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2010 Vol. 31, No. 2
Published:
论文
109
A Second-Order Cone Linear Complementarity Approach for Contact Problems with orthotropic friction law
Abstract: We propose a linear second-order cone complementarity formulation for the contact problem with orthotropic friction law by the parametric variational principle. Picking up on the analogy with the elastic-perfectly plastic constitutive model, and employing the concept of second-order cone complementary, the contact condition with orthotropic friction law is formulated as a linear second-order cone complementarity condition. Then we reformulate the governing equations of the contact problem as a linear second-order cone complementarity problem (SOCCP) via the parametric variational principle and the finite element method. The SOCCP formulation avoids the polyhedral approximation to the elliptical Coulomb friction cone so that the problem to be solved has much smaller size and the solution has better accuracy. Numerical results are reported for elastic contact problems with orthotropic friction law, which confirm the effectiveness and robustness of the SOCCP formulation.
2010 Vol. 31 (2): 109-118 [
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585
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119
Investigation on fracture characteristics of sandstone after thermal effects through three-bending point experiments
It is very important to investigate fracture behavior of rock after different temperature effects. The aim of this paper is to investigate the influence of temperature on fracture behavior of sandstone through three-point bending test with pre-crack. The paper indicates that the effects of temperature on sandstone fracture behavior are obvious. And the temperature of 125℃ is a threshold temperature. In the temperature point, the average fracture toughness of sandstone reaches maximum, and the crack propagation mode also change. Namely, the intergranular fracture mechanism and the mix fracture mechanism of intergranular and transgranular dominate before and after the effects of 125℃, respectively. In the domain of 100-150℃, the mechanical behavior of sandstone is unstable. The main reasons maybe that the change of pore structure and mechanical behavior of clay material due to the evaporation of internal adsorbed water and interlayer water. From 125℃ to 600℃, the average fracture toughness of sandstone decrease approximately 50%. Some potential reasons, such as the effects of temperature on the consolidation degree between clay and minerals, thermal cracking on sandstone, and the residual stress due to the different thermal property of mineral particles and clay materials after cooling, have been discussed in the paper.
2010 Vol. 31 (2): 119-126 [
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684
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127
The effects of heterogeneous deformation on void growth in FCC crystals
To investigate the influence of crystallographic orientation and deformation mismatch on the growth and coalescence of spherical void, a unit cell was used to address the growth behavior of voids in single crystals and voids located at grain boundary in FCC crystals with the three dimensional crystal plasticity finite element method, which was implemented with the rate dependent crystal plasticity theory as user material subroutine. Simulation results show that the void shape and growth direction significantly depend on the crystallographic orientation, and the growth rate of voids at the grain boundary of the two-grain is faster than that in single crystal. Due to inter-grain heterogeneous deformation, the growth of void located at the grain boundary accelerated, and the material trends to fail by intergranular fracture. With the orientation factor’s difference between the two grains increasing, the void prefers to coalescence along grain boundary.
2010 Vol. 31 (2): 127-132 [
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786
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133
PROGRESSIVE DAMAGE ANALYSIS AND STRENGTH PREDICTION OF 3D FIVE-DIRECTIONAL BRAIDED COMPOSITES
A representative volume element (RVE)-based micromechanical damage model by using the nonlinear finite element method are presented to predict the damage propagation and strength of 3D five-directional braided composites, combined with the averaging methods. By adopting the software ABAQUS, the progressive damage of 3D five-directional braided composites with typical braiding angles were studied subjected to tensile loading.The macroscopic stress-strain curves and ultimate strength of the samples were obtained. Numerical results verify the effectiveness of the model. Effects of braiding angle on the mechanical behavior of 3D five-directional braided composites were discussed in detail. Some valuable conclusions are drawn herein.
2010 Vol. 31 (2): 133-141 [
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637
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142
Thermal Residual Stresses in a Composite with Fiber/Matrix Interphase
The thermal residual stresses distribution in a composite with interphase was analysed in this article. A 3D single fiber model with three phases was established based on the material’s micro structure. Homogeneous and gradient functions were used to simulate the Young’s modulus variations in the interphase region. Single fiber model’s residual stresses was calculated based on mechanics of symmetrical elasticity. The result shows that gradient interphase of T300/epoxy reduces the residual stresses, and close to experimental value by electrical method . Fields superposition method was used to get the coupled stress field in representative volume element(RVE) of close-packed hexagonal structure. This theory is verified by FEA.
