal element of BFEM was proposed. The performance of this quadrilateral element with 4 mid-edge nodes in the BFEM on complementary energy principle is studied. Four examples of linear elastic analysis for plane frame structure are presented. The influence of aspect ratio of the element is analyzed. The feasibility of the 4 mid-edge node element model of BFEM on complementary energy principles researched for plane frame problems. The results using the BFEM are compared with corresponding analytical solutions and those obtained from the standard displacement finite element method. It is revealed that the BFEM has better performance compared to the displacement model in the case of large aspect ratio.

• Journal of applied mathematics & informatics
• /
• 제9권1호
• /
• pp.311-320
• /
• 2002

For second order linear elliptic problems over smooth domains, it is well known that the rate of convergence of the error in the $L_2$norm is one order higher than that in the $H^1$norm. For polygonal domains with reentrant corners, it has been shown in [15] that this extra order cannot be fully recovered when the h-version is used. We present theoretical and computational examples showing the sharpness of our results.

• 대한기계학회논문집A
• /
• 제28권10호
• /
• pp.1492-1499
• /
• 2004

In this paper, defect formation in ring rolling is revealed by computer simulation of ring rolling processes. The rigid-plastic finite element method is employed for this study. An analysis model having relatively fine mesh system near the roll gap is used for reducing the computational time and a scheme of minimizing the volume change is applied. The formation of the central cavity formation defect in ring rolling of a taper roller bearing outer race and the polygonal shape defect in ring rolling of a ball bearing outer race has been simulated. It has been seen that the results are qualitatively good with actual phenomena.

• Journal of applied mathematics & informatics
• /
• 제7권2호
• /
• pp.493-506
• /
• 2000

Recently the first author and his coworker report a new finite element method for the Poisson equations with homogeneous Dirichlet boundary conditions on a polygonal domain with one re-entrant angle [7], They use the well-known fact that the solution of such problem has a singular representation, deduced a well-posed new variational problem for a regular part of solution and an extraction formula for the so-called stress intensity factor using tow cut-off functions. They use Fredholm alternative an Garding's inequality to establish the well-posedness of the variational problem and finite element approximation, so there is a maximum bound for mesh h theoretically. although the numerical experiments shows the convergence for every reasonable h with reasonable size y imposing a restriction to the support of the extra cut-off function without using Garding's inequality. We also give error analysis with similar results.

• 한국산학기술학회논문지
• /
• 제13권4호
• /
• pp.1900-1907
• /
• 2012

일반적으로 활용되고 있는 원통형 단면쉘 구조로 이루어진 타워구조의 대형화에 한계가 있어 다각형 단면쉘 기둥구조의 활용이 대두되고 있다. 현재 대형 다각형 단면쉘 기둥구조의 국부좌굴강도에 대한 자료가 충분치 않고 관련 기준이나 지침이 명확히 제시되고 있지 않은 실정이다. 이에 3차원 유한요소프로그램인 ABAQUS를 이용한 다양한 변수해석 모델을 수립하여 탄성좌굴 및 비선형비탄성 변수해석을 수행하였다. 이 때, 단면제원은 대형 풍력발전타워 기둥구조에 적용하는 것을 가정하여 선정하였고, 다각형의 각형 수, 잔류응력의 크기 및 분포특성, 강재 항복강도 등의 변수를 고려한 해석결과를 토대로 다각형 단면쉘 기둥구조의 국부좌굴 특성을 분석하였다. 본 변수해석 연구결과로부터 세부적인 잔류응력 분포양상 보다는 잔류응력의 최대크기가 축방향 압축을 받는 다각형 쉘의 국부좌굴강도에 중요한 영향인자인 것을 알 수 있다. 다각형 단면 쉘 구조의 국부좌굴강도는 4변 단순지지된 평판구조의 기준을 적용하여 평가할 수 있을 것으로 판단된다.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제12권1호
• /
• pp.13-23
• /
• 2008

In [7, 8], they proposed a new singular function(NSF) method to compute singular solutions of Poisson equations on a polygonal domain with re-entrant angles. Singularities are eliminated and only the regular part of the solution that is in $H^2$ is computed. The stress intensity factor and the solution can be computed as a post processing step. This method was extended to the interface problem and Poisson equations with the mixed boundary condition. In this paper, we give NSF method for the Helmholtz equations ${\Delta}u+Ku=f$ with homogeneous Dirichlet boundary condition. Examples with a singular point are given with numerical results.

• Structural Monitoring and Maintenance
• /
• 제4권3호
• /
• pp.195-220
• /
• 2017

Nowadays, railway system plays a significant role in transportation, conveying cargo, passengers, minerals, grains, and so forth. Railway ballasted track is a conventional railway track as can be seen all over the world. Ballast, located underneath the sleepers, is the most important elements on ballasted track, which has many functions and requires routine maintenance. Ballast needs to be maintained frequently to prevent rail buckling, settlement, misalignment so that ballast has to be modelled accurately. Continuum model was introduced to model granular material and was extended in ballast. However, ballast is a heterogeneous material with highly nonlinear behaviour. Hence, ballast could not be modelled accurately in continuum model due to the discontinuities nature and material degradation of ballast. Discrete element modelling (DEM) is proposed as an alternative approach that provides insight into constitutive model, realistic particle, and contact algorithm between each particle. DEM has been studied in many recent decades. However, there are limitations due to the high computational time and memory consumption, which cause the lack of using in high range. This paper presents a review of recent ballast modelling with benefits and drawbacks. Ballast particles are illustrated either circular, circular crump, spherical, spherical crump, super-quadric, polygonal and polyhedral. Moreover, the gaps and limitations of previous studies are also summarized. The outcome of this study will help the understanding into different ballast modelling and particle. The insight information can be used to improve ballast modelling and monitoring for condition-based track maintenance.

• East Asian mathematical journal
• /
• 제14권1호
• /
• pp.63-76
• /
• 1998

we consider the hp-version to solve non-constant coefficients elliptic equations $-div(a{\nabla}u)=f$ with Dirichlet boundary conditions on a bounded polygonal domain $\Omega$ in $R^2$. In [6], M. Suri obtained an optimal error-estimate for the hp-version: ${\parallel}u-u^h_p{\parallel}_{1,\Omega}{\leq}Cp^{(\sigma-1)}h^{min(p,\sigma-1)}{\parallel}u{\parallel}_{\sigma,\Omega}$. This optimal result follows under the assumption that all integrations are performed exactly. In practice, the integrals are seldom computed exactly. The numerical quadrature rule scheme is needed to compute the integrals in the variational formulation of the discrete problem. In this paper we consider a family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties, which can be used for calculating the integrals. Under the numerical quadrature rules we will give the variational form of our non-constant coefficients elliptic problem and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_{1,\Omega}$.