• Structural Engineering and Mechanics
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• 제30권1호
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• pp.119-129
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• 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
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• 제86권3호
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• pp.311-324
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• 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
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• 제62권1호
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• pp.11-20
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• 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
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• 제9권1호
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• pp.311-320
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• 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
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• 제28권10호
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• pp.1492-1499
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• 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
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• 제7권2호
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• pp.493-506
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• 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
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• 제13권4호
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• pp.1900-1907
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• 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.

• Steel and Composite Structures
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• 제51권4호
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• pp.363-375
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• 2024

Within the optimization field, addressing the intricate posed by fluidic pressure loads on functionally graded structures with frequency-related designs is a kind of complex design challenges. This paper thus introduces an innovative density-based topology optimization strategy for frequency-constraint functionally graded structures incorporating Darcy's law and a drainage term. It ensures consistent treatment of design-dependent fluidic pressure loads to frequency-related structures that dynamically adjust their direction and location throughout the design evolution. The porosity of each finite element, coupled with its drainage term, is intricately linked to its density variable through a Heaviside function, ensuring a seamless transition between solid and void phases. A design-specific pressure field is established by employing Darcy's law, and the associated partial differential equation is solved using finite element analysis. Subsequently, this pressure field is utilized to ascertain consistent nodal loads, enabling an efficient evaluation of load sensitivities through the adjoint-variable method. Moreover, this novel approach incorporates load-dependent structures, frequency constraints, functionally graded material models, and polygonal meshes, expanding its applicability and flexibility to a broader range of engineering scenarios. The proposed methodology's effectiveness and robustness are demonstrated through numerical examples, including fluidic pressure-loaded frequency-constraint structures undergoing small deformations, where compliance is minimized for structures optimized within specified resource constraints.

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

• Steel and Composite Structures
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• 제51권3호
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• pp.261-270
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• 2024

This paper proposes an effective method for optimizing the structure of functionally graded isotropic and incompressible linear elastic materials. The main emphasis is on utilizing a specialized polytopal composite finite element (PCE) technique capable of handling a broad range of materials, addressing common volumetric locking issues found in nearly incompressible substances. Additionally, it employs a continuum model for bi-directional functionally graded (BFG) material properties, amalgamating these aspects into a unified property function. This study thus provides an innovative approach that tackles diverse material challenges, accommodating various elemental shapes like triangles, quadrilaterals, and polygons across compressible and nearly incompressible material properties. The paper thoroughly details the mathematical formulations for optimizing the topology of BFG structures with various materials. Finally, it showcases the effectiveness and efficiency of the proposed method through numerous numerical examples.