A Simple Method to Calculate Mode Components of Strain Energy Release Rate of Free-Edge Delaminatins in Composite Laminates

Kim, Inkweon,Yang, Gwangyoung,Kim, Taekhyun,Park, Sanggee CHOSUN UNIVERSITY 1997 Basic Science and Engineering Vol.1 No.1

A simple method of calculating the mode components of the strain energy release rate of free-edge delaminations in the laminates is proposed. The interlaminar stresses are evaluated as an interface moment and interface shear forces that are obtained from the equilibrium equations at the interface between the adjacent layers. Deformation of an edge-delaminated laminate is calculated by using a generalized quasi-three dimensional classical lamination theory developed bythe authors. The analysis provides closed-form expressions for the three components of the strain energy release rate. The analyses are performed on[+30/-30/90]s laminates subjected to uniaxial extension, with free-edge delaminations located symmetrically and asymmetrically with respect to the laminate midplane. Comparison of the results with a finite element solution using the virtual crack closure technique shows good agreement. The simple nature of this method makes it suitable for primary design analysis for the delaminations of composite laminates.

Exact mathematical solution for free vibration of thick laminated plates

Mohammad Asadi Dalir,Alireza Shooshtari 국제구조공학회 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.56 No.5

In this paper, the modified form of shear deformation plate theories is proposed. First, the displacement field geometry of classical and the first order shear deformation theories are compared with each other. Using this comparison shows that there is a kinematic relation among independent variables of the first order shear deformation theory. So, the modified forms of rotation functions in shear deformation theories are proposed. Governing equations for rectangular and circular thick laminated plates, having been analyzed numerically so far, are solved by method of separation of variables. Natural frequencies and mode shapes of the plate are determined. The results of the present method are compared with those of previously published papers with good agreement obtained. Efficiency, simplicity and excellent results of this method are extensible to a wide range of similar problems. Accurate solution for governing equations of thick composite plates has been made possible for the first time.

A thermo-mechanical stress prediction improvement of using the classical lamination theory via Saint-Venant’s principle for laminated composite plates

정용민,김준식 대한기계학회 2018 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.32 No.2

Saint-Venant’s principle was introduced as the principle of the stress resultant equivalence for one dimensional structures, such as beams, cylindrical and prismatic structures. According to the principle, the stress distributions may be different around the area where forces are applied, but their resultants are invariant. In this paper, we apply the Saint-Venant’s principle to improve the thermomechanical stresses calculated by the Classical lamination theory (CLT). First we solve the CLT for laminated composite plates, calculate the transverse shear stresses using three-dimensional stress equilibrium equations, and obtain the improved displacement field with perturbation terms via transverse shear constitutive equations. At this point, these perturbation terms are unknown, which can be determined by applying the stress resultant equivalence (or the Saint-Venant’s principle). Once the terms are calculated, the improved displacements and stresses are obtained. To verify the accuracy of the proposed approach, simply-supported plates under mechanical and/or thermal loadings are taken as a test-bed, in which symmetric and anti-symmetric cross-ply layups are considered. The results obtained are compared to those of three-dimensional elasticity as well as first-order shear deformation theory. Finally the errors induced by the present approach are systematically analyzed in terms of the stress resultants.

Automatic analysis of thin-walled laminated composite sections

A. Prokic,D. Lukic,Dj. Ladjinovic 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.16 No.3

In this paper a computer program is developed for the determination of geometrical and material properties of composite thin-walled beams with arbitrary open cross-section and any arbitrary laminate stacking sequence. Theory of thin-walled composite beams is based on assumptions consistent with the Vlasov's beam theory and classical lamination theory. The program is written in Fortran 77. Some numerical examples are given, with complete information about input and output.