2010 Vol. 31 (2): 142-148 [
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676
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149
Stress Wave Propagations in Viscoelastic Specimen during SHPB Tests
The governing partial differential equations describing one-dimensional stress wave propagations within a viscoelastic specimen in a Split Hopkinson Pressure Bar (SHPB) test are established. Coupled boundary conditions at both ends of the specimen are derived by using the characteristic equations in the incident bar and the transmitting bar. Laplace transform of the governing equations turns the group of PDEs into an ordinary differential equation, which is solved analytically with the transformed BCs. The inverse Laplace transform of the solution gives the time histories of stress at arbitrary site. A modified Fixed Talbot (FT) algorithm is proposed to do the inverse transform numerically. Results calculated by using this algorithm agree very well with the results obtained by finite difference simulation of the same problem. This proves the efficiency and accuracy of the developed technique. Using this technique, parametric investigations are conducted to study the influences on the transmitting stress waves of specimen length and material parameters.
2010 Vol. 31 (2): 149-156 [
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639
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157
ISOLATION OF PLANE P WAVES BY DISCONTINUOUS BARRIERS COMPOSED OF A ROW OF ELASTIC HOLLOW PIPE PILES
The lengths of the piles are larger than their diameters, so the vibration isolation of incident plane P waves by the discontinuous barriers composed of a row of elstic hollow pipe piles can be simplified as two-dimensional plane problem. The expansion method of wave functions and Graf’s addition theorem are adopted, the stresses and displacements at the boundaries between the piles and their adjacent soils are considered as continuous and the inner boundaries are free, and then the theoretical solutions are obtained about the vibration isolation. Finally the effects of the piles’ thickness, the modulus ratio of piles to their adjacent soils, the distance between the piles and number of piles on the vibration isolation are studied, and some important conclusions are drawn out, which are that: (1) the isolation effects increase when the piles’ thickness and the distance between the piles deccrease, (2) the isolation effects increase with the modulus ratio of piles to soils, but when the ratio is larger than 500, the isolation effects increase little and are appromimate to those of rigid piles, (3) when the number of piles increase, the best isolation areas increase, and the position with best isolation effects moves forward, which provided theoretical basis for the design of discontinuous barrier for vibration isolation.
2010 Vol. 31 (2): 157-163 [
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613
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164
A New Algorithm for Electromigration Failure Analysis of Metal Interconnects
This paper presents a new algorithm for electromigration (EM) failure analysis based on ANSYS Multi-physics commercial software and FORTRAN codes with considering the four driving forces mechanism which includes the electron wind force, temperature gradient, stress gradient, as well as atomic density gradient. The electric-thermal-structural coupled analysis based on ANSYS multi-physics simulation platform is performed to obtain the current density distribution, the temperature distribution and stess distribution of analysis model. EM atomic density redistribution algorithm is then developed using FORTRAN code to get atomic density distribution of different time. The dynamic simulation of EM void evolution is performed to get failure lifetime based on the criterion of void incubation and propagation. Finally, the comparisons of voids generation through numerical example of SWEAT and CSP structure with the measurement results are discussed.
2010 Vol. 31 (2): 164-172 [
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719
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173
CORRECTNESS VERIFICATION OF THE IMPLEMENTATION OF YIELD CRITERIONS INTO FINITE ELEMENT SOFTWARE
It is necessary to implement the yield criterion we need into the finite element software and verify the correctness of the implementation of the yield criterion. And so far, the method for verifying the correctness of the implementation of the yield criterions has not been reported. In this paper, Yld2000-2d yield criterion is implemented into ABAQUS commercial finite element software. A method which can effectively verify the correctness of the yield criterion implementation is proposed based on strict mechanical deduction. For 5754O aluminum alloy sheet, the correctness of the implementation of Yld2000-2d yield criterion into ABAQUS finite element software is verified.
