• Coupled systems mechanics
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• 제11권6호
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• pp.543-556
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• 2022

Delamination of multilayered inhomogeneous beam that exhibits non-linear relaxation behavior is analyzed in the present paper. The layers are inhomogeneous in the thickness direction. The dealamination crack is located symmetrically with respect to the mid-span. The relaxation is treated by applying a non-linear stress-straintime constitutive relation. The material properties which are involved in the constitutive relation are distributed continuously along the thickness direction of the layer. The delamination is analyzed by applying the J-integral approach. A time-dependent solution to the J-integral that accounts for the non-linear relaxation behavior is derived. The delamination is studied also in terms of the time-dependent strain energy release rate. The balance of the energy is analyzed in order to obtain a non-linear time-dependent solution to the strain energy release rate. The fact that the strain energy release rate is identical with the J-integral value proves the correctness of the non-linear solutions derived in the present paper. The variation of the J-integral value with time due to the non-linear relaxation behavior is evaluated by applying the solution derived.

• Coupled systems mechanics
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• 제6권1호
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• pp.97-111
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• 2017

The present paper reports an analytical study of delamination fracture in the Mixed Mode Flexure (MMF) functionally graded beam with considering the material non-linearity. The mechanical behavior of MMF beam is modeled by using a non-linear stress-strain relation. It is assumed that the material is functionally graded along the beam height. Fracture behavior is analyzed by the J-integral approach. Non-linear analytical solution is derived of the J-integral for a delamination located arbitrary along the beam height. The J-integral solution derived is verified by analyzing the strain energy release rate with considering the non-linear material behavior. The effects of material gradient, crack location along the beam height and material non-linearity on the fracture are evaluated. It is found that the J-integral value decreases with increasing the upper crack arm thickness. Concerning the influence of material gradient on the non-linear fracture, the analysis reveals that the J-integral value decreases with increasing the ratio of modulus of elasticity in the lower and upper edge of the beam. It is found also that non-linear material behavior leads to increase of the J-integral value. The present study contributes for the understanding of fracture in functionally graded beams that exhibit material non-linearity.

• Structural Engineering and Mechanics
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• 제71권2호
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• pp.153-163
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• 2019

Longitudinal fracture behavior of non-linear elastic beam configurations is studied in terms of the strain energy release rate. It is assumed that the beams exhibit continuous material inhomogeneity along the width as well as along the height of the crosssection. The Ramberg-Osgood stress-strain relation is used for describing the non-linear mechanical behavior of the inhomogeneous material. A solution to strain energy release rate is derived that holds for inhomogeneous beams of arbitrary cross-section under combination of axial force and bending moments. Besides, the solution may be applied at any law of continuous distribution of the modulus of elasticity in the beam cross-section. The longitudinal crack may be located arbitrary along the beam height. The solution is used to investigate a longitudinal crack in a beam configuration of rectangular cross-section under four-point bending. The crack is located symmetrically with respect to the beam mid-span. It is assumed that the modulus of elasticity varies continuously according a cosine law in the beam cross-section. The longitudinal fracture behavior of the inhomogeneous beam is studied also by applying the J-integral approach for verification of the non-linear solution to the strain energy release rate derived in the present paper. Effects of material inhomogeneity, crack location along the beam height and non-linear mechanical behavior of the material on the longitudinal fracture behavior are evaluated. Thus, the solution derived in the present paper can be used in engineering design of inhomogeneous non-linear elastic structural members to assess the influence of various material and geometrical parameters on longitudinal fracture.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2004년도 춘계학술발표대회 논문집
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• pp.87-90
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• 2004

In this paper, geometrically non-linear finite element analyses were performed to study the mechanical behavior of the material system of the envelope of stratospheric airships. The microstructure of the load­bearing plain weave layer was identified and modeled. The Updated Lagrangian formulation was employed to consider the geometric non-linearity as well as the induced structural non-linearity for the fiber tows. The stress-strain behavior was predicted and the effective elastic modulus was calculated by numerical experiments. It was found the non-linear stress-strain curves were largely different from those by linear analysis with much higher non-linear elastic moduli. The difference was more distinguishable when the tow waviness was smaller.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1990년도 봄 학술발표회 논문집
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• pp.1-5
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• 1990

The object of this study introducts simple formula being based on energy principle to investigate span truss's non-linear, and considers the relation of member's length, height rate and slenderness ratio to rise prymid truss's economic structure ability through each example. This paper considered space truss's geometric non-linear behavior and material non-linear behavior, so acquired under result through as saying energy principle.

