• Steel and Composite Structures
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• 제29권6호
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• pp.785-802
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• 2018

In this paper, two different computational methods, called Rayleigh-Ritz and collocation are developed to estimate the ultimate strength of composite plates. Progressive damage behavior of moderately thick composite laminated plates is studied under in-plane compressive load and uniform lateral pressure. The formulations of both methods are based on the concept of the principle of minimum potential energy. First order shear deformation theory and the assumption of large deflections are used to develop the equilibrium equations of laminated plates. Therefore, Newton-Raphson technique will be used to solve the obtained system of nonlinear algebraic equations. In Rayleigh-Ritz method, two degradation models called complete and region degradation models are used to estimate the degradation zone around the failure location. In the second method, a new energy based collocation technique is introduced in which the domain of the plate is discretized into the Legendre-Gauss-Lobatto points. In this new method, in addition to the two previous models, the new model named node degradation model will also be used in which the material properties of the area just around the failed node are reduced. To predict the failure location, Hashin failure criteria have been used and the corresponding material properties of the failed zone are reduced instantaneously. Approximation of the displacement fields is performed by suitable harmonic functions in the Rayleigh-Ritz method and by Legendre basis functions (LBFs) in the second method. Finally, the results will be calculated and discussions will be conducted on the methods.

• Structural Engineering and Mechanics
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• 제29권2호
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• pp.117-134
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• 2008

A new adaptive dual reciprocity boundary element method for dynamic analysis of 3-D structures is presented in this paper. It is based on finding the best approximation function of a radial basis function (RBF) group $f=r^n+c$ which minimize the error of displacement field expansion. Also, the effects of some parameters such as the existence of internal points, number of RBF functions and position of collocation nodes in discontinuous elements are investigated in this adaptive procedure. Three numerical examples show improvement in dynamic response of structures with adaptive RBF in dual reciprocity with respect to ordinary BEM.

• 한국전산구조공학회논문집
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• 제22권1호
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• pp.117-124
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• 2009

2차원 포텐셜 문제를 해석하기 위해 고차의 르장드르 형상함수에 기초를 둔 p-수렴 경계요소법이 제안되었다. p-수렴 경계요소법은 종래의 경계요소법에서 사용되는 형상함수와 성질이 다른 르장드르 다항식을 형상함수로 사용한다. p-수렴 유한요소법과 마찬가지로 고차의 형상함수에 따른 절점의 위치가 경계상에서 정해지지 않는다. 따라서 형상함수가 증가함에 따라 선형방정식을 구성하기 위한 수단으로 선점법을 이용하였다. p-수렴 경계요소법에서 선점법은 비대칭 계층적 선점법과 대칭 비계층적 선점법을 선택하여 수치해석을 수행하였다. 선택점들은 형상함수가 증가함에 따라 증가하는 성질을 나타내며 계층적 또는 대칭적으로 선택될 수 있다. p-수렴 경계요소법에서 나타나는 특이 적분항을 계산하기 위해 special numeric quadrature technique와 semi-analytical integration technique를 사용하였다. 사각모서리부에서 특이성을 가지는 L-형 영역문제를 해석한 결과 적은 수의 자유도에서 기존문헌의 결과와 차이가 거의 없는 정도인 $10^{-2}%$단위 이하의 정확도를 보여주었다. 또한 같은 조건에서는 대칭형 선점의 위치를 이용해 계산한 값이 가장 높은 정확도를 보여주었다.

• International Journal of Aeronautical and Space Sciences
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• 제15권2호
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• pp.183-189
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• 2014

Pseudo-spectral method typically converges at an exponential rate. However, it requires a special set of fixed collocation points (CPs) to get highly accurate formulas for partial integration and differentiation. In this study, computational nodes for defining the discrete variables of states and controls are built independently of the CPs. The state and control variables at each CP, which are required to transcribe an NOCP into the corresponding NLP, are interpolated, using those variables allocated at each node. Additionally, Lagrange interpolation and spline interpolation are investigated, to provide a guideline for selecting a favorable interpolation method. The proposed techniques are applied to the solution of an NOCP using equally spaced nodes, and the computed results are compared to those using the standard PS approach, to validate the usefulness of the proposed methods.

• 한국수학사학회지
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• 제18권4호
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• pp.49-66
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• 2005

유한요소법(Finite Element Methods)은 지난 수십 년 동안 다양한 공학문제를 해석하는 주요 수치해석기법으로서, 지속적으로 연구$\cdot$개발되어 오늘에 이르고 있다. 그러나, 유한요소법은 계산을 위하여 요소망을 구성해야 하고 일부의 문제에 대하여서는 요소망을 재구성하는 등 특별한 처리기법과 계산의 소요가 필요하다. 이와같은 단점을 극복하기 위하여 무요소법(Meshfree Methods)이라 불리우는 일단의 수치해석 기법들이 고안되었다. 무요소법은 요소를 사용하지 않고 절점(node)만을 이용하여 함수를 근사하는 수치해석기법이다. 본 논문에서는 무요소법이 고안된 배경과 그 연산구조를 소개하고 무요소법의 대표적인 방법들인 Smoothed Particle Hydrodynamics(SPH)방법, 무요소 갤러킨 방법(Meshfree Galerkin Methods) 그리고 무요소 선점법(Meshfree Point Collocation Methods)의 기본 개념과 이들 수치해석기법의 방법론을 알아본다. 그리고 이들 방법의 장단점과 그 적용 예를 통하여 무요소 계산법의 유효함을 보인다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.740-745
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• 2003

The so-called boundary node method (or NDIF method) that was developed by the authors has been extended for free vibration analysis of arbitrarily shaped plates with free edges. Since the proposed method is based on the collocation method, no integration procedure is needed on boundary edges of the plates and only a small amount of numerical calculation is required. A special coordinate transformation has been devised to consider the complicated free boundary conditions at boundary nodes. By the use of the special coordinate transformation, the radius of curvature involved in the free boundary conditions can be successfully dealt with. Finally, verification examples show that natural frequencies obtained by the present method agree well with those given by exact method and other analytical methods.

• 한국소음진동공학회논문집
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• 제18권6호
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• pp.674-680
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• 2008

A new meshless method for obtaining natural frequencies of arbitrarily shaped plates with the free boundary condition is introduced in the paper. In order to improve the characteristics of convergence and accuracy of the method, a special local polar coordinates system is devised and located for each of nodes distributed along the boundary of the plate of interest. In addition, a new way of decreasing the size of the system matrix that gives natural frequencies of the plate is employed to reduce the amount of numerical calculations, which is needed for computing the determinant of the system matrix. Finally the excellence of the characteristics of convergence and accuracy of the method is shown in several case studies, which indicate that natural frequencies by the proposed method are very accurate and converged swiftly to exact values as the number of boundary nodes increases.