고전적층판 이론을 이용한 카본튜브의 재료특성 해석과 원형 콘크리트 기둥의 압축강도 향상에 관한 연구

이경훈(Kyoung-Hun Lee) 한국열환경공학회 2022 열환경공학 Vol.17 No.2

Carbon fiber is a material that has a very high tensile strength and is flexible, so it is easy to manufacture into a desired shape. If carbon fiber is processed into a thin carbon sheet and then a circular concrete column is wound, the compressive strength can be improved due to the confined effect. In this study, the characteristics of multi-layered carbon sheets were identified by applying the Classical Lamination Theory. To directly measure tensile strength and lateral restraint pressure, tensile test and split disk test specimens were fabricated and then material experiments were conducted using a 2,000kN capacity UTM. The lateral restraint pressure of carbon sheet tube was about 5.4MPa and the tensile strength was 3,790Mpa, which is about 9.5 times the strength of steel reinforcing bars. The equation for predicting compressive strength of circular concrete confined by carbon sheet tubes manufactured at various angles was proposed through regression analysis. It is judged that this can be used as an analytical equation that can predict the strength in advance when a concrete column whose bearing strength has been lowered due to an earthquake, etc. is reinforced with a carbon sheet.

고전적층판 이론을 이용한 카본튜브의 재료특성 해석과 원형 콘크리트 기둥의 압축강도 향상에 관한 연구

이경훈 (사)한국열환경공학회 2022 열환경공학 Vol.17 No.2

Carbon fiber is a material that has a very high tensile strength and is flexible, so it is easy to manufacture into a desired shape. If carbon fiber is processed into a thin carbon sheet and then a circular concrete column is wound, the compressive strength can be improved due to the confined effect. In this study, the characteristics of multi-layered carbon sheets were identified by applying the Classical Lamination Theory. To directly measure tensile strength and lateral restraint pressure, tensile test and split disk test specimens were fabricated and then material experiments were conducted using a 2,000kN capacity UTM. The lateral restraint pressure of carbon sheet tube was about 5.4MPa and the tensile strength was 3,790Mpa, which is about 9.5 times the strength of steel reinforcing bars. The equation for predicting compressive strength of circular concrete confined by carbon sheet tubes manufactured at various angles was proposed through regression analysis. It is judged that this can be used as an analytical equation that can predict the strength in advance when a concrete column whose bearing strength has been lowered due to an earthquake, etc. is reinforced with a carbon sheet.

FRP 바닥판의 휨 해석모델 개발

김영빈,이재홍 한국공간구조학회 2005 한국공간구조학회지 Vol.5 No.3

본 연구에서는 사각형 모듈의 인발성형된 복합재료 바닥판의 휨 거동에 대한 해석 모델을 개발하였다. FRP 바닥판의 해석 모델은 FSDT 평판 이론을 기반으로 임의 적층각을 지닌 FRP 바닥판의 처짐을 예측할 수 있었다. 수치적 예제에서는 네 변이 단순 지지된 등분포 하중을 받는 사각형 모듈의 FRP 바닥판을 2차원 평판 유한 요소해석을 적용하여 수행하였고, 해석 결과에 대해서는 바닥판 길이-높이의 비와 화이버 각도의 변화에 따른 효과에 대해 역점을 두고 다루었다. 연구 결과, 본 연구에서 제안한 해석 모델이 FRP 바닥판의 휨 거동을 해석하고 예측하는데 효과적이고 정확하다는 것이 입증되었다. 또한, FRP 바닥판의 높이가 높아질수록 plate 해석 이론에 있어서 일차전단변형이론(First order Shear Deformable laminated plate Theory : FSDT)이 아닌 고차전단변형(Higher order Shear Deformable plate Theory : HSDT)의 필요성에 대해 언급하였다. An analytical model was developed to investigate the flexural behavior of a pultruded fiber-reinforced plastic deck of rectangular unit module. The model is based on first-order shea. deformable plate theory (FSDT), and capable of predicting deflection of the deck of arbitrary laminate stacking sequences. To formulate tile problem, two-dimensional plate finite element method is employed. Numerical results are obtained for FRP decks under uniformly-distributed loading, addressing the effects of fiber angle and span-to-height ratio. It is found that the present analytical model is accurate and efficient for solving flexural behavior of FRP decks. Also, as the height of FRP deck plate is higher, the necessity of higher order Shear deformable plate theory(HSDT) is announced, not the FSDT in the plate analysis theory.

