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2013 Vol. 34, No. 2
Published:
109
Snap-through and pull-in behaviors of MEMS devices with the initial configurations
A microstructure-dependent large deformation electrodynamic model of MEMS devices with the initial configurations is established in an arc coordinate system based on the large deformation theory of the curved beam. The differential quadrature method (DQM) is applied to discretize the nonlinear mathematical model in the special domain. Afterwards, a set of the first order nonlinear differential & algebra system equations can be derived. The Petzold-Gear BDF method is used to solve the first order nonlinear differential & algebra system equations in the temporal domain. The transient micro-electromechanical behaviors, including snap-through and pull-in, of the MEMS switches under the electric force are studied in detail, and compares the obtained results with the existing experiment.
2013 Vol. 34 (2): 109-116 [
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117
Dynamic Fracturing of the Intermetallic Compound Layer in Solder Joints Under Impact Drop Loading
The great difference of the failure modes between lead-containing and lead-free solder joints subjected to drop impact loading has not been well understood. In this paper, a feasible finite element approach is proposed to model the cracking behavior of lead-containing and lead-free solder joints under drop impact loading. In the model, the damage at the intermetallic compound layer/solder bulk interface is calculated by the cohesive zone model, and the failure in the intermetallic compound layer is evaluated by computing the energy release rate. The numerical simulation result shows that, for the lead-containing Sn37Pb solder joint, the damage in the intermetallic compound layer/solder bulk interface initiates earlier and much greater than that in the lead-free Sn3.5Ag solder joint. This damage can relieve the stress in the intermetallic compound layer and reduce the risk of intermetallic compound layer fracturing in the lead-containing Sn37Pb solder joint.
2013 Vol. 34 (2): 117-124 [
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351
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125
Research on Rubbing Dynamic Behavior of Hub-Plate with Analytical Method
For rubbing faults caused between large rotating machinery blades and casing, a dynamic model of cantilever plate attached to a rotating rigid hub is established. The equation of motion is derived to include centrifugal stiffening effect by using Hamilton's principle. Based on the experimental and finite element analysis results of rubbing forces, approximate mathematical expressions are proposed. And analytical solutions for hub-plate system are obtained. Compared with the experimental results, models and methods are proved to be accurate. Their respective applicable conditions of the blade's beam and thin plate model are discussed. The influence of rotation speed on rubbing dynamic response is analyzed. It is showed that analytical solutions are accurate, and the thin plate model which can fully reflect the dynamic characteristics of a blade in the case of various rubbing is more accurate and reliable than the beam. Furthermore, as rotation speed increase, rubbing force causes amplitude of the thin plate in free end sudden change, which is important reason for loss corner faults or even break failure of blades in engineering.
2013 Vol. 34 (2): 125-132 [
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247
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133
Shakedown of three-dimensional structures under cyclic loading with the direct analysis method
A direct method for three-dimensional structures under cyclic loading has been established based on elastic-linear-kinematic-hardening materials. An incremental loading method has been adopted to construct loading space, and the range of back stress is bounded based on some research results. The direct method consists of an operator split technique, which transforms the elastic-plastic problem into a purely elastic problem and a residual problem with prescribed eigenstrains. The eigenstrains are determined using an incremental projection method. The shakedown limited, the residual stress and residual strain of structures under shakedown conditions are obtained. The direct method is applied to rolling-sliding contact and three-dimensional holed plate, and the computing results are in agreement with reference’s results.
2013 Vol. 34 (2): 133-139 [
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290
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140
Analysis of elastic properties of 2D triaxial braided composites
A geometrical model was proposed for the 2D triaxial braided composites with the consideration of the undulation, the twist and the spatial interlacing of the yarns. Based on the volume-averaged method, an analytical model was developed for the prediction of engineering constants of 2D triaxial braided composites. Furthermore, a finite element model was established for the analysis of the mechanical properties by introducing an improved periodical boundary condition and the mesoscopic entity structure of 2D triaxial braided composites. The predication results of both models show good agreements with experimental results. The mesoscopic stress distribution of the material under loads was investigated and the influences of braiding parameters on the elastic constants were discussed. It shows that axial mechanical property is reinforced and the stresses are well-distributed; braid angle and fiber volume fraction have great influence on material’s elastic properties.
