• 한국전산구조공학회논문집
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• 제18권2호
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• pp.103-111
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• 2005

본 논문에서는 수치적분 정도를 향상시킬 수 있는 새로운 무요소 기법을 제안한파 저자들에 의해 페트로프-갤러킨 자연요소법(PG-NEM)이라 명명된 이 새로운 기법은 보로노이 다이어그램과 델라우니 삼각화에 기반을 두고 있으며, 이는 BG-NEM이라 불리는 기존의 자연요소법과 개념적으로 동일하다. 하지만, 동일한 시험 형상함수와 시도 형상함수를 선택하는 BG-NEM과는 달리, PG-NEM에서는 지지영역이 적분을 위한 배경격자에 정확하게 일치하도록 시험 형상함수를 독립적으로 선택하는 페트로프-갤러킨 개념에 기반을 두고 있다. 따라서, 제안된 기법은 BG-NEM과 비교하여 수치적분 정도를 현저히 향상시킬 것으로 기대된다.

• 한국전산구조공학회논문집
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• 제18권2호
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• pp.123-131
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• 2005

기존의 부브노프-갤러킨 자연요소법(BG-NEM)에서 발생하는 수치적분의 부정확성을 페트로프-갤러킨 자연요소법(PG-NEM)에서 완벽히 해결할 수 있음을 저자들의 이전 논문에서 확인하였다. 본 논문에서는 PG-NEM을 확장하여 2차원 기하학적 비선형 문제를 다룬다. 해석을 위해 선형화된 토탈 라그랑지 정식화를 도입하고 PG-NEM을 적용하여 근사화한다. 각 하중 단계마다 절점은 새로운 위치로 갱신되며, 재분포된 절점을 바탕으로 형상함수를 새롭게 구성한다. 이러한 과정은 PG-NEM이 더 정확하고 안정적인 근사함수를 제공하는 것을 가능하게 한다. 개발된 포트란 시험 프로그램을 이용하여 대표적인 수치 예제를 수행하였으며, 수치결과로부터 PG-NEM이 효율적이고 정확하게 대변형 문제를 근사화하는 것을 확인하였다.

• 한국정밀공학회지
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• 제25권2호
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• pp.105-114
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• 2008

Natural element method (NEM) is quick in research activities by natural sciences and mechanical engineering fields, and from which good results are watched by various engineering fields and applied too. However no paper or research about the applied case has announced yet. Therefore on this paper, I will rediscover an optimum design and apply NEM into other fields with NEM for existing optimum design of mainly using FEM. NEM and genetic algorithm (GA) are applied to optimize a membrane with a center hole. The optimal design obtained by NEM is compared to the counterpart obtained by the finite element method (FEM). Result by NEM is found to be better than the result by FEM. NEM can be a feasible analysis tool in design optimization.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 추계학술대회
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• pp.474-479
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• 2004

According to our previous study, it is confirmed that the Petrov-Galerkin natural element method (PGNEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin natural element method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem.

• 한국전산구조공학회논문집
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• 제18권2호
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• pp.113-121
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• 2005

무요소기법이 공통적으로 내재하고 있는 수치적분의 부정확성을 해결하기 위해, 페트로프-갤러킨 자연요소법이라 불리는 향상된 자연요소법을 제안한다. 제안된 방법은 라플라스 기저함수를 시도 형상함수로 사용하는 반면, 시험 형상함수로서 델라우니 삼각형이 지지영역이 되는 함수를 새롭게 정의한다. 이러한 접근은 통상적인 적분영역과 적분함수 지지영역간의 불일치를 제거하게 하며, 이는 적용이 편리할 뿐만 아니라 수치적분의 정확성을 보장한다 본 논문에서는 2차윈 선형 탄성의 대표적인 검증문제를 통하여 제안된 방법의 타당성을 검증한다. 비교를 위해 기존의 부브노프-갤러킨 자연요소법과 일정 변형률 유한요소법을 이용한 해석을 동시에 수행한다. 조각 시험과 수렴율 평가를 통해 제안된 기법의 우수성을 확인할 수 있다.

