Nonlinear thermal displacements of laminated composite beams

Akbas, Seref D. Techno-Press 2018 Coupled systems mechanics Vol.7 No.6

In this paper, nonlinear displacements of laminated composite beams are investigated under non-uniform temperature rising with temperature dependent physical properties. Total Lagrangian approach is used in conjunction with the Timoshenko beam theory for nonlinear kinematic model. Material properties of the laminated composite beam are temperature dependent. In the solution of the nonlinear problem, incremental displacement-based finite element method is used with Newton-Raphson iteration method. The distinctive feature of this study is nonlinear thermal analysis of Timoshenko Laminated beams full geometric non-linearity and by using finite element method. In this study, the differences between temperature dependent and independent physical properties are investigated for laminated composite beams for nonlinear case. Effects of fiber orientation angles, the stacking sequence of laminates and temperature on the nonlinear displacements are examined and discussed in detail.

유한 요소법을 이용한 비선형 슬러싱 문제 해석

경조현,배광준,김장환,조석규 한국해양환경·에너지학회 2004 한국해양환경·에너지학회지 Vol.7 No.4

A nonlinear sloshing problem is numerically simulated. During excessive sloshing the sloshing-induced impact load can cause a critical damage on the tank structure. A three-dimensional free-surface flow in a tank is formulated in the scope of potential flow theory. The exact nonlinear free-surface condition is satisfied numerically. A finite-element method based on Hamiltons principle is employed as a numerical scheme. The problem is treated as an initial-value problem. The computations are made through an iterative method at each time step. The hydrodynamic loading on the pillar in the tank is computed. 본 논문에서는 3차원 비선형 슬러싱 유동에 대한 수치해법을 개발하였다. 탱크내에서 과도한 슬러싱 유동이 일어 나는 경우에는 슬러싱 유동에 의해 유기되는 유체 충격력에 의해 탱크 내부 부재나 탱크 자체의 손상을 야기할 수 있다. 비선형 슬러싱 유동을 포텐셜 유동 이론에 근거한 자유표면파 문제로 정식화하고, 엄밀한 비선형 자유표면 경 계조건을 적용하여 수치적으로 해석하였다. 안정된 수치 해법 개발을 위해 해밀톤 원리에 근거한 변분법을 사용하 였으며 얻어진 변분식에 유한 요소법을 적용하여 해석하였다. 비선형 자유표면 유동은 시간영역에서의 초기치 문제 로 해석하였으며 자유표면의 위치는 매 계산 시간 간격마다 반복계산에 의해 결정되었다. 수치 해석 결과로는 탱크 내에 위치한 파이프에 비선형 슬러싱 유동에 의해 야기되는 유체 충격력을 구하였다.

S. I. 기법을 이용한 유한요소모델의 신뢰도 제고에 관한 연구

양경택 한국전산구조공학회 1997 전산구조공학 Vol.10 No.2

본 연구에서는 경계부 및 연결부를 지닌 기계 구조물의 유한요소모델 수립시 상대적으로 불확실성이 많은 경계부 및 연결부를 정확히 모델링하여 전체 구조계에 대한 해석적 모델의 신뢰도를 제고하는데 그 목적을 두고, 현장에서 간단히 측정할 수 있는 측정 데이터와 축약된 형태의 유한요소모델을 이용하는 S.I.기법을 제시하였다. 제시된 방법은 연결부를 제외한 연속체를 유한요소법으로 모델링하고 연결부의 동적 계수를 변수 상태로 하여 시간 영역에서의 비선형 상태 방정식을 구성하였으며 계수 규명 문제를 비선형 상태 방정식의 상태 추정 문제로 변환하여 해결하였다. 두 가지 예제에 대한 수치 해석을 통하여 제시된 기법의 타당성을 검증하였다. Mechanical structures are composed of substructures connected by joints and boundary elements. While the finite element representation of plain substructures is well developed and reliable, joints have a lot of uncertainties in being accurately modelled and affect dynamic behavior of a total system. In order to improve the accuracy of a finite element model, a new method is proposed, in which reduced finite element model is combined with a system identification technique. After substructures except joints are modelled with finite element method and joint properties are represented by parameter states, non-linear state equation is derived in which parameter states are multiplied by physical states such as displacements and velocities. So the joint parameter identification is transformed into non-linear state estimation problem. The methods are tested and discussed numerically and the feasibility for physical application has been demonstrated through two example structures.