2013 Vol. 34 (2): 140-151 [
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375
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152
The Derivation of governing equations for dynamic buckling of structures when dynamic buckling and stress wave propagating are coupling
Because of the coupling of dynamic buckling and stress wave propagating, the traveling time of the stress wave becomes one of the parameters in dynamic buckling caused by stress waves. So the real displacement and the adjacent displacement of the dynamic buckling caused by stress waves occur at different time and different area, which make it unsuitable for using of the integral variational principle in derivation of governing equations for dynamic buckling of structure under compression wave; By use of the conservation law of energy transformation in the instant course of buckling, the governing equations, boundary conditions and supplementary restraint-equation at the compression-wave front of column under elastic compression wave are derived; At last, the physical meaning of the supplementary restraint-equation is studied, and the appearance of the supplementary restraint-equation is attributed to the coupling of dynamic buckling and stress wave propagating.
2013 Vol. 34 (2): 152-157 [
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275
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158
Numerical simulation of acoustic-elastic interaction based on multi-time-step unstructured finite volume time domain method
An improved unstructured finite volume time domain method is presented to solve the acoustic-elastic interaction problems. The computational domain is divided into acoustic and elastic sub-domains and the interaction between them is implemented by interface boundary conditions. The quadrilateral element, which is treated as the bilinear element while considering the linear term and the constant term, and the triangular element are employed to deal with mixed grid problems. The stability criterions are provided for the quadrilateral element and the triangular element respectively for the acoustic wave equation. Different time steps are adopted for different sub-domains which could improve the efficiency of the present method. One elastic wave problem and two acoustic-elastic interaction problems are solved. According to the comparisons between the calculated results and the published results, the improved method can treat the acoustic-elastic interaction problem effectively and accurately with good numerical stability.
2013 Vol. 34 (2): 158-168 [
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219
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169
Analysis on Thermal Stress Field at the moment of Crack Prevention by using Electromagnetic Heating in Metal Component with Elliptical Embedding Crack
Theoretical analysis is made on the thermal stress field at the time of pulse current discharge in a metal structure with an elliptical embedding crack. In finding the thermal stress field, theories of heat conduction and unsteady thermal stress are used. It can be found from the formula for solving the thermal stress field that thermal stress field of the crack tip at time of pulse current discharge is formed, and thermal pressure field can effectively inhibit the crack propagation. And taking an example of Cr12MoV die steel with elliptical embedding crack, distribution of thermal stress field at time of pulse current discharge is calculated. The study provides a theoretic basis to the applications of stopping spatial crack with electromagnetic heating.
2013 Vol. 34 (2): 169-173 [
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233
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174
Complex Variable Method for Axisymmetric Problem of Linear Viscoelasticity involving Time-dependent Boundary Regions
This paper presents the complex variable method for viscoelastic problem which boundaries are varied with time. Laplace transformation is introduced to complex variable method to solve the axisymmetric problem of viscoelasticity. Stress and displacement fields, and boundary conditions are expressed by two analytical functions in terms of time and space. And coefficients in analytical functions can be determined by the boundary conditions. The equations about the coefficients are generally in integral form, but analytical solutions can be obtained in special cases. For the axisymmetric problems of stress, displacement or mixed boundary, the corresponding coefficients are determined exactly by boundary conditions and analytical solutions of displacement and stresses are given also. As an application example, Boltzmann viscoelastic model is employed. The solutions show that stresses and displacements are correlated with boundary variation process. The method in this paper can be applied to axisymmetric problems with random variation of inner or outer radius. In addition, problems with asymmetric load or non-circular section can be solved similarly.
2013 Vol. 34 (2): 174-180 [
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244
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181
Prediction of elastic properties of 2.5D self-healing C/SiC composite
The plane elastic modulus of self-healing 2.5D C/SiC composite (2.5D-C/SiC ) were studied by experiment. According to the micro-structure characteristic of composite, the prediction model of elastic modulus of 2.5D-C/SiC was founded. The results agreed with the experiments very well, the model and calculation method were proved to be right. As the parameters， including knit angle of warp, the number of fiber in fiber bundle and the number of layers the warp crossed, increased respectively, the variation tendency of four parameters, including the volume fraction of weft, the volume fraction of warp, the volume fraction of the whole fiber and the elastic modulus, were obtained. As the total volume fraction of silicon carbide and boron carbide was a constant, the variation tendency of elastic modulus was obtained with the ratio of boron carbide and silicon carbide (α) increasing.