Pressure loading, end- shortening and through- thickness shearing effects on geometrically nonlinear response of composite laminated plates using higher order finite strip method

Mohammad H. Sherafat,Seyyed Amir M. Ghannadpour,Hamid R. Ovesy 국제구조공학회 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.45 No.5

A semi-analytical finite strip method is developed for analyzing the post-buckling behavior of rectangular composite laminated plates of arbitrary lay-up subjected to progressive end-shortening in their plane and to normal pressure loading. In this method, all the displacements are postulated by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. Thin or thick plates are assumed and correspondingly the Classical Plate Theory (CPT)or Higher Order Plate Theory (HOPT) is applied. The in-plane transverse deflection is allowed at the loaded ends of the plate, whilst the same deflection at the unloaded edges is either allowed to occur or completely restrained. Geometric non-linearity is introduced in the strain–displacement equations in the manner of the von-Karman assumptions. The formulations of the finite strip methods are based on the concept of the principle of the minimum potential energy. The Newton–Raphson method is used to solve the non-linear equilibrium equations. A number of applications involving isotropic plates, symmetric and unsymmetric cross-ply laminates are described to investigate the through-thickness shearing effects as well as the effect of pressure loading, end-shortening and boundary conditions. The study of the results has revealed that the response of the composite laminated plates is particularly influenced by the application of the Higher Order Plate Theory (HOPT) and normal pressure loading. In the relatively thick plates, the HOPT results have more accuracy than CPT.

Pressure loading, end- shortening and through- thickness shearing effects on geometrically nonlinear response of composite laminated plates using higher order finite strip method

Sherafat, Mohammad H.,Ghannadpour, Seyyed Amir M.,Ovesy, Hamid R. Techno-Press 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.45 No.5

A semi-analytical finite strip method is developed for analyzing the post-buckling behavior of rectangular composite laminated plates of arbitrary lay-up subjected to progressive end-shortening in their plane and to normal pressure loading. In this method, all the displacements are postulated by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. Thin or thick plates are assumed and correspondingly the Classical Plate Theory (CPT) or Higher Order Plate Theory (HOPT) is applied. The in-plane transverse deflection is allowed at the loaded ends of the plate, whilst the same deflection at the unloaded edges is either allowed to occur or completely restrained. Geometric non-linearity is introduced in the strain-displacement equations in the manner of the von-Karman assumptions. The formulations of the finite strip methods are based on the concept of the principle of the minimum potential energy. The Newton-Raphson method is used to solve the non-linear equilibrium equations. A number of applications involving isotropic plates, symmetric and unsymmetric cross-ply laminates are described to investigate the through-thickness shearing effects as well as the effect of pressure loading, end-shortening and boundary conditions. The study of the results has revealed that the response of the composite laminated plates is particularly influenced by the application of the Higher Order Plate Theory (HOPT) and normal pressure loading. In the relatively thick plates, the HOPT results have more accuracy than CPT.

A mathematical model for smart functionally graded beam integrated with shape memory alloy actuators

H. Sepiani,F. Ebrahimi,H. Karimipour 대한기계학회 2009 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.23 No.12

This paper presents a theoretical study of the thermally driven behavior of a shape memory alloy (SMA)/FGM actuator under arbitrary loading and boundary conditions by developing an integrated mathematical model. The model studied is established on the geometric parameters of the three-dimensional laminated composite box beam as an actuator that consists of a functionally graded core integrated with SMA actuator layers with a uniform rectangular cross section. The constitutive equation and linear phase transformation kinetics relations of SMA layers based on Tanaka and Nagaki model are coupled with the governing equation of the actuator to predict the stress history and to model the thermo-mechanical behavior of the smart shape memory alloy/FGM beam. Based on the classical laminated beam theory, the explicit solution to the structural response of the structure, including axial and lateral deflections of the structure, is investigated. As an example, a cantilever box beam subjected to a transverse concentrated load is solved numerically. It is found that the changes in the actuator's responses during the phase transformation due to the strain recovery are significant.