• Structural Engineering and Mechanics
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• 제70권3호
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• pp.279-287
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• 2019

This paper intends to introduce a near-tip grid refinement and to explore its usefulness in the crack analysis by the natural element method (NEM). As a sort of local h-refinement in FEM, a NEM grid is locally refined around the crack tip showing the high stress singularity. This local grid refinement is completed in two steps in which grid points are added and Delaunay triangles sharing the crack tip node are divided. A plane-state plate with symmetric edge cracks is simulated to validate the proposed local grid refinement and to examine its usefulness in the crack analysis. The crack analysis is also simulated using a uniform NEM grid for the sake of comparison. The near-tip stress distributions and SIFs that are obtained using a near-tip refined NEM grid are compared with the exact values and those obtained using uniform NEM grid. The convergence rates of global relative error to the total number of grid points between the refined and non-refined NEM grids are also compared.

• Structural Engineering and Mechanics
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• 제76권4호
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• pp.505-512
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• 2020

This paper presents an error estimation technique for 2-D crack analysis by an enriched natural element (more exactly, enriched Petrov-Galerkin NEM). A bare solution was approximated by PG-NEM using Laplace interpolation functions. Meanwhile, an accurate quasi-exact solution was obtained by a combined use of enriched PG-NEM and the global patch recovery. The Laplace interpolation functions are enriched with the near-tip singular fields, and the approximate solution obtained by enriched PG-NEM was enhanced by the global patch recovery. The quantitative error amount is measured in terms of the energy norm, and the accuracy (i.e., the effective index) of the proposed method was evaluated using the errors which obtained by FEM using a very fine mesh. The error distribution was investigated by calculating the local element-wise errors, from which it has been found that the relative high errors occurs in the vicinity of crack tip. The differences between the enriched and non-enriched PG-NEMs have been investigated from the effective index, the error distribution, and the convergence rate. From the comparison, it has been justified that the enriched PG-NEM provides much more accurate error information than the non-enriched PG-NEM.

• Structural Engineering and Mechanics
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• 제84권6호
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• pp.723-731
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• 2022

Functionally graded materials (FGMs) have been spotlighted as an advanced composite material, accordingly the intensive studies have focused on FGMs to examine their mechanical behaviors. Among them is thermal buckling which has been a challenging subject, because its behavior is connected directly to the safety of structural system. In this context, this paper presents the numerical analysis of thermal buckling of metal-ceramic functionally graded (FG) plates. For an accurate and effective buckling analysis, a new numerical method is developed by making use of (1,1,0) hierarchical model and 2-D natural element method (NEM). Based on 3-D elasticity theory, the displacement field is expressed by a product of 1-D assumed thickness monomials and 2-D in-plane functions which are approximated by NEM. The numerical method is compared with the reference solutions through the benchmark test, from which its numerical accuracy has been verified. Using the developed numerical method, the critical buckling temperatures of metal-ceramic FG plates are parametrically investigated with respect to the major design parameters.

• Steel and Composite Structures
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• 제31권1호
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• pp.43-51
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• 2019

This paper is concerned with the numerical calculation of mixed-mode stress intensity factors (SIFs) of 2-D isotropic functionally graded materials (FGMs) by the natural element method (more exactly, Petrov-Galerkin NEM). The spatial variation of elastic modulus in non-homogeneous FGMs is reflected into the modified interaction integral ${\tilde{M}}^{(1,2)}$. The local NEM grid near the crack tip is refined, and the directly approximated strain and stress fields by PG-NEM are enhanced and smoothened by the patch recovery technique. Two numerical examples with the exponentially varying elastic modulus are taken to illustrate the proposed method. The mixed-mode SIFs are parametrically computed with respect to the exponent index in the elastic modulus and external loading and the crack angle and compared with the other reported results. It has been justified from the numerical results that the present method successfully and accurately calculates the mixed-mode stress intensity factors of 2-D non-homogeneous functionally graded materials.

• Steel and Composite Structures
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• 제44권2호
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• pp.171-181
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• 2022

Functionally graded material (FGM) has been spotlighted as an advanced composite material due to its excellent thermo-mechanical performance. And the buckling of FGM resting on elastic foundations has been a challenging subject because its behavior is directly connected to the structural safety. In this context, this paper is concerned with a numerical buckling analysis of metal-ceramic FG plates resting on a two-parameter (Pasternak-type) elastic foundation. The buckling problem is formulated based on the neutral surface and the (1,1,0) hierarchical model, and it is numerically approximated by 2-D natural element method (NEM) which provides a high accuracy even for coarse grid. The derived eigenvalue equations are solved by employing Lanczos and Jacobi algorithms. The numerical results are compared with the reference solutions through the benchmark test, from which the reliability of present numerical method has been verified. Using the developed numerical method, the critical buckling loads of metal-ceramic FG plates are parametrically investigated with respect to the major design parameters.