2013 Vol. 34 (2): 181-187 [
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226
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188
Optimization Design of Artificial Muscle Actuator by Parameters
As a class of materias in the family of smart materias, electroactive polymers (EAPs) have attracted much attention recently due to their many unique attributes such as large strain, fast response, high energy-converting efficiency etc. in response to an applied voltage. These attributes make the EAPs promising for broad applications as actuators, sensors as well as energy harvesters in engineering. However, because of the nonlinearity of equations of states, and diverse modes of failure caused by the combination of force and voltage, modeling and designing electroactive polymer transducers have been challenging. In this paper, we focuse on investigating the opimization design of a specific actuator presented by the Artificial Muscle Inc.. The essential part of the actuaror was made of a layer of membrane of dieledtric elastomers, a specific class of EAPs. Under the action of applied force and voltage, the actuator deforms into an out-of plane axisymmetric shape. The mechanical model characterizing the out-of plane axisymmetric large deformation of the actuator is established and the corresponding state equations are formulated. The effects of initial prestretches on the thickness of the membrane, stretches, stresses and electric field are obtained and illustrates graphically. The results show that the electric field in the membrane tends to be uniform under certain set of initial prestretches. The method proposed here provides basic analysis pattern for optimization design for such actuators.
2013 Vol. 34 (2): 188-193 [
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317
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194
Study on the constitutive model of metal sheet under the second order size effect in hydraulic bulge
The size effect has been the major subject in the research of micro forming. For the phenomena of the stress change in the metal hydraulic bulge experiment could not be explained properly by the classical plasticity theory, a new constitutive mode based on the strain gradient theory is built to study the size effect. Based on the model，the influences of the thickness of metal sheet and the die diameter on the stress in hydraulic bulge experiment is studied. Compared with the experiment, the stress under the second order size effect can be described well by theoretical analysis basing on the model. And its rationality is testified.
2013 Vol. 34 (2): 194-199 [
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243
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200
Estimation of structural fatigue lifetime under fuzzy constraints set
In order to overcome the limitations of the ordinary convex set in expressing the uncertainty of the actual parameters, a fuzzy set model for fatigue life parameters and method for fatigue life estimation were proposed. The scale parameter of the hyper ellipsoid model was considered to be a positive fuzzy number. The inner and outer ellipsoid model on the basis of the interval model were the inside and outside edge the fuzzy set, and the membership function of the scale parameter was determined. Thus the fuzzy constraint set for fatigue life was built. Based on the Taylor series and Lagrange multiplier method, an approach for estimating the extreme values of fatigue lifetime in the ordinary set was proposed. The fuzzy maximal set and fuzzy minimal set were constructed. Through the normalization of the hyper ellipsoid model and spherical coordinate conversion, the sample points inside the fuzzy set can be extracted and estimation of fatigue life under fuzzy constraints can be realized. In a project example, the proposed method was compared with the convex set method and the probabilistic method. The results illustrated that the fuzzy set method is closer to the engineering practice and can provide more reasonable solutions, so it is a development and improvement of previous methods.
2013 Vol. 34 (2): 200-204 [
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199
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205
Effective Stress Model for Fatigue Life Distribution of Notched Specimen
The effective stress model for predicting the fatigue life distribution of notched specimens from fatigue life test data of smooth specimens is developed in this paper. In this model, the possible crack initiation surface of the notched specimen is separated into many elements and the surface is considered as a series model of these elements. Thus, according to the series failure model, the fatigue strength failure probability of the notched specimen can be calculated from that of the elements, which can be determined from the fatigue strength failure probability of the smooth specimen by using the weakest-link theory. In the formula of the notched specimen fatigue strength failure probability, the parameter of effective stress is introduced. Employing this parameter to refer to the fatigue life test data of smooth specimens would lead to the fatigue life distribution of notched specimens. This model reflects the influence of both stress gradient and component size on the notched specimen fatigue life distribution. An example of centre hole notched LY12CZ specimens was accomplished. The predicted result is in good agreement with the test result, which shows that this method is effective and practical.
2013 Vol. 34 (2): 205-212 [
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230
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