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1.
Bending analysis of thin functionally graded plates using generalized differential quadrature method
A. Fereidoon M. Asghardokht seyedmahalle A. Mohyeddin 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(11):1523-1539
In this paper, the differential quadrature (DQ) method is presented for easy and effective analysis of isotropic functionally
graded (FG) and functionally graded coated (FGC) thin plates with constant Poisson’s ratio and varying Young’s modulus in
the thickness direction. The bending of FG and FGC plates under transverse loading has been studied using the polynomial differential
quadrature (PDQ) and the harmonic differential quadrature (HDQ) methods. A three-dimensional elasticity solution for a moderately
thick FG plate with exponential Young’s modulus is used as the benchmark. Two examples, including a thin FG rectangular plate
and a thin FGC rectangular plate with sigmoidal Young’s modulus, are investigated. The numerical results of PDQ and HDQ methods
reveal good agreement with other solutions. Also, it is shown that the formulations for thin FG plates and homogeneous plates
are similar, except that the plane strain components of the middle surface in FG plates are not zero. 相似文献
2.
Identification of Dynamic (Young’s and Shear) Moduli of a Structural Adhesive Using Modal Based Direct Model Updating Method 总被引:1,自引:1,他引:0
In this paper, mechanical characteristics (Young’s modulus and shear modulus) of an adhesive are identified using modal based
direct model updating method and experimental modal data. The results show that both Young’s and shear moduli of adhesive
are frequency dependent. Also, it is demonstrated that the thickness and length of the adhesive-line have influence on these
properties. All experiments and subsequent identifications are conducted both in bending and shear modes, and it has been
shown that the shear modulus of adhesive is more sensitive to length and thickness variations. The repeatability and consistency
of method is proved through repeating the process several times and with different adherends. 相似文献
3.
I. INTRODUCTION Microelectromechanical systems (MEMS) have achieved impressive progress and become a very area of research. But long-term durability of various MEMS devices requires a fundamental understaof the fatigue and fracture characteristics of su… 相似文献
4.
Quanquan Yang Cun-Fa Gao Wentao Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(8):895-907
This paper is to study the two-dimensional stress distribution of a functional graded material plate (FGMP) with a circular
hole under arbitrary constant loads. With using the method of piece-wise homogeneous layers, the stress distribution of the
functional graded material plate having radial arbitrary elastic properties is derived based on the theory of the complex
variable functions. As examples, numerical results are presented for the FGMPs having given radial Young’s modulus or Poisson’s
ratio. It is shown that the stress is greatly reduced as the radial Young’s modulus increased, but it is less influenced by
the variation of the Poisson’s ratio. Moreover, it is also found that the stress level varies when the radial Young’s modulus
increased in different ways. Thus, it can be concluded that the stress around the circular hole in the FGMP can be effectively
reduced by choosing the proper change ways of the radial elastic properties. 相似文献
5.
Effect of nonhomogeneity on the vibrational characteristics of thin orthotropic rectangular plates of bilinearly varying thickness
has been studied using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. The thickness variation
is taken as the Cartesian product of linear variations along two concurrent edges of the plate. The orthogonal polynomials
in two variables are generated using the Gram-Schmidt process. The nonhomogeneity of the plate material is assumed to arise
due to linear variations in Young’s moduli, shear modulus and density of the plate with the in-plane coordinates. Numerical
results have been computed for four different combinations of clamped, simply supported and free edges. Effect of thickness
variation together with varying values of aspect ratio and nonhomogeneity on the natural frequencies is illustrated for the
first three modes of vibration. Three dimensional mode shapes have been presented. Comparison has been made with the known
results. 相似文献
6.
This paper presents the effect of non-homogeneity of the material of plate structures on the vibration frequencies. The non-homogeneity
of the plate is characterized by taking a variety of combinations of linear as well as quadratic variations in the Young’s
modulus and density of the material. Boundary characteristic orthogonal polynomials using Gram-Schmidt procedure have been
employed in the Rayleigh Ritz method. The results have been included for the first few frequencies of the plate element for
all the boundary conditions viz. clamped, simply supported and free. Related Tables and graphs are incorporated to show the
effect of the non-homogeneity parameter on the frequencies of the vibration of elliptic and circular plates. 相似文献
7.
