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Two-dimensional thermoelasticity solution for functionally graded thick beams

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Science china(Physics,{1. & Astronomy) 2006年第4期49卷 451-460页

作者： Lü Chaofeng1, CHEN Weiqiu1 & zhong zheng2 1. Department of Civil engineering, Zhejiang university, Hangzhou 310027, china 2. Key Laboratory of Solid mechanics of Ministry of Education, school of aerospace engineering and Ap- plied mechanics, tongji university, shanghai 2.0092. china Department of Civil engineering Zhejiang University Hangzhou China Key Laboratory of Solid mechanics of Ministry of Education School of Aerospace Engineering and Applied Mechanics Tongji University Shanghai China

Two-dimensional thermoelasticity analysis of functionally graded thick beams is presented using the state space method coupled with the technique of differential quadrature. Material properties vary continuously and smoothly through the beam thickness, leading to variable coefficients in the state equation derived from the elasticity equations. Approximate laminate model is employed to translate the state equation into the one with constant coefficients in each layer. To avoid numerical instability, joint coupling matrices are introduced according to the continuity conditions at interfaces in the approximate model. The differential quadrature procedure is applied to discretizing the beam in the axial direction to make easy the treatment of arbitrary end conditions. A simply-supported beam with exponentially varying material properties is considered to validate the present method. Numerical examples are performed to investigate the influences of relative parameters.

关键词： state equation differential quadrature approximate laminate model joint coupling matrices thermal stresses.

Morphological design and tunable mechanical properties of 3D spinodal membrane structures:adaptive coarse-grained modelling

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Acta Mechanica Sinica 2024年第8期40卷 166-178页

作者： Yujie Xiang Jie Tian Keke Tang Xianqiao Wang zheng {1. school of {1. engineering and applied mechanics Tongji UniversityShanghai200092China Key Laboratory of AI-aided Airworthiness of Civil Aircraft Structures Civil Aviation Administration of ChinaTongji UniversityShanghai200092China school of school of Environmental CivilAgricultural and Mechanical EngineeringUniversity of GeorgiaAthensGA30602USA school of Science Harbin Institute of TechnologyShenzhen518055China

The spinodal decomposition method emerges as a promising methodology,showcasing its potential in exploring the design space for metamaterial ***,spinodal structures design is still largely limited to regular structures,due to their relatively easy parameterization and *** predicting the mechanical properties of 3D spinodal membrane structure remains a challenge,given that the features of the membrane necessitate adaptive mesh through the modelling *** paper proposes an integrated approach for morphological design with customized mechanical properties,incorporating the spinodal decomposition method and adaptive coarse-grained modeling,which can produce various morphologies such as lamellar,columnar,and cubic ***-periodic parameterβand orientational parameterΘ(θ_(1.,θ_(2),θ_(3))are identified to achieve the optimal goal of anisotropic mechanical *** analysis is conducted to reveal the correlation between the customized spinodal structure and mechanical *** work provides an integrated approach for morphological variation and tuning mechanical properties,paving the way for the design and development of customized functional materials similar to 3D spinodal membrane structures.

关键词： Morphological design Spinodal decomposition Adaptive coarse-grained modeling Mechanical properties Parametric design

SH wave dispersion of the functionally graded piezoelectric hollow cylinder

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SH wave dispersion of the functionally graded piezoelectric ...

Determination of the surface wave dispersion of a coating excited by laser

201.年全国压电和声波理论及器件应用研讨会

作者： Yong-Dong PAN ~(1,*) zheng zhong~2 1 Institute of Acoustics,tongji university,shanghai 2.0092.china 2 school of aerospace engineering and applied mechanics,tongji university,shanghai 2.0092.china

＜正＞The SH wave propagation in a functionally graded piezoelectric hollow cylinder is *** the piezoelectricity of the hollow cylinder,the wave equations and system matrices for state vector are obtained for the SH w... 详细信息

关键词： Functionally graded piezoelectric hollow cylinder SH wave

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Determination of the surface wave dispersion of a coating ex...

FRACTURE ANALYSIS OF A FUNCTIONALLY GRADED STRIP UNDER PLANE DEFORMATION

201.年全国压电和声波理论及器件应用研讨会

作者： Xue-Hang SONG~1 zheng zhong~1 Yong-Dong PAN~(2,*) 1 school of aerospace engineering and applied mechanics,tongji university,shanghai 2.0092.china 2 Institute of Acoustics,tongji university,shanghai 2.0092.china

＜正＞A detailed study is undertaken to analyze the dispersion characteristics of a coating under laser excitation. The surface wave dispersion of the coating is one of its inherent ***-dimensional Fourier transform is applied to the experiment data in the time-space domain into the frequency-wave-number domain,where the peaks form the dispersive ***,the peaks is so flat that it makes the method not very precise.A coherent method is proposed to measure the dispersive curves of *** use of the phase information and magnitude spectrum makes the measuements more precise and stable than traditional noncoherent ***,storage depth of oscillograph affects the precision of dispersion *** technique of obtaining the dispersive curves with high precesion is an efficient tool to solve the inversion problem.

