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Geometrically nonlinear dynamic formulation for three-dimensional co-rotational solid elements
Cho, Haeseong,Kim, Haedong,Shin, SangJoon Elsevier 2018 Computer methods in applied mechanics and engineer Vol.328 No.-
<P><B>Abstract</B></P> <P>This study presents a three-dimensional nonlinear dynamic formulation based on a co-rotational (CR) approach for solid elements. The CR formulation is relatively efficient, but it is based on the assumption of small strains during large displacement. The novel idea of the present formulation involves the use of the CR formulation through a three-dimensional solid element for inertial quantities in addition to an internal force vector and a stiffness matrix. The present dynamic formulation is derived from Lagrange’s equation of motion. In this procedure, the CR formulation, (i.e., element-independent CR) is one of the most attractive features that is strongly manifested in an efficient manner. Consequently, this obtains the governing equation of motion including motion-driven inertial components (physical quantities induced by the prescribed motion). Four examples are presented to demonstrate the accuracy of the present dynamic formulation. Finally, the results are compared with those obtained by ABAQUS, and the findings reveal that the proposed dynamic formulation is in good agreement with existing predictions.</P>
Co-rotational 비선형 정식화 및 FETI-local 기법을 결합한 비선형 대용량/다물체 구조 해석 알고리듬 개발
조해성(Haeseong Cho),주현식(HyunShig Joo),이영헌(Younghun Lee),곽민철(Min-cheol Gwak),신상준(SangJoon Shin),여재익(Jack J. Yoh) 한국항공우주학회 2016 韓國航空宇宙學會誌 Vol.44 No.9
본 논문에서는 비선형 다물체 동역학 해석에 적용 가능한 구조해석을 개발하였다. 비선형 구조 해석을 위해 Co-rotational 이론 기반의 유한요소를 개발하였다. 그리고 국부 Lagrange 승수를 활용한 영역분할해석 기법을 적용하여 대용량/다물체 해석이 가능한 구조해석 알고리듬을 개발하였다. 기 개발한 구조 해석은 외팔보 및 다물체 구조에 대한 비선형 정적 해석예제에 적용하였다. 병렬 계산에 따른 성능 평가는 희박행렬 계산 라이브러리인 PARDISO와 비교하였다. 이를 통해 기 개발 구조해석의 계산 속도 향상을 확인하였다. In this paper, a computational algorithm of an improved and versatile structural analysis applicable for large-size flexible nonlinear structures is developed . In more detail, nonlinear finite element based on the co-rotational (CR) framework is developed. Then, a finite element tearing and interconnecting method using local Lagrange multipliers (FETI-local) is combined with the nonlinear CR finite element. The resulting computational algorithm is presented and applied for nonlinear static analyses, i.e., cantilevered beam and multibody structure. Finally, the proposed analysis is evaluated with regard to its parallel computation performance, and it is compared with those obtained by serial computation using the sparse matrix linear solver, PARDISO.