• 대한기계학회논문집A
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• 제21권6호
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• pp.925-932
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• 1997

Two shear-flexible curved axisymmetric shell elements with two nodes, LCCS(linear curvature and constant strain) and CCCS(constant curvature and constant strain) are designed based on the assumed meridional strain fields and shallow shell geometry. At the element level, meridional curvature, membrane strain and shear strain fields are assumed by using polynomials and the displacement fields are obtained by integrating the assumed strain fields along the shallowly curved meridian. The formulated elements have high order displacement fields consistent with the strain field. Several test problems are given to demonstrate the performance of the two elements. Analysis results obtained reveal that the elements are very accurate in the displacement and the stress predictions.

• Structural Engineering and Mechanics
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• 제13권4호
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• pp.387-410
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• 2002

Formulation of an 8 nodes assumed strain shell element is presented for the analysis of shells. The stiffness matrix based on the Mindlin-Reissner theory is analytically integrated through the thickness. The element is free of membrane and shear locking behavior by using the assumed strain method such that the element performs very well in modeling of thin shell structures. The material is assumed to be isotropic and laminated composite. The element has six degrees of freedom per node and can model the stiffened plates and shells. A great number of numerical testing carried out for the validation of present 8 node shell element are in good agreement with references.

• 대한기계학회논문집A
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• 제23권7호
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• pp.1205-1214
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• 1999

A new quadrilateral plane stress element is developed for efficient and accurate analysis of thermal stress problems. It is convenient to use the same mesh and the same shape functions for thermal analysis and stress analysis. But, because of the inconsistency between deformation related strain field and thermal strain field, oscillatory responses and considerable errors in stresses are resulted in. To avoid undesired oscillations, strain approximation is enhanced by supplementing several assumed strain terms based on the variational principle. Thermal deformation is incorporated into the generalized mixed variational principle for displacement, strain and stress fields, and basic equations for the modified enhanced assumed strain method are derived. For the stress approximation of bilinear elements, the $5{\beta}$ version of Pian and Sumihara is adopted. The numerical results for several problems show that the present element behaves well and reduces oscillatory responses. it also results in almost the same magnitude of error as compared with the quadratic element.

• Structural Engineering and Mechanics
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• 제18권5호
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• pp.671-690
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• 2004

An assumed strain finite strip method(FSM) using the non-periodic B-spline for a shell is presented. In the present method, the shape function based on the non-periodic B-splines satisfies the Kronecker delta properties at the boundaries and allows to introduce interior supports in much the same way as in a conventional finite element formulation. In the formulation for a shell, the geometry of the shell is defined by non-periodic B3-splines without any tangential vectors at the ends and the penalty function method is used to incorporate the drilling degrees of freedom. In this study, new assumed strain fields using the non-periodic B-spline function are proposed to overcome the locking problems. The strip formulated in this way does not posses any spurious zero energy modes. The versatility and accuracy of the new approach are demonstrated through a series of numerical examples.

• Structural Engineering and Mechanics
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• 제37권2호
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• pp.253-256
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• 2011

• Structural Engineering and Mechanics
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• 제2권1호
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• pp.17-34
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• 1994

This paper proposes a new four node degenerated shell element. In the formulation of the new element, the assumed covariant shear strains are used to avoid the shear locking problem, and the assumed covariant membrane strains are applied to alleviate the membrane locking problem and also to improve the membrane bending performance. The assumed covariant strains are obtained from the covariant strain field defined with respect to the element natural coordinate system. This formulation enables us to obtain a shell element, which does not produce spurious singular modes, avoids locking phenomena, and excels in calculation efficiency. Several examples in this paper indicate that, despite its simplicity, the achieved accuracy and convergence are satisfactory.

