Formulation Method for Solid-to-Beam Transition Finite Elements

임장권,송대한,송병호,Im, Jang-Gwon,Song, Dae-Han,Song, Byeong-Ho 대한기계학회 2001 KSME International Journal Vol.15 No.11

Various transition elements are used in general for the effective finite element analysis of complicated mechanical structures. In this paper, a solid-to-beam transition finite element, which can b e used for connecting a C1-continuity beam element to a continuum solid element, is proposed. The shape functions of the transition finite element are derived to meet the compatibility condition, and a transition element equation is formulated by the conventional finite element procedure. In order to show the effectiveness and convergence characteristics of the proposed transition element, numerical tests are performed for various examples. As a result of this study, following conclusions are obtained. (1) The proposed transition element, which meets the compatibility of the primary variables, exhibits excellent accuracy. (2) In case of using the proposed transition element, the number of nodes in the finite element model may be considerably reduced and the model construction becomes more convenient. (3) This formulation method can be applied to the usage of higher order elements.

Spectral element modeling and analysis of the transverse vibration of a laminated composite plate

Park, Ilwook,Lee, Usik Elsevier 2015 COMPOSITE STRUCTURES -BARKING THEN OXFORD- Vol.134 No.-

<P><B>Abstract</B></P> <P>This paper presents a frequency-domain spectral element model for the symmetric laminated composite plates which have finite dimensions in two orthogonal directions, i.e., in the <I>x</I>- and <I>y</I>-directions. The spectral element model is developed by using two methods in combination: the splitting of original boundary conditions and the so-called super spectral element method in which both the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are utilized. The present spectral element model has nodes (or degrees of freedom (DOFs)) only on four edges of a finite element, i.e., no nodes inside the finite element. Accordingly the total number of DOFs used in the dynamic analysis can be drastically decreased to lead to a significant decrease of the computation cost, when compared with the standard finite element method (FEM). The high accuracy of the present spectral element model is verified in due course by the comparison with the results by two solution methods: the exact theory available in the literature and the standard finite element model developed in this study.</P>

Adaptive Finite Element Mesh Generation for Dynamic Planar Problems

윤종열 한국방재학회 2012 한국방재학회논문집 Vol.12 No.6

In structural design and analysis used for hazard mitigation systems, automation is becoming an essential feature. For analysis,the finite element method has proven to be an effective approximate method if proper element types and meshes are chosen. Recently, the method has been successfully applied to solve complex dynamic and nonlinear problems; and with a properly chosen element type and mesh, reliable results have been obtained. However, in automation and in complex analyses of a structures,using the initial mesh throughout the analysis may involve some elements to go through strains beyond the elements' reliable limits. Thus, the finite element mesh for these types of analyses must be dynamically adaptive, and considering the rapid process of analysis in real time, the dynamically adaptive finite element mesh generating schemes must be computationally efficient. In this paper, a computationally efficient dynamically adaptive finite element mesh generation scheme for dynamic analyses of planar problems is described. The concept of representative strain value is used for error estimates and the refinements of meshes use combinations of the h-method (node movement) and the r-method (element division). A coefficient that depends on shape of elements is used to correct overly distorted elements. The validity of the scheme is shown by a deep cantilever beam example under a dynamic concentrated load. The example shows reasonable accuracy and efficient computing time. Furthermore, the study shows the potential for the scheme's effective use in complex structural problems such as those under severe environmental hazards such as seismic or erratic wind loads.

An efficient contact algorithm for the interaction of material particles with finite elements

Cheon, Young-Jo,Kim, Hyun-Gyu Elsevier 2018 Computer methods in applied mechanics and engineer Vol.335 No.-

<P><B>Abstract</B></P> <P>In this paper, we propose an efficient contact algorithm to analyze the interaction of material particles with finite elements. The contact forces between material particles and finite elements are computed at the (background) grid nodes in material point method, and transferred to finite element nodes. A weighted average method is used to obtain the velocities at grid nodes contributed from finite element nodes, and a cut-off weight is applied to the contact condition to avoid an early contact occurring in a grid-based contact algorithm. A severe penetration of material particles into finite elements when the finite element mesh is coarser than the background grid can be prevented by introducing distributed interaction (DI) nodes on the contact faces of finite elements. Numerical examples show the effectiveness of the present method to treat the contact interaction between material particles and finite elements.</P>