Nonlinear finite element model updating with a decentralized approach

P.H. Ni,X.W. Ye 국제구조공학회 2019 Smart Structures and Systems, An International Jou Vol.24 No.6

Traditional damage detection methods for nonlinear structures are often based on simplified models, such as the mass-spring-damper and shear-building models, which are insufficient for predicting the vibration responses of a real structure. Conventional global nonlinear finite element model updating methods are computationally intensive and time consuming. Thus, they cannot be applied to practical structures. A decentralized approach for identifying the nonlinear material parameters is proposed in this study. With this technique, a structure is divided into several small zones on the basis of its structural configuration. The unknown material parameters and measured vibration responses are then divided into several subsets accordingly. The structural parameters of each subset are then updated using the vibration responses of the subset with the Newton-successive-over-relaxation (SOR) method. A reinforced concrete and steel frame structure subjected to earthquake loading is used to verify the effectiveness and accuracy of the proposed method. The parameters in the material constitutive model, such as compressive strength, initial tangent stiffness and yielding stress, are identified accurately and efficiently compared with the global nonlinear model updating approach.

비선형 비압축성 물질의 해석을 위한 3차원 Smoothed FEM

이창계,이정재 대한건축학회 2019 大韓建築學會論文集 : 構造系 Vol.35 No.9

This work presents the three-dimensional extended strain smoothing approach in the framework of finite element method, so-called smoothedfinite element method (S-FEM) for quasi-incompressible hyperelastic materials undergoing the large deformations. The proposed method isknown that the incompressible limits, such as over-estimation of stiffness and distorted mesh sensitivity, can be overcome in two dimensions. Therefore, in this paper, the idea of Cell-based, Edge-based and Node-based strain smoothing approaches is extended to three-dimensions. Theconstruction of subcells and smoothing domains for each methods are explained. The smoothed strain-displacement matrix and the stiffnessmatrix are obtained on each smoothing domain in the same manner with two-dimensional S-FEM. Various numerical tests are studied todemonstrate the validity and accuracy of 3D-S-FEM. The obtained results are compared with analytical solutions to express the efficacy ofthe methods. 본 연구에서는 2차원 변형률 평탄화기법을 유한요소기법에 도입한 Smoothed Finite Element Method를 비선형 비압축성 물질의 해석을 위하여 3차원으로 확대하였다. 각 기법의 하위요소 생성 및 평탄화 영역의 생성 기법을 설명하고, 변형률-변위 행렬 및 강성행렬 계산법을 설명하였다. 이를 바탕으로 비선형 해석을 위한 정식화를 수행하고 그에 따른 여러 수치예제를 수행하였다. 제안된 기법의 해는 정해 및 참조해와 비교하여 그 우수성을 입증하고자 한다.

Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material

Dinh-Kien Nguyen,Buntara S. Gan,Thanh-Huong Trinh 국제구조공학회 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.49 No.6

Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material (FGM) by using the finite element method is presented. The material property of the structures is assumed to be graded in the thickness direction by a power law distribution. A nonlinear beam element based on Bernoulli beam theory, taking the shift of the neutral axis position into account, is formulated in the context of the co-rotational formulation. The nonlinear equilibrium equations are solved by using the incremental/iterative procedure in a combination with the arc-length control method. Numerical examples show that the formulated element is capable to give accurate results by using just several elements. The influence of the material inhomogeneity in the geometrically nonlinear behavior of the FGM beam and frame structures is examined and highlighted.

