• Journal of Korean Association for Spatial Structures
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• v.8 no.4
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• pp.81-90
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• 2008

This paper presents a finite element formulation for the three-dimensional hierarchical solid element using Integrals of Legendre polynomials. The proposed hexahedral solid element is composed of four different modes including vertex, edge, face, and internal mode, respectively. The eigenvalue and patch test have been carried out to confirm the zero-energy mode and constant strain condition. In addition to these, a posteriori error estimation has been studied for the p-adaptive finite element analysis that is based on a smoothing technique to compute a post-processed solution from the finite element solution. The uniform p-refinement and non-uniform p-refinement are compared in terms of convergence rate as the number of degree of freedom is increased. The simple cantilever beam is tested to show the performance of the proposed solid element.

• Computational Structural Engineering
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• v.6 no.4
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• pp.107-118
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• 1993

New methods of visualizing the data from finite element analyses of 3-dimensional solids were developed in this study. Their efficiency and practicality were examined through their application and implementation into a finite element analysis software. The major effort of the study was to provide a way of representing data inside of volume, which is the most difficult problem in the postprocessing of 3-dimensional solids. Section representation, volume slice and separation, and isosurface representation were proposed for this purpose.

• Journal of Power System Engineering
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• v.16 no.1
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• pp.78-83
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• 2012

The authors suggest the algorithm for the static analysis of a three dimensional solid structure by using the finite element-transfer stiffness coefficient method (FE-TSCM) and the hexahedral element of the finite element method (FEM). MATLAB codes were made by both FE-TSCM and FEM for the static analysis of three dimensional solid structure. They were applied to the static analyses of a very thick plate structure and a three dimensional solid structure. In this paper, as we compare the results of FE-TSCM with those of FEM, we confirm that FE-TSCM introducing the hexahedral element for the static analysis of a three dimensional solid structure is very effective from the viewpoint of the computational accuracy, speed, and storage.

• Journal of Ocean Engineering and Technology
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• v.12 no.2 s.28
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• pp.1-21
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• 1998

In this paper, a non-conforming 3-D 8-node solid element(MQM10) has beets applied to the analyses of static and dynamic bending problems of laminated composite plates The QM10 element exhibits stiffer bending stiffness which is caused by the reduction of degree of freedom from Q11 element. As an effective way to correct the relative stiffness stiffening phenomenon the modification of Gauss sampling points for composite plates is proposed. The quantity of modification is a function of material properties. Also, another two modified equations are obtained, one is modification for stress, and the other is modification of coefficient of shear modulus in free vibration. It is noted that MQM10 element can analyse the static and free vibration problems of various 3-dimensional composite plates composed of unidirectional laminae, woven laminae or braided laminae. The results of MQM10 element are in good agreement with those of 20-node element.

• Computational Structural Engineering
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• v.10 no.4
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• pp.117-130
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• 1997

In this paper, a modified 10-node equivalent solid element(MQM10 element), which has smallest degrees of freedom among 3-dimensional solid elements accounting bending deformation as well as extensional and shear deformations of isotropic plates, is proposed. The proposed MQM10 element exhibits stiffer bending stiffness due to the reduction of degrees of freedom from 20-node element or Q11 element. As an effective way to correct the relative stiffness stiffening phenomenon, the modification equation of Gauss sampling points is proposed. The quantity of modification is a function of Poisson's ratio. The effectiveness of MQM10 element is tested by applying it to several examples. It is noted that the results of static and free vibration analysis of isotropic plates using MQM10 elements show a good agreement with those using 20-node element.

• Magazine of the Korea Concrete Institute
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• v.8 no.2
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• pp.119-127
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• 1996

Objection of this study is to present the three-dimensional material nonlinear analysis of reinforced concrete. A concrete is idealized with three-dimensional 16-node solid element including triaxial nonlinear stress-strain behavior, cracking, crushing and strain softening: a steel with three-dimensional 3 node truss element including elastic-plastic behavior with strain hardening. The cracked shear retention factor is introduced to estimate the effective shear modulus con sidering aggregate interlock after c:racking and a modified newton method is used to obtain a nu merical solution. Numerical results in a gauss point is displayed graphically. Numerical examples of Krahl's reinforced concrete beam and Hedgreds shell are selected to compare with the experimental and numerical results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.04a
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• pp.9-16
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• 1995

A new three-dimensional transition solid element with drilling degrees of freedom is presented. The proposed transition element is established by adding variable nodes to a basic 8-node element for an effective connection between the refined region and the coarse. The derivation of the element in this paper is based on the variational principles in which the drilling rotations are introduced as independent variables. This element was also improved through the addition of modified non-conforming modes. Numerical examples show that performance of the element and the applicability to 3D adaptations are satisfactory.