• 한국항공우주학회지
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• 제32권4호
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• pp.18-23
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• 2004

본 논문에서는 고 전압, 고 응력 하에 있는 압전 재료의 재료 비선형 거동을 실험적으로 밝히고, 수치적으로 모사하였다. 응력 하에서, 압전 재료의 비선형 거동을 표현 할 수 있는 실험식을 압전 변형율에서 만들어 내었다. 그 식은 재료 비선형 해석을 위하여, 증분 형태의 유한요소 식에 적용되었다. 압전 상수에 대한 새로운 정의와 증분 형태로 표현된 압전 변형율이 보다 나은 비선형 거동의 복원을 위하여 유한 요소 정식화과정에 적용되었다. 이것으로, 높은 전기장 영역에서도, 박판형 압전 재료의 비선형 거동을 정확하게 복원하였다. 일련의 수행된 실험과 연구 과정의 검증을 위하여, 압전재료 바이모프 보 작동기가 수치적으로와 실험적으로 사용되었다. 재료 비선형 유한요소해석으로 예측된 변위와 실험으로 구해진 변위가 잘 일치함을 확인하였다.

• Structural Engineering and Mechanics
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• 제65권6호
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• pp.721-730
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• 2018

This paper aims to inspect the effectiveness of the Simple Adaptive Control Method (SACM) to control the response of asymmetric buildings with rotationally non-linear behavior under seismic loads. SACM is a direct control method and was previously used to improve the performance of linear and non-linear structures. In most of these studies, the modeled structures were two-dimensional shear buildings. In reality, the building plans might be asymmetric, which cause the buildings to experience torsional motions under earthquake excitation. In this study, SACM is used to improve the performance of asymmetric buildings, and unlike conventional linear models, the non-linear inertial coupling terms are considered in the equations of motion. SACM performance is compared with the Linear Quadratic Regulator (LQR) algorithm. Moreover, the LQR algorithm is modified, so that it is appropriate for rotationally non-linear buildings. Active tuned mass dampers are used to improve the performance of the modeled buildings. The results show that SACM is successful in reducing the response of asymmetric buildings with rotationally non-linear behavior under earthquake excitation. Furthermore, the results of the SACM were very close to those of the LQR algorithm.

• Composites Research
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• 제18권2호
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• pp.30-37
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• 2005

본 논문에서는 평직구조를 갖는 성층권 비행선 기낭의 하중막재에 대한 비선형 유한요소 해석 결과를 기술하였다. 평직구조를 갖는 하중막재의 미세구조를 3차원적으로 구현하였고, Updated Lagrangian 방법을 사용하여 기하학적 비선형성을 고려하였다 계산결과, 큰 변형률에서 비선형해석으로부터 얻은 응력-변형률 곡선은 선형해석의 결과와 큰 차이를 보였다. 또한 응력-변형률 곡선으로부터 얻은 비선형 탄성계수 값은 선형 탄성계수보다 큰 값을 보였는데 그 차이는 섬유의 굴곡도가 작은 경우 더욱 두드러지게 나타났다

• 한국지진공학회논문집
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• 제20권5호
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• pp.301-310
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• 2016

There are differences in seismic behavior between non-skewed bridges and skewed bridges due to in-plane rotations caused by pounding between the skewed deck and its abutments during strong earthquake. Many advances have been made in developing design codes and guidelines for dynamic analyses of non-skewed bridges. However, there remain significant uncertainties with regard to the structural response of skewed bridges caused by unusual seismic response characteristics. The purpose of this study is performing non-linear time history analysis of the bridges using abutment-soil interaction model considering pounding between the skewed deck and its abutments, and analyzing global seismic behavior characteristics of the skewed bridges to assess the possibility of unseating. Refined bridge model with abutment back fill, shear key and elastomeric bearing was developed using non-linear spring element. In order to evaluate the amplification of longitudinal and transverse displacement response, non-linear time history analysis was performed for single span bridges. Far-fault and near-fault ground motions were used as input ground motions. According to each parameter, seismic behavior of skewed bridges was evaluated.

• Steel and Composite Structures
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• 제23권3호
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• pp.263-271
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• 2017

A theoretical study was carried-out of mode II delamination fracture behavior of the End Loaded Split (ELS) functionally graded beam configuration with considering the material non-linearity. The mechanical response of ELS was modeled analytically by using a power-law stress-strain relation. It was assumed that the material is functionally graded transversally to the beam. The non-linear fracture was investigated by using the J-integral approach. Equations were derived for the crack arm curvature and zero axes coordinate that are needed for the J-integral solution. The analysis developed is valid for a delamination crack located arbitrary along the beam height. The J-integral solution was verified by analyzing the strain energy release rate with considering material non-linearity. The effects of material gradient, non-linear material behavior and crack location on the fracture were evaluated. The solution derived is suitable for parametric analyses of non-linear fracture. The results obtained can be used for optimization of functionally graded beams with respect to their mode II fracture performance. Also, such simplified analytical models contribute for the understanding of delamination fracture in functionally graded beams exhibiting material non-linearity.