Time-varying meshing stiffness calculation of an internal gear pair with small tooth number difference by considering the multi-tooth contact problem

Guangjian Wang,Qing Luo,Shuaidong Zou 대한기계학회 2021 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.35 No.9

Due to the multiple tooth contact problem involving internal gear pair with small tooth number difference (IGPSTND), the existing analytical methods applied for standard spur or helix gear pairs to calculate the time-varying meshing stiffness (TVMS) are not suitable. In this paper, two methods are proposed for calculating the time-varying meshing stiffness in internal gear pairs with small tooth difference. In the first method, an analytical model is established by using the potential energy method, considering the clearance of initial contact tooth and the external load. The second method proposes the application of a hybrid finite elementanalytical method. The proposed two methods are validated by the application of the finite element method. By taking the results of finite element analysis as a comparative reference, the results show that the finite element - analytical method is closer to the reference results than the results obtained by the analytical method, and both methods are less computationally expensive than finite element analysis.

Sound transmission analysis of plate structures using the finite element method and elementary radiator approach with radiator error index

Jung, Jaesoon,Kook, Junghwan,Goo, Seongyeol,Wang, Semyung Elsevier 2017 Advances in engineering software Vol.112 No.-

<P><B>Abstract</B></P> <P>In this paper, an accurate and efficient numerical method for sound transmission analysis is presented. As an alternative to conventional numerical methods, such as the Finite Element Method (FEM), Boundary Element Method (BEM) and Statistical Energy Analysis (SEA), the FE-ERA method, which combines the FEM and Elementary Radiator Approach (ERA) is proposed. The FE-ERA method analyzes the vibrational response of the plate structure excited by incident sound using FEM and then computes the transmitted acoustic pressure from the vibrating plate using ERA. In order to improve the accuracy and efficiency of the FE-ERA method, a novel criterion for the optimal number of elementary radiators is proposed. The criterion is based on the radiator error index that is derived to estimate the accuracy of the computation with used number of radiators. Using the proposed criterion a radiator selection method is presented for determining the optimum number of radiators. The presented radiator selection method and the FE-ERA method are combined to improve the computational accuracy and efficiency. Several numerical examples that have been rarely addressed in previous studies, are presented with the proposed method. The accuracy and efficiency of the proposed method are validated by comparison with the results of the three dimensional (3D) FEM structure-acoustic interaction models.</P> <P><B>Highlights</B></P> <P> <UL> <LI> An efficient and accurate numerical method (i.e. FE-ERA method) is proposed to compute the sound transmission loss. </LI> <LI> The FE-ERA method combines the finite element method (FEM) and elementary radiator approach (ERA). </LI> <LI> The radiator error index is derived to estimate the accuracy of the computation using ERA. </LI> <LI> The accuracy and efficiency of the FE-ERA method are further improved using radiator error index. </LI> <LI> The results of several numerical examples validate the accuracy and efficiency of the FE-ERA method. </LI> </UL> </P>

Polyhedral smoothed finite element method for thermoelastic analysis

김호범,임세영 대한기계학회 2017 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.31 No.12

Thermoelastic analysis by means of three-dimensional polyhedral elements based on the Smoothed Finite elements method (S-FEM), for example nodal Cell-based S-FEM (CS-FEM), Node-based S-FEM (NS-FEM), and Edge-based S-FEM (ES-FEM), was studied. SFEM allows implicit shape functions, making it possible to construct shape functions of S-FEM based polyhedral elements in a straightforward manner. The performance of S-FEM based polyhedral elements was compared with one another and with the conventional finite elements including hexahedral and tetrahedral element. Numerical examples show that the polyhedral elements by means of CS-FEM and ES-FEM provide better accuracy and convergence rate than conventional hexahedral finite elements, while the polyhedral elements by means of NS-FEM leads to spurious mode.