• Journal of the KSME
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• v.17 no.1
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• pp.40-44
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• 1977

먼저번에는(대한기계학회지 제16권 제4호 1976) 유한요소법의 중심부를 통하는 기본로선을 따라 가면서 기초 개념을 해설하였다. 이 해설에서 앞으로 취급될 사항은 다음과 같다. 1. 트러스 구조물의 정역학적 문제를 예제로 다루며 방향변환에 따르는 "변환매트릭스"해설 2. 기둥의 탄성 안정 문제를 예제로 다루며 비 선형 문제에서 등장하는 "추가 강성매트 릭스 (Incremental Stiffness Matrix)[N]의 해설 3. 1차원 문제에 있어서의 여러 가지 유한요소 해설 4. 2차원 문제에 있어서 평면형을 갖는 여러 가지 유한요소 해설 5. 2차원 문제에 있어서 곡면형을 갖는 여러 가지 유한요소 해설 6. 유한요소법의 발전 전망 7. 전자계산기 프로그래밍에 있어서의 여러문제 해설의 대상자는 공과대학 기계계열의 상급학년 학생 또는 고체역학 부문에 경력을 갖는 기술자 들로서 이 부문의 기본지식을 갖고 있는 자로 한다. 이번회에는 유한요소의 자유도 즉 미지상 수로 다루어지는 자변수의 좌표축이 바뀔 때 부수적으로 등장하는 변환 매트릭스에 대하여 해 설한다.트릭스에 대하여 해 설한다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2010.04a
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• pp.314-317
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• 2010

본 논문에서는 p-수렴 천이요소의 층별이론을 사용하여 균열을 갖는 적층판의 팻취보강 효과에 대해 알아보았다. 이 모델의 면내 변위는 각 구간별로 연속인 선형변화로 가정하였고, 두께방향으로의 면외 변위는 일정한 상수로 가정하여 적용하였다. 변위장의 정의는 적분형 르장드로 다항식을 적용하였다. 또한 에너지 방출률법과 VCCT 방법을 사용하여 응력확대계수를 산출하였다. 수치적분은 별도의 외삽법 없이 각층별의 절점에서 방생하는 적분 값을 바로 얻을 수 있는 가우스-로바토 적분법을 사용하여 계산하였으며, 수치예제를 통해 제안된 모델의 정확도와 기존의 3차원 고체요소를 사용한 것보다 동일한 정확도를 얻기 위해 휠씬 적은 요소 및 자유도가 사용됨을 알 수 있었다.

• Computational Structural Engineering
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• v.8 no.4
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• pp.87-97
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• 1995

For the same configuration of two-dimensional finite element models, 6-node element exhibits stiffer bending stiffness than 8-node element. This is true in the relation between 16-node element and 20-node element for three-dimensional model. This stiffening phenomenon comes from the elimination of several mid nodes from full-node elements. Therefore, this may be called 'relative stiffness stiffening phenomenon'. It seems that there are a couple of ways to correct the stiffening effect, however, we could find only one effective method-the method of modification of Gauss sampling points-which passes the patch test and does not alter other kinds of stiffness, such as extensional stiffness. The quantity of modification is a function of Poisson's ratios of the constituent materials. We could obtain two modification equations, one for plane stress case and the other for plane strain case. This method can be extended to 3-dimensional solid elements. Except the exact plane strain cases, most 3-dimensional plates could be modeled successfully with 16-node element modified by the equation for the plane stress case. The effectiveness of the modification method is checked by applying it to several examples with excellent improvements. In numerical examples, beams with various boundary conditions are subjected to static and time-dependent loads. Free and forced motion analyses of beams and plates are also tested. The beam and plate may be composed of isotropic multilayers as well as a single layer.