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Mixed State-Vector Finite Element Analysis for a Higher-Order Box Beam Theory
장강원(Gang-Won Jang),김윤영(Yoon Young Kim) 대한기계학회 2005 대한기계학회 춘추학술대회 Vol.2005 No.11
If thin-walled closed beams are analyzed by the standard Timoshenko beam elements, their structural behavior, especially near boundaries, cannot be accurately predicted because of the incapability of the Timoskenko theory to predict the sectional warping and distortional deformations. If a higher-order thin-walled box beam theory is used, on the other hand, accurate results comparable to those obtained by plate finite elements can be obtained. However, currently available two-node displacement based higher-order beam elements are not efficient in capturing exponential solution behavior near boundaries. Based on this motivation, we consider developing higher-order mixed finite elements. Instead of using the standard mixed formulation, we propose to develop the mixed formulation based on the state-vector form so that only the field variables that can be prescribed on the boundary are interpolated for finite element analysis. By this formulation, less field variables are used than by the standard mixed formulation, and the interpolated field variables have the physical meaning as the boundary work conjugates. To facilitate the discretization, two-node elements are considered. The effects of interpolation orders for the generalized stresses and displacements on the solution behavior are investigated along with a numerical example.
고차 박판보 해석을 이용한 직사각단면 박판보 조인트 구조물 해석
장강원(Gang-Won Jang),최수민(Soomin Choi),김윤영(Yoon Young Kim) 대한기계학회 2011 대한기계학회 춘추학술대회 Vol.2011 No.4
세 개의 직사각 단면 박판보가 하나의 조인트에서 맞물리는 구조물을 고차 박판보 이론에 기반하여 해석을 수행한다. 워핑, 디스토선을 포함하는 일차원 변위들 간의 연성효과를 조인트의 공유 모서리들에서 삼차원 변위의 연속성을 고려함으로써 이끌어 낼 수 있다. 제안한 고차 박판보 이론 기반의 조인트 변위 관계식을 사용할 경우 예측한 조인트 유연성 효과는 조인트 구조물을 삼차원 쉘 요소로 상세 모델링할 경우와 거의 비슷한 결과를 얻을 수 있다. 세 개의 박판보가 등각으로 맞물리는 조인트 구조물이 평면의 정적 굽힘을 받는 예제를 살펴봄으로써 제안한 이론의 정확성을 검증하도록 한다. A three-beam-jo int structure which consists of thin-walled beams with a rectangular cross-section is analyzed based on a higher order thin-walled beam theory. Coupling effect among one-dimensional deformation measures including warping and distortion is found by considering continuity condition on shared edges of joints. Joint flexibility effect which is observed when the joint structure is modeled by using full three-dimensional shell elements can be accurately calculated by applying the proposed joint match condition for a higher order beam theory. Static analysis results for a three-beam-joint structure with equal joint angles show the effectiveness of the proposed approach.