2010 Vol. 31 (2): 173-180 [
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693
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简报
181
Constibutive relation electromechanical stability analysis of Ogden type dielectirc elastomer with linear permittivity
Any free energy functions can be applied to analyse the stability performance of dielectric elastomer electromechanical coupling system, proposed by Zhao and Suo. In this paper, Mooney-Rivlin elastic strain energy function with two material constants is used to analyse the stability performance of dielectric elastomer electromechanical coupling system. It is coupled with the electric energy density function with linear permittivity to obtain the free energy function of the system. Numerical results are also calculated for further understanding of the dielectric elastomer stability performance and the actuators’ design and fabrication.
2010 Vol. 31 (2): 181-192 [
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1302
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577
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193
The nucleation rate model for microscopic domain evolution of ferroelectric ceramics
A lot of experiments have proved the basic reason of the nonlinear and hysteresis constitutive curve in ferroelectric ceramics is domain switching. The micro domains witching behaviors of ferroelectric ceramics have been studied detailed. According to the physical experimental results and the classic equation of nucleation rate, a nucleation rate model is developed in order to get the evolution equation of the volume fraction of domain switching. The model is compared to nonlinear behaviors of ferroelectric ceramics. It turns out that the model can represent the typical nonlinear electromechanical coupling phenomena. The mechanism of domain switching of the nucleation rate model can further improve the macro phenomenological model.
2010 Vol. 31 (2): 193-197 [
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622
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198
Solving inverse bimodular problems of truss structures via two-level sensitivity analysis
A new smoothed elastic bimodular constitutive relationship is presented, therefore the sensitivity of stiffness matrix with respect to displacement and the sensitivity of displacement with respect to elastic modulus can be obtained conveniently. A FEM and sensitivity analysis based numerical model is developed to solve direct problems of truss structures with dual extensional/compressive modulus, and Newton-Raphson algorithm is employed in the solution process. By utilizing the solutions of direct problems, a two level sensitivity analysis based algorithm is presented for the identification of bimodulus, Gauss—Newton algorithms is used in the identification. Numerical verification with noisy data is provided with satisfactory results.
2010 Vol. 31 (2): 198-204 [
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205
Line sampling method based on saddlepoint approximation for reliability analysis with non-normal random variables
For reliability analysis of non-linear limit state function with non-normal random variables, a novel saddlepoint based line sampling method is presented on the combination of saddlepoint approximation and line sampling. For the structural reliability problem with non-normal variables, traditional line sampling reliability analysis method requires the transformation from the original non-normal variable space into the equivalent standard normal space. This transformation is nonlinear, which tends to increase the nonlinearity of the performance function and difficulty of estimating the failure probability. The presented saddlepoint based line sampling method does not require this nonlinear transformation. By use of saddlepoint approximation to estimate the probability distribution directly for the linear performance function with non-normal variables, and the traditional line sampling method expressing the failure probability of nonlinear performance function as the arithmetic average of a set of failure probabilities of the linear performance functions. The presented method can realize the high precision estimation of the failure probability of non-linear limit state function with non-normal variables. Before employing the saddlepoint based line sampling method, the linear standardized transformation is needed to eliminate the dimensions of variables. The theoretical derivation verifies that the saddlepoint based line sampling method degenerates into traditional line sampling when all the random variables are normally distributed. The results of the illustrations show that the presented method has higher precision than the direct saddlepoint approximation for non-linearperformance function reliability problem.
2010 Vol. 31 (2): 205-210 [
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639
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635
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211
A class of approximate calculation of polar decomposition and the corresponding comparison
Based on the series expansion, the series forms of right stretch tensor in polar decomposition are given, and the different approximate expressions of right strech tensor are obtained by selecting different number of series terms. From the different expressions, the series expansion with the least error is found. The effectiveness of the approximate expression is verified using some simple examples. Compared with the approximate expressions of right strech tensor and rotation tensor proposed by Huang Mojia, the approximate expressions of right strech tensor and rotation tensor given in this paper are of simple forms, high accurate and widely applicability.
2010 Vol. 31 (2): 211-216 [
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631
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