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.

비선형 유한요소법을 이용한 신발 해석 및 설계

문병영 ( Mun Byeong Yeong ),김병수 ( Kim Byeong Su ) 한국고무학회 2003 엘라스토머 및 콤포지트 Vol.38 No.3

본 논문에서는 미드솔에 에어싸이클 펌프를 장착한 골프화에 대한 해석적 방법과 설계 기술을 보여준다. 골프화는 유한요소법으로 모델링 하였으며, 더 나은 설계를 위해서 신발을 구성하는 미드솔과 아웃솔의 형상을 고려하였다. 또한 미드솔에 있는 에어싸이클 펌프의 최적의 크기와 형상을 조사하였다. 표준 인체 압력 값을 유한요소해석의 경계 값으로 채택하였다. 오그덴 타입의 변형률에너지 함수의 미지 상수는 인장시험에 따라서 조사하였다. 비선형해석을 위해서 상용 유한요소해석 프로그램 MARC V7.3을 이용하여 미드솔과 아웃솔의 변형률과 부피 변화 값을 각각 구하였다. 미드솔과 아웃솔 유한요소법에 의해 구해진 값은 탄성체의 특성에 따라서 달리 나타난다. 여기에 보인 결과는 보다 나은 골프화 해석에 사용될 것이다. 더욱이, 결과 값들은 보다 효과적인 방법을 개발하기 위한 방법으로 신발산업체에 사용되어 질 수 있다. This paper presents an analytic method and a design technique for golf shoes with air-cycled pump in the midsole. The golf shoes are modeled using the finite element method for better design by considering the configuration of the misole and the outsole, which compose the golf shoes. Also the optimum size and shape of air-cycled pump in the midsole is examined. The values of standard human pressure for boundary conditions are adopted for the FEA(Finite Element Analysis). The unknown constants of the strain energy function of Ogden type are observed in accordance with the axial tension test. By the commercial FEM software for nonlinear analysis, MARC V7.3, the strains and the values of volume change for the midsole and the outsole are obtained, respectively. It can be concluded that results obtained by FEM in the midsole and the outsole are different depending on the characteristic of elastomer. The results reported herein provide better understanding of analyzing the golf shoes. Moreover, it is believed that those properties of the results can be utilized in the shoes industry to develop the effective design method.

SEA-FEM hybrid analysis for predicting Inter-floor impact noise

Kim, Tae-Min,Kim, Jeung-Tae,Kim, Jung-Soo Elsevier 2018 Applied acoustics Vol.129 No.-

<P><B>Abstract</B></P> <P>A hybrid method for predicting inter-floor impact noise in an apartment house is developed. Statistical Energy Analysis (SEA) is useful for predicting mid- to high-frequency noise by utilizing simple equivalent models of structures that have complex geometry and material properties. For low frequencies with concomitant low modal density, however, the error can be significant. Finite Element Method (FEM) is useful for predicting low frequency noise but entails complex modelling process and can be computation intensive. The inter-floor impact noise contains a significant low frequency component arising from floor vibration engendered by a person walking on the floor. The force of impact at 30–300Hz frequency range excites the first and second bending modes of the floor and causes sound to radiate, and for the component of the sound less than 100Hz, the SEA prediction error can be quite significant. In the present study, a modular hybrid method in which the floor structure is modelled using FEM and the vibration energy transmission through walls is modelled using SEA is proposed. The low frequency vibration of the floor due to impact is analyzed by modelling the floor asa clamped uniform plate while the propagation of vibratory energy to adjacent walls is analyzed by determining CLF and DLF values. The proposed SEA-FEM hybrid analysis method is capable of providing accurate estimation of the impact noise for low-, medium- and high-frequencies. Compared with a FEM−based method, the proposed method is found to yield results that are similar while reducing computation time by 70%.</P>

FINITE ELEMENT METHOD FOR SOLVING BOUNDARY CONTROL PROBLEM GOVERNED BY ELLIPTIC VARIATIONAL INEQUALITIES WITH AN INFINITE NUMBER OF VARIABLES

Ghada Ebrahim Mostafa 경남대학교 수학교육과 2023 Nonlinear Functional Analysis and Applications Vol.28 No.3

In this paper, finite element method is applied to solve boundary control problem governed by elliptic variational inequality with an infinite number of variables. First, we introduce some important features of the finite element method, boundary control problem governed by elliptic variational inequalities with an infinite number of variables in the case of the control and observation are on the boundary is introduced. We prove the existence of the solution by using the augmented Lagrangian multipliers method. A triangular type finite element method is used.