A general stress-optic law in a plate made of a single crystal with birefringence is developed, the plate has an arbitrary
crystallographic direction. From the general stressoptic law, a condition for obtaining stress distributions in the plate
under a plane stress state is derived. Some optical and mechanical properties when the plate is used as a photoanisotropic
model are also explained. Experiments on silicon beams in pure bending are performed by using an infrared photoelastic method.
Experimental results show that the stress-optic law is valid. The optical and mechanical properties of silicon beams are shown
in tables. 相似文献
8.
基于精化锯齿理论和新修正偶应力理论,建立了能够准确预测功能梯度夹心微板挠度、位移和应力的静弯曲模型。为了描述微板不同方向上的尺度效应,将两个正交材料尺度参数引入本文模型。以受双向正弦载荷作用的简支板为例,探究了夹心微板弯曲行为中尺度效应对结构刚度的影响。算例结果表明,当微板几何参数与材料尺度参数接近时,基于本文模型所测微板的最大弯曲挠度、局部位移和应力均小于传统精化锯齿理论给出的结果,捕捉到了尺度效应;尺度效应随着微板几何尺寸的增大而逐渐减弱,当微板几何尺寸远大于材料尺度参数时,尺度效应消失。此外,板的跨厚比和功能梯度变化指数也会对尺度效应产生一定影响。 相似文献
9.
Bending analysis of micro-sized beams based on the Bernoulli-Euler beam theory is presented within the modified strain gradient
elasticity and modified couple stress theories. The governing equations and the related boundary conditions are derived from
the variational principles. These equations are solved analytically for deflection, bending, and rotation responses of micro-sized
beams. Propped cantilever, both ends clamped, both ends simply supported, and cantilever cases are taken into consideration
as boundary conditions. The influence of size effect and additional material parameters on the static response of micro-sized
beams in bending is examined. The effect of Poisson’s ratio is also investigated in detail. It is concluded from the results
that the bending values obtained by these higher-order elasticity theories have a significant difference with those calculated
by the classical elasticity theory. 相似文献
10.
I. Yu. Tsvelodub 《Journal of Applied Mechanics and Technical Physics》2008,49(1):129-135
A variant of the multimodulus elasticity theory for isotropic materials is proposed under the assumption that the shear modulus
in Hooke’s law is a constant and the volume modulus depends on the sign of the first invariant of the stress tensor. Plane
problems (plane strain and generalized plane stressed state) and problems of plate bending are considered. Some examples are
given.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 157–164, January–February, 2008. 相似文献
11.
Refractory castables exhibit very low fracture strain levels when subjected to tension or bending. The main objective of this
work is to show that 3-D digital image correlation (3-D DIC) allows such low strain levels to be measured. Compared to mechanical
extensometer measurements, 3-D DIC makes it possible to reach similar strain resolution levels and to avoid the problem of
position dependance related to the heterogeneous nature of the strain and to strain localization phenomena. First, the 3-D
DIC method and the experimental set-up are presented. Secondly, an analysis of the 3-D DIC method is performed in order to
evaluate the resolution, the standard uncertainty and the spatial resolution for both displacement and strain measurements.
An optimized compromise between strain spatial resolution and standard uncertainty is reached for the configuration of the
experimental bending test. Finally, the macroscopic mechanical behavior of a fiber reinforced refractory castable (FRRC) is
studied using mechanical extensometry and 3-D DIC in the case of tensile and four-point bending tests. It is shown that similar
results are obtained with both methods. Furthermore, in the case of bending tests on damaged castable, 3-D DIC results demonstrate
the ability to determine Young’s modulus from heterogeneous strain fields better than by using classical beam deflection measurements. 相似文献
12.
In the present research, microstructure of akind of limnetic shell (Hyriopsis cumingii) is observed and measured by using the scanning electron microscopy, and mechanical behavior experiments of the shell nacre are carried out by using bending and tensile tests. The dependence of mechanical properties of the shell nacre on its microstructure is analyzed by using a modified shear-lag model, and the overall stress-strain relation is obtained. The experimental results reveal that the mechanical properties of shell nacre strongly depend on the water contents of the limnetic shell. Dry nacre shows a brittle behavior, whereas wetting nacre displays a strong ductility. Compared to the tensile test, the bending test overestimates the strength and underestimates the Young's modulus. The modified shear-lag model can characterize the deformation features of nacre effectively. 相似文献
13.
