• Structural Engineering and Mechanics
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• v.30 no.1
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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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• v.86 no.3
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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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• v.75 no.6
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• pp.685-699
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• 2020

Polygonal finite element provides a great flexibility in mesh generation of crack propagation problems where the topology of the domain changes significantly. However, the control of the discretization error in such problems is a main concern. In this paper, a polygonal-FEM is presented in modeling of crack propagation problems via an automatic adaptive mesh refinement procedure. The adaptive mesh refinement is accomplished based on the Zienkiewicz-Zhu error estimator in conjunction with a weighted SPR technique. Adaptive mesh refinement is employed in some steps for reduction of the discretization error and not for tracking the crack. In the steps that no adaptive mesh refinement is required, local modifications are applied on the mesh to prevent poor polygonal element shapes. Finally, several numerical examples are analyzed to demonstrate the efficiency, accuracy and robustness of the proposed computational algorithm in crack propagation problems.

• Journal of applied mathematics & informatics
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• v.9 no.1
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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.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.4
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• pp.1900-1907
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• 2012

Since the subpanels of polygonal-section shell have the corners of an obtuse angle larger than 90 degree unlike general plate or box-section structures, this could have an influence on forming nodal lines against local plate buckling or stress distributions. However, there is not sufficient material in the relevant study results or design recommendations. The very feasible models of the initial imperfections were acquired through the literature studies and then the parametric studies were conducted along with the initial imperfection models by using the finite element method. The parameters like the size of residual stresses, the portion of compressive residual stresses, and steel grades were considered. From the parametric studies, it was found that the maximum residual stress is more influential factor than the distribution pattern of residual stresses. In addition, The design strength equations for the simply supported plates can be applicable to the determination of the local buckling strength of the polygonal cross-section shell structures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.10
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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.

• Steel and Composite Structures
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• v.51 no.4
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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.

• Structural Engineering and Mechanics
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• v.62 no.1
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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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• v.7 no.2
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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.

• Korean Journal of Computational Design and Engineering
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• v.17 no.6
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• pp.436-442
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• 2012

Traumatic loading during car accidents or sports activities can lead to cervical spinal cord injury. Experiments in spinal cord injury research are mainly carried out on rabbit or rat. Finite element models that include the rat cervical spinal cord and adjacent soft tissues should be developed for efficient studies of mechanisms of spinal cord injury. Images of a rat were obtained from high resolution MRI scanner. Polygonal surfaces were extracted structure by structure from the MRI data using the ITK-SNAP volume segmentation software. These surfaces were converted to Non-uniform Rational B-spline surfaces by the INUS Rapidform rapid prototyping software. Rapidform was also used to generate a thin shell surface model for the dura mater which sheathes the spinal cord. Altair's Hypermesh pre-processor was used to generate finite element meshes for each structure. These processes in this study can be utilized in modeling of other biomedical tissues and can be one of examples for reverse engineering on biomechanics.