• Structural Engineering and Mechanics
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• 제15권2호
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• pp.199-223
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• 2003

The formulation of a non-linear shear deformable shell element is presented for the solution of stability problems of stiffened plates and shells. The formulation of the geometrical stiffness presented here is exactly defined on the midsurface and is efficient for analyzing stability problems of thick plates and shells by incorporating bending moment and transverse shear resultant force. As a result of the explicit integration of the tangent stiffness matrix, this formulation is computationally very efficient in incremental nonlinear analysis. The element is free of both membrane and shear locking behaviour by using the assumed strain method such that the element performs very well in the thin shells. By using six degrees of freedom per node, the present element can model stiffened plate and shell structures. The formulation includes large displacement effects and elasto-plastic material behaviour. The material is assumed to be isotropic and elasto-plastic obeying Von Mises's yield condition and its associated flow rules. The results showed good agreement with references and computational efficiency.

• 한국전산구조공학회논문집
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• 제20권3호
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• pp.353-364
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• 2007

이 논문에서는 원전 격납건물의 극한내압능력 및 파괴모드 평가를 위해 개발된 비선형 유한요소해석 프로그램 NUCAS 코드에 대하여 기술하였다. NUCAS는 미시적인 재료모델을 도입한 퇴화 쉘 요소와 탄소성 재료모델을 도입한 저차고체요소로 구성되어 있고, 퇴화 쉘 요소와 저차고체요소는 유한요소에서 발생할 수 있는 강성과대(overstiffness) 및 묶임현상(locking phenomenon)을 방지하기 위해서 각각 가변형도법(assumed strain method)과 개선된 가변형도법(enhanced assumed strain method)을 적용하였다. 개발된 NUCAS코드의 성능을 검증하기 위해서 다양한 철근콘크리트 구조물의 벤치마크 테스트를 수행하였고, 그 결과로부터 이 논문에서 개발한 유한요소해석 프로그램의 해석결과는 실험결과와 잘 일치하였다.

• Structural Engineering and Mechanics
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• 제17권1호
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• pp.113-140
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• 2004

A mixed eight-node hexahedral element formulated via the Hu-Washizu principle as well as the field extrapolation technique is presented. The mixed element with only three translational degrees of freedom at each node can provide extremely accurate and reliable performance for popular benchmark problems such as spacial beams, plates, shells as well as general three-dimensional elasticity problems. Numerical calculations also show that when extremely skewed and coarse meshes and nearly incompressible materials are used, the proposed mixed element can still possess excellent behaviour. The mixed formulation starts with introduction of a parallelepiped domain associated with the given general eight-node hexahedral element. Then, the assumed strain field at the nodal level is constructed via the Hu-Washizu variational principle for that associated parallelepiped domain. Finally, the assumed strain field at the nodal level of the given hexahedral element is established by using the field extrapolation technique, and then by using the trilinear shape functions the assumed strain field of the whole element domain is obtained. All matrices involved in establishing the element stiffness matrix can be evaluated analytically and expressed explicitly; however, a 24 by 24 matrix has to be inverted to construct the displacement extrapolation matrix. The proposed hexahedral element satisfies the patch test as long as the element with a shape of parallelepiped.

• 한국항공우주학회지
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• 제30권2호
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• pp.67-74
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• 2002

본 논문에서는 18절점 가정 변형률 솔리드 요소를 이용하여, 기계적 물리량과 전기적 물리량이 완전히 연성된 정적 문제를 해석할 수 있는 유한요소 정식화 과정을 유도하였다. 요소 결점의 축방향 변위 자유도 외에 전기 자유도를 추가하여 주어진 변위와 하중에 의해 발생하는 유도전압을 계산할 수 있다. 또한 가정 변형률 요소를 사용함으로써 박판형 구조물을 모델할 때 발생할 수 있는 잠김현상을 해소하였다. 유도된 유한요소 정식을 바탕으로 프로그램을 작성하였으며, 몇가지 수치예제에 적용하여 작성된 코드를 검증하였다. 본 요소를 이용하여, 여러 가지 변수가 THUNDER의 작동변위에 미치는 영향을 분석하였다. 이를 통하여, 특정한 재료와 곡률을 갖출 경우 THUNDER의 작동성능이 향상됨을 확인하였다.