In this article, a new method based on the detection of the second harmonic of the displacement signal to determine mechanical properties of materials from dynamic nanoindentation testing, is presented. With this technique, the Young’s modulus and hardness of homogeneous materials can be obtained at small penetration depths from the measurement of the second harmonic amplitude. With this innovative method, the measurement of the normal displacement is indirectly used, avoiding the need for very precise contact detection. Moreover, the influence of the tip defect and thermal drift on the measurements are reduced. This method was used for dynamic nanoindentation tests performed on fused silica and on an amorphous polymer (PMMA) because these materials are supposed not to exhibit an indentation size effect at small penetration depths. The amplitude of the second harmonic of the displacement signal was correctly measured at small depths, allowing to calculate the Young’s modulus and the hardness of the tested materials. The mechanical properties calculated with this method are in good agreement with values obtained from classical nanoindentation tests. 相似文献
14.
The effects of fluid viscosity on the kinematics of a small swimmer at low Reynolds numbers are investigated in both experiments
and in a simple model. The swimmer is the nematode Caenorhabditis elegans, which is an undulating roundworm approximately 1 mm long. Experiments show that the nematode maintains a highly periodic
swimming behavior as the fluid viscosity is varied from 1.0 to 12 mPa s. Surprisingly, the nematode’s swimming speed (~0.35 mm/s)
is nearly insensitive to the range of fluid viscosities investigated here. However, the nematode’s beating frequency decreases
to an asymptotic value (~1.7 Hz) with increasing fluid viscosity. A simple model is used to estimate the nematode’s Young’s
modulus and tissue viscosity. Both material properties increase with increasing fluid viscosity. It is proposed that the increase
in Young’s modulus may be associated with muscle contraction in response to larger mechanical loading while the increase in
effective tissue viscosity may be associated with the energy necessary to overcome increased fluid drag forces. 相似文献
15.
Xian-Fang Li Bao-Lin Wang Jie-Cai Han 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(10):1197-1212
The higher-order theory is extended to functionally graded beams (FGBs) with continuously varying material properties. For
FGBs with shear deformation taken into account, a single governing equation for an auxiliary function F is derived from the basic equations of elasticity. It can be used to deal with forced and free vibrations as well as static
behaviors of FGBs. A general solution is constructed, and all physical quantities including transverse deflection, longitudinal
warping, bending moment, shear force, and internal stresses can be represented in terms of the derivatives of F. The static
solution can be determined for different end conditions. Explicit expressions for cantilever, simply supported, and clamped-clamped
FGBs for typical loading cases are given. A comparison of the present static solution with existing elasticity solutions indicates
that the method is simple and efficient. Moreover, the gradient variation of Young’s modulus and Poisson’s ratio may be arbitrary
functions of the thickness direction. Functionally graded Rayleigh and Euler–Bernoulli beams are two special cases when the
shear modulus is sufficiently high. Moreover, the classical Levinson beam theory is recovered from the present theory when
the material constants are unchanged. Numerical computations are performed for a functionally graded cantilever beam with
a gradient index obeying power law and the results are displayed graphically to show the effects of the gradient index on
the deflection and stress distribution, indicating that both stresses and deflection are sensitive to the gradient variation
of material properties. 相似文献
16.
A new micro-system for the on-chip mechanical characterization of thin polysilicon films was designed, fabricated and tested.
The device contains a micro electro-thermo mechanical actuator which is able to load a specimen until rupture in purely tensile
conditions. The elongation of the specimen is measured during the test through the capacitance variation of a set of parallel
plate capacitors, while the force in the specimen can be computed starting from the applied voltage. Through a unique loading
cycle in which the voltage is first increased until specimen rupture and then decreased, the new device allows for the determination
of the specimen elastic stiffness and nominal tensile strength. The obtained experimental results were compared with values
previously obtained by means of different on-chip test devices. Multi-physics FE simulations were performed for additional
comparison with analytical formulae used in the data reduction procedure and with the obtained experimental results. 相似文献
17.