关键词： Coating Phase Spectrum Surface Wave Dispersion

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Acta Mechanica Solida Sinica 2006年第2期19卷 114-121页

作者： cheng {1. zhong zheng school of {1. engineering and applied mechanics Tongji University Shanghai 200092 China Collage of Civil engineering Zhengzhou University Zhengzhou 450002 China

In this paper the plane elasticity problem for a functionally graded strip containing a crack is considered. It is assumed that the reciprocal of the shear modulus is a linear function of the thickness-coordinate, while the Possion＇s ratio keeps constant. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the geometric parameters and the graded parameter on the stress intensity factors and the strain energy release rate are investigated. The numerical results show that the graded parameters, the thickness of the strip and the crack size have significant effects on the stress intensity factors and the strain energy release rate.

关键词： functionally graded materials strip fracture stress intensity factors strain energy release rate

CRACK PROPAGATING IN FUNCTIONALLY GRADED COATING WITH ARBITRARILY DISTRIBUTED MATERIAL PROPERTIES BONDED TO HOMOGENEOUS SUBSTRATE

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Acta Mechanica Solida Sinica 2010年第5期23卷 437-446页

作者： zhanqi {1. Danying Gao zheng zhong school of Civil {1. Zhengzhou University Zhengzhou 450001 China school of {1. engineering and applied mechanics Tongji University Shanghai 200092 China

In this paper, a finite crack with constant length （Yoffe type crack） propagating in a functionally graded coating with spatially varying elastic properties bonded to a homogeneous substrate of finite thickness under anti-plane loading was studied. A multi-layered model is employed to model arbitrary variations of material properties based on two linearly-distributed material compliance parameters. The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. Some numerical examples are given to demonstrate the accuracy, efficiency and versatility of the model. The numerical results show that the graded parameters, the thicknesses of the interfacial layer and the two homogeneous layers, the crack size and speed have significant effects on the dynamic fracture behavior.

关键词： functionally graded material~ moving crack dynamical stress intensity factors multi-layered model

Analysis of a crack in a functionally graded strip with a power form shear modulus

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Analysis of a crack in a functionally graded strip with a po...

ANALYSIS OF TWO DISSIMILAR FUNCTIONALLY GRADED STRIPS CONTAINING INTERFACE CRACK UNDER PLANE DEFORMATION

损伤、断裂与微纳米力学学术研讨会

作者： Jinju Ma~1,zheng zhong~(1,*),Chuanzeng Zhang~2 1 school of aerospace engineering and applied mechanics,tongji university,shanghai 2.0092.china 2 Department of Civil engineering,university of Siegen,Siegen D-57068,Germany

In this paper,the plane strain problem of a crack in a functionally graded strip with a power form shear modulus is *** governing equation in terms of Airy's stress function is solved exactly by means of Fourier *** mixed boundary problem is then reduced to a system of singular integral equations and solved numerically to obtain the stress intensity factors at *** maximum circumferential stress criterion and the strain energy density criterion are respectively employed to predict the direction of crack *** examples are given to show the influence of the material gradation models and the crack sizes on the mode-Ⅰand mode-Ⅱstress intensity *** dependence of the critical kink-angle on the crack size is examined and it is found that the crack kink-angle decreases with the increase of the normalized crack length, indicating that a bigger crack tends to propagate along the direction near the original crack-line while a smaller crack is much easier to extend deviating from the original crack-line.

关键词： Functionally graded material Crack Stress intensity factors Fracture criterion

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Acta Mechanica Solida Sinica 2013年第1期26卷 35-45页

作者： Haiyang Li Xingtao Zhang zhanqi {1. Danying Gao zheng zhong zhengzhou Electromechanic {1. Research Institute school of Civil {1. Zhengzhou University school of {1. engineering and applied mechanics Tongji University

In this paper the plane elasticity problem of two bonded dissimilar functionally graded strips containing an interface crack is studied. The governing equation in terms of Airy stress function is formulated and exact solutions are obtained for several special variations of material properties in Fourier transformation domain. The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. Numerical results show that fracture toughness of materials can be greatly improved by graded variation of elastic modulus and the influence of the specific form of elastic modulus on the fracture behavior of FGM is limited.

关键词： functionally graded materials stress intensity factor Fourier transformation singular integral equations

Modeling of mechanical behaviors for natural fiber reinforced composites under hygrothermal ageing

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Science china(Physics,{1. & Astronomy) 2017年第12期60卷 80-82页

作者： zheng {1. Fang Tian school of Science Harbin Institute of Technology school of {1. engineering and applied mechanics Tongji University

In recent years,natural fiber reinforced composites have been widely applied to various industrial products for their excellent environmental-friendly *** is essential to understand the mechanical properties of natural fiber reinforced composites under their in-service *** with synthetic fibers,the hydrophilicity of natural fibers could result in a much larger quantity of water absorption from the moisture atmosphere,which would have adverse consequences for the durability of natural fiber reinforced composites[1..The environmental temperature would affect the

关键词： reinforced durability moisture consequences friendly ageing constitutive have hydrolysis deterioration