Finite element compatible matrix interpolation for parametric model order reduction of electrothermal microgripper

Roy Ananya,Nabi M,Rahman Najmur 한국CDE학회 2021 Journal of computational design and engineering Vol.8 No.6

Electrothermal microgrippers are nowadays commonly used as they are small in size, low cost, and easy to manufacture. The microgripper is modeled through partial differential equations, which are discretized by the finite element method (FEM), producing a large number of ordinary differential equations. This makes model order reduction (MOR) a fruitful proposition. Moreover, in design applications, the microgripper needs to be simulated repeatedly, with varying values of certain parameters. When these parameters are geometric in nature, matrix interpolation-based parametric model order reduction (pMOR) is the most suited method. However, in finite element applications, the sizes of the FE matrices change for varying geometrical parameters. The conventional matrix interpolation-based pMOR method becomes inapplicable for such cases, which remains a major drawback of this otherwise powerful algorithm. In this paper, this major hurdle is removed, and a new finite element compatible matrix interpolation (FEMI) for pMOR is proposed. A three-dimensional electrothermal microgripper is modeled parametrically using this proposed methodology. The effectiveness of the proposed method is shown through simulation results.

유한요소해석을 활용한 장신구디자인 사례연구 - 예술장신구 사례를 중심으로 -

민복기 ( Min Bog Ki ) 한국기초조형학회 2020 기초조형학연구 Vol.21 No.1

본 연구의 목적은 응용수학분야에서 연구되어 토목, 건축 등의 분야에서 활용되고 있는 유한요소해석에 대해 살펴보고, 이를 장신구 분야에 적용할 가능성을 탐색하는 데 있다. 유한요소법(Finite Element Method; FEM)은 미분방정식 문제를 다른 형태로 바꾸고 이 해(解)를 어떤 함수의 일차결합으로 나타내는 수치적인 근사해법(approximation method)의 하나이다. 이러한 수학적 원리를 바탕으로 재료역학 등의 공학분야에서 물성과 하중 등 외부적 요인을 설정하고 대상물의 물리적 변위의 근사값을 도출하여 구조를 해석하는 것이 유한요소해석(Finite Element Analysis; FEA)이다. FEA는 컴퓨터의 계산을 통한 시뮬레이션 기술로 빠르게 정립되었고, 이후 CAD의 모델링데이터를 활용할 수 있도록 통합되어 강도, 열, 유동, 진동 등 다양한 물리적 환경의 시뮬레이션을 통해 효율적 설계를 도출하는데 활용되고 있다. 장신구는 매우 작은 사물이지만 신체 위에 착용되는 필연적 조건을 가지므로 안정적 구조로 제작되어야 하지만 이를 위해 FEA를 활용한 사례는 없었다. 연구자는 이러한 장신구의 요구조건을 충족하는 새로운 난발(Prong)의 구조연구를 위해 FEA를 활용한 난발구조를 연구하였고 4개 혹은 6개로 이루어진 일반적인 난발구조에서 난발의 개수를 최소화하여 2개의 난발구조를 가지도록 하였다, 그리고 빛의 유입을 위해 오브제를 기저부에서 2mm 위로 띄워 고정할 수 있는 난발구조를 개발하였다. 이러한 사례에서와 같이 FEA는 주얼리의 구조안정성 검증 뿐 아니라 새로운 컨셉의 디자인탐색에 도움을 줄 수 있고 주얼리산업의 생산과정에서도 열과 유동의 해석을 통해 주조생산성과 품질을 개선시킬 수 있다. 또한 금속공예의 대공분야에서도 하중이나 낙하, 바람 등 다양한 물리적 외력을 시뮬레이션 하여 좀 더 안정적인 구조를 도출하는데 활용될 수 있을 것이다. The purpose of this study is to examine the Finite Element Analysis, studied in Applied Mathematics and used in the fields of Civil Engineering and Architecture, and to explore the possibilities of applying it to the field of jewelry. Finite Element Method changes differential equations into different forms and appears as one of the numerical approximation methods. With this mathematical principle background, the linear combination of the certain function’s value sets the external factors such as property and weight in the engineering field, material mechanics and Finite Element Analysis is the evaluation of the structure by approximating the physical displacement of the object. FEA quickly became a computerized simulation technology, and later integrated to utilize CAD modeling data to simulate various physical environments such as strength, heat, flow, and vibration, etc. for effective design. A jewelry is a very small object it has an inevitable condition to be worn on top of the body; therefore, needs to be made with a secure structure but, there has been no case for it with FEA. This research studies the required conditions of this kind of jewelry with new prong structure research that uses FEA and minimizes the number of prongs in the prongs’ structure to two from four or six, and developed new prong structures for the object to float 2mm above the basis for light to pass. In such a case, FEA not only verifies the structural stability but make new concept design exploration possible and can improve productivity and quality through the interpretation of heat and flow in the casting process of the jewelry industry’s production process. Moreover, various physical external forces such as weight, fall or wind can be simulated to construct safer structures for vessel making in the field of Metal Craft as well.