Development of high speed computation algorithm for transient analysis of rectangular plates

M. S. Choi,D. J. Jang,Y. B. Kim,장지성,문덕홍 대한기계학회 2009 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.23 No.12

A new transient analysis method for a rectangular plate structure comprised of a large number of plate elements was developed in order to significantly reduce computational time and memory. This algorithm was derived from the combination of the transfer technique of the transfer mass coefficient method, the modeling technique of the finite element method, and the numerical integration technique of Newmark’s method. In this paper, the algorithm for the transient analysis of a rectangular plate structure is formulated by the proposed method. In order to verify the computational accuracy and efficiency of the proposed method, the results obtained by the proposed method were compared with those obtained by the finite element method and the finite element-transfer matrix method. The proposed method, the finite element-transfer mass coefficient method, could considerably reduce the computation time without the loss of accuracy, in spite of using small computation memory, by using the transfer rules successively.

이차원 탄성 정적 문제를 위한 유한요소법과 경계요소법의 근사 결합 방법

송명관(Myung-Kwan Song) 한국지반신소재학회 2021 한국지반신소재학회 논문집 Vol.20 No.3

본 논문에서는 유한요소법과 경계요소법을 결합하여 기하학적으로 급변 부위가 있는 이차원 탄성 정적 문제에 대하여 효율적이고 정확한 해석 결과를 얻기 위한 유한요소법과 경계요소법의 근사 결합 방법을 제시한다. 이차원 문제의 유한요소로서는 3절점, 4절점 평면응력 요소를 적용하고, 이차원 문제의 경계요소로는 3절점 경계요소를 적용한다. 모델링 단계에서는 우선 전체 해석 대상을 유한요소로 모델링한 후에 기학학적 급변 부위를 경계요소로 모델링 하는데, 유한요소의 모델링을 위하여 정의된 절점을 이용하여 경계요소를 정의한다. 해석 단계에서는 전체 해석 대상에 대하여 유한요소 해석을 우선적으로 수행하고, 이후에 경계요소 해석을 자동으로 수행하는데, 경계부에서의 경계조건은 유한요소 해석 결과인 변위 조건과 응력 조건을 적용한다. 수치예제로서 이차원 탄성 정적 문제인 균열이 있는 평판에 대한 해석 결과를 제시하고 고찰한다. In this paper, the approximately coupled method of finite element method and boundary element method to obtain efficient and accurate analysis results is proposed for a two-dimensional elasto-static problem with a geometrically abruptly changing part. As the finite element of a two-dimensional problem, three-node and four-node plane stress element is applied, and as the boundary element of a two-dimensional problem, three-node boundary element is applied. In the modeling stage, firstly, an entire analysis target object is modeled as finite elements, and then a geometrically abruptly changing part is modeled as boundary elements. The boundary element is defined using the nodes defined for modeling finite elements. In the analysis stage, finite element analysis is firstly performed on a entire analysis target object, and boundary element analysis is automatically performed afterwards. As for the boundary conditions at boundary element analysis, displacement conditions and stress conditions, which are the results of finite element analysis, are applied. As a numerical example, the analysis results for a two-dimensional elasto-static problem, a plate with a crack, are presented and investigated.

Quasi-brittle and Brittle Fracture Simulation Using Phase-field Method based on Cell-based Smoothed Finite Element Method

이창계,Sundararajan Natarajan,이정재 한국전산구조공학회 2023 한국전산구조공학회논문집 Vol.36 No.5

This study introduces a smoothed finite-element implementation into the phase-field framework. In recent years, the phase-field method has recieved considerable attention in crack initiation and propagation since the method needs no further treatment to express the crack growth path. In the phase-field method, high strain-energy accuracy is needed to capture the complex crack growth path; thus, it is obtained in the framework of the smoothed finite-element method. The salient feature of the smoothed finite-element method is that the finite element cells are divided into sub-cells and each sub-cell is rebuilt as a smoothing domain where smoothed strain energy is calculated. An adaptive quadtree refinement is also employed in the present framework to avoid the computational burden. Numerical experiments are performed to investigate the performance of the proposed approach, compared with that of the finite-element method and the reference solutions.