기하학적 비선형 판재 해석을 위한 혼합형 FE Model 연구

김우람(Wooram Kim),최윤대(Youn Dae Choi) 대한기계학회 2010 대한기계학회 춘추학술대회 Vol.2010 No.5

A mixed finite element model was developed using the classical plate theory to analyze nonlinear bending of plate. The Lagrange multiplier method and the principal of minimum virtual energy were employed to find proper weight functions for the constraints which state the constitutive relations of force like variables and strains. All detail terms of element wise coefficient matrices and associate tangent matrices are presented to use the Newton iterative method. Then, linear solutions of the current model and traditional displacement model under the SS(simple support) boundary conditions were compared along with existing analytic solution. Post processed images of the nonlinear result of force like variables are presented to show the continuity of the solutions at the joint of the element boundaries. Finally, converged nonlinear finite element solutions of the current model are compared with those of existing traditional displacement model.Put Abstract text here.

Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material

Nguyen, Dinh-Kien,Gan, Buntara S.,Trinh, Thanh-Huong Techno-Press 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.49 No.6

Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material (FGM) by using the finite element method is presented. The material property of the structures is assumed to be graded in the thickness direction by a power law distribution. A nonlinear beam element based on Bernoulli beam theory, taking the shift of the neutral axis position into account, is formulated in the context of the co-rotational formulation. The nonlinear equilibrium equations are solved by using the incremental/iterative procedure in a combination with the arc-length control method. Numerical examples show that the formulated element is capable to give accurate results by using just several elements. The influence of the material inhomogeneity in the geometrically nonlinear behavior of the FGM beam and frame structures is examined and highlighted.

Comparison Between Static Nonlinear and Time History Analysis Using Flexibility-Based Model for An Existing Structure and Effect of Taking Into Account Soil Using Domain Reduction Method for a Single Media

Belgasmia Mourad,Moussaoui Sabah 대한토목학회 2015 KSCE JOURNAL OF CIVIL ENGINEERING Vol.19 No.3

This work is divided into two parts; the first one presents the nonlinear methods of analyses for seismic design of structures. Thefirst method is the nonlinear pushover procedure, which is based on the N2 method. The second method is the classical nonlineartime history analysis. The objective of this paper is to make a comparative study of an existing reinforced concrete building inBonefro, Italy between static nonlinear analysis and time history analysis using flexibility-based finite element, and the sensitivity ofthe time history analyses to the seismic parameters. The second part presents an elegant method called Domain Reduction Method,which takes into account a small adjacent part of subsoil including structure. With this way the size of the problem to be solved issubstantially reduced. All this through Z_Soil; engineering software based on the finite-element method.

Performance-based structural fire design of steel frames using conventional computer software

Y.K. Chan,F.G. Albermani,S.L. Chan,C.K. Iu 국제구조공학회 2010 Steel and Composite Structures, An International J Vol.10 No.3

Fire incident in buildings is common, so the fire safety design of the framed structure is imperative, especially for the unprotected or partly protected bare steel frames. However, software for structural fire analysis is not widely available. As a result, the performance-based structural fire design is urged on the basis of using user-friendly and conventional nonlinear computer analysis programs so that engineers do not need to acquire new structural analysis software for structural fire analysis and design. The tool is desired to have the capacity of simulating the different fire scenarios and associated detrimental effects efficiently, which includes second-order P-D and P-d effects and material yielding. Also the nonlinear behaviour of large-scale structure becomes complicated when under fire, and thus its simulation relies on an efficient and effective numerical analysis to cope with intricate nonlinear effects due to fire. To this end, the present fire study utilizes a second-order elastic/plastic analysis software NIDA to predict structural behaviour of bare steel framed structures at elevated temperatures. This fire study considers thermal expansion and material degradation due to heating. Degradation of material strength with increasing temperature is included by a set of temperature-stress-strain curves according to BS5950 Part 8 mainly, which implicitly allows for creep deformation. This finite element stiffness formulation of beam-column elements is derived from the fifth-order PEP element which facilitates the computer modeling by one member per element. The Newton-Raphson method is used in the nonlinear solution procedure in order to trace the nonlinear equilibrium path at specified elevated temperatures. Several numerical and experimental verifications of framed structures are presented and compared against solutions in literature. The proposed method permits engineers to adopt the performance-based structural fire analysis and design using typical second-order nonlinear structural analysis software.