An edge-based smoothed finite element method for adaptive analysis

Chen, L.,Zhang, J.,Zeng, K.Y.,Jiao, P.G. Techno-Press 2011 Structural Engineering and Mechanics, An Int'l Jou Vol.39 No.6

An efficient edge-based smoothed finite element method (ES-FEM) has been recently developed for solving solid mechanics problems. The ES-FEM uses triangular elements that can be generated easily for complicated domains. In this paper, the complexity study of the ES-FEM based on triangular elements is conducted in detail, which confirms the ES-FEM produces higher computational efficiency compared to the FEM. Therefore, the ES-FEM offers an excellent platform for adaptive analysis, and this paper presents an efficient adaptive procedure based on the ES-FEM. A smoothing domain based energy (SDE) error estimate is first devised making use of the features of the ES-FEM. The present error estimate differs from the conventional approaches and evaluates error based on smoothing domains used in the ES-FEM. A local refinement technique based on the Delaunay algorithm is then implemented to achieve high efficiency in the mesh refinement. In this refinement technique, each node is assigned a scaling factor to control the local nodal density, and refinement of the neighborhood of a node is accomplished simply by adjusting its scaling factor. Intensive numerical studies, including an actual engineering problem of an automobile part, show that the proposed adaptive procedure is effective and efficient in producing solutions of desired accuracy.

A novel coupled finite element method for hydroelastic analysis of FG-CNTRC floating plates under moving loads

Vu X. Nguyen,Qui X. Lieu,Tuan A. Le,Thao D. Nguyen,Takayuki Suzuki,Van Hai Luong 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.42 No.2

A coupled finite element method (FEM)-boundary element method (BEM) for analyzing the hydroelastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) floating plates under moving loads is firstly introduced in this article. For that aim, the plate displacement field is described utilizing a generalized shear deformation theory (GSDT)-based FEM, meanwhile the linear water-wave theory (LWWT)-relied BEM is employed for the fluid hydrodynamic modeling. Both computational domains of the plate and fluid are coincidentally discretized into 4-node Hermite elements. Accordingly, the C1−continuous plate element model can be simply captured owing to the inherent feature of third-order Hermite polynomials. In addition, this model is also completely free from shear correction factors, although the shear deformation effects are still taken into account. While the fluid BEM can easily handle the free surface with a lower computational effort due to its boundary integral performance. Material properties through the plate thickness follow four specific CNT distributions. Outcomes gained by the present FEM-BEM are compared with those of previously released papers including analytical solutions and experimental data to validate its reliability. In addition, the influences of CNT volume fraction, different CNT configurations, water depth, and load speed on the hydroelastic behavior of FG-CNTRC plates are also examined.

Mean dilatational based finite element formulation for a nearly incompressible nonlinear large deformation analysis

아닉 다스 안토,Hee Keun Cho 대한기계학회 2022 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.36 No.5

The finite element method (FEM) is one of the most powerful tools that can be used to solve engineering problems. Standard displacement-based isoparametric elements are the most popular in the engineering community for their simple implementation. However, loworder displacement-based elements exhibit locking in the incompressible. Our proposed formulation is a locking removing method that is free from the need to store any extra integration point. We calculate the modified deformation gradient from the mean dilatation of the element and also modify the finite element equations using the mean dilatation. This method is also different from the B-bar method as the B matrix is not modified, but rather the weak form is linearized for the modified deformation gradient. Therefore, this method is a unique implementation of the average dilatation of the element. Here we also present an implementation algorithm of the proposed formulation and compare the results with available methods.

An Edge-based Smoothed Finite Element Method (ES-FEM) for Dynamic Analysis of 2D Fluid-Solid Interaction Problems

T. Nguyen-Thoi,P. Phung-Van,V. Ho-Huu,L. Le-Anh 대한토목학회 2015 KSCE JOURNAL OF CIVIL ENGINEERING Vol.19 No.3

The paper presents an extension of the Edge-based Smoothed Finite Element Method (ES-FEM-T3) using triangular elements forthe dynamic response analysis of two-dimension fluid-solid interaction problems based on the pressure-displacement formulation. Inthe proposed method, both the displacement in the solid domain and the pressure in the fluid domain are smoothed by the gradientsmoothing technique based on the smoothing domains associated with the edges of the triangular elements. Thanks to the softeningeffect of the gradient smoothing technique used in the ES-FEM-T3, the numerical solutions for the coupled systems by the ES-FEMT3are improved significantly compared to those by some other existing FEM methods.