J.M. Antunes J.V. Fernandes N.A. Sakharova M.C. Oliveira L.F. Menezes 《International Journal of Solids and Structures》2007,44(25-26):8313-8334
The main difficulty with the characterization of thin coatings using depth-sensing indentation tests is related to the determination of the contributions of the substrate and the film to the measured properties. In this study, three-dimensional numerical simulations of the Vickers hardness test are used in order to examine the influence of the elastic and plastic properties of the substrate and the film on the composite’s Young’s modulus results. The hardness of the film is equal to or higher than the substrate hardness. A study of the stress distributions and the indentation geometry of composites, film/substrate, was performed, taking into account the relative mechanical properties of the film and substrate. In addition, stress evolution during indentation was studied, in order to quantify the critical indentation depth under which the substrate is not elastically deformed. The accurate evaluation of the Young’s modulus of the films using weight functions is also examined: some of these have previously been proposed and one was introduced for this study. Two different fitting procedures were used to compare the results obtained from eight fictive film/substrate combinations using six weight functions. The first procedure, commonly used, considers the substrate’s modulus as a known parameter in the fitting process. In the second, the film and the substrate’s modulus are considered as unknown variables that are calculated simultaneously during the fitting process. The validity of the conclusions obtained using the fictive materials was checked by applying the weight functions to four real composites. 相似文献
18.
In this paper, the radial basis function neural networks (RBFNN) was applied to the problem of identifying dynamic Young’s
modulus and damping characteristic of a structural adhesive, using modal data. To identify Young’s modulus from undamped model,
an appropriate RBFNN using modal data (mode shape and natural frequency) in each mode is developed. Based on a previous work,
in order to identify loss factor, two approaches adopted in the identification process. In the first one, a two stage RBFNN
is developed. In stage I, Young’s modulus is identified from undamped model and in stage II using the results of stage I an
appropriate RBFNN is developed in each mode for identification of loss factor by implementing real parts of eigenvalues of
damped model. In the second approach, a one stage RBFNN is developed using real and imaginary parts of eigenvalues of damped
model to identify Young’s moduli and loss factors simultaneously. The repeatability and consistency of the method is proved
by repeating the identification process for several times. The validity of results is proved by comparing the results with
those identified in a previous work. 相似文献
19.
Lihua Jin 《Journal of the mechanics and physics of solids》2010,58(11):1907-1927
Liquid crystal elastomer is a kind of anisotropic polymeric material, with complicated micro-structures and thermo-order-mechanical coupling behaviors. In this paper, we propose a method to systematically model these coupling behaviors. We derive the constitutive model in full tensor structure according to the Clausius-Duhem inequality. Two of the constitutive equations represent the mechanical equilibrium and the other two represent the phase equilibrium. Choosing the total free energy as the combination of the neo-classical free energy and the Landau-de Gennes nematic free energy, we obtain the Cauchy stress-deformation gradient relation and the order-mechanical coupling equations. We find the analytical homogeneous solutions of the deformation for the typical mechanical loadings, such as uniaxial stretch, and simple shear in any directions. We also compare the compression behavior of prolate liquid crystal elastomers with the stretch behavior of oblate liquid crystal elastomers. As a result, the stress, strain, temperature, order parameter, biaxiality and the direction of the director of liquid crystal elastomers couple with each other. When the prolate liquid crystal elastomer sample is stretched in the direction parallel to its director, the deviatoric stress makes the mesogens more order and increase the transition temperature. When the sample is sheared or stretched in the direction non-parallel to the director, the director of the liquid crystal elastomer will rotate, and the biaxiality will be induced. Because of the order-mechanical coupling, under infinitesimal deformation, liquid crystal elastomer has anisotropic Young’s modulus and zero shear modulus in the direction parallel or perpendicular to the director. While for the oblate liquid crystal elastomers, the stretch parallel to the director will cause the rotation of the director and induce the biaxiality. 相似文献
20.
In material nano- and micro-indentation research, it is well accepted to use the initial unloading stiffness of the load-depth
curve to determine the material’s Young’s modulus. This approach requires the use of high-precision displacement sensors in
order to calibrate the loading apparatus system compliance and thus obtain the load-depth curve accurately. In this research,
using a transparent spherical indenter coupled with a multi-partial unloading technique, we present a simpler approach to
measure the material’s Young’s modulus. Experimental results of several metallic alloys and related discussions are presented. 相似文献