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2013 Vol. 34, No. 6
Published:
论文
541
Three Dimensional Numerical Simulation for Mechanical Behavior of Carbon Black Filled Rubber Composites
Based on the hypothesis of periodic well-distributed microstructure of carbon black filled rubber composites, three-dimensional Representative Volume Elements containing multi-sphere particles randomly distributed have been generated using a new modified Random Sequential Adsorption algorithm, and the macro mechanical properties of the carbon black filled rubber composites have been studied and analyzed by the micromechanical finite element method. The research shows that the models generated by the modified Random Sequential Adsorption algorithm are more suitable for finite element discretization and the simulations can describe the reality better by the periodic boundary conditions. It’s also shown that the modulus of the rubber composite is increased considerably with the introduction of carbon black filler particles, and the effective elastic modulus of the rubber composite is increased with the increase of the particle volume fraction. By comparison, it is shown that the results of the predictions on the stress-strain behavior and the effective elastic modulus of the rubber composite made with this three-dimensional numerical model containing multi-sphere particles randomly distributed are consistent well with the experimental results, which demonstrate that this model can be used for simulation analysis of effective properties of the carbon black filler particle reinforced rubber matrix composites.
2013 Vol. 34 (6): 541-549 [
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436
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550
Adaptability of Four Strength Criterions in Polymer Bonded Explosives Strength Analysis
Strength criterion is an important component in explosive failure mechanics, and is also the basis of appraising the supporting capacity of explosive parts. Two types of polymer bonded explosives (PBXs), HMX-based PBX and TATB-based PBX, are employed. An end-bounded cylinder collapse method, based on uniaxial loading technique, is proposed to test strength failure under complex stress states. The stress field is presented according to finite element simulation, and the adaptability of criterions in PBXs’ strength analysis is illustrated based on principal stresses of initial failure position at last. Among these four criterions, Mohr-Coulomb criterion has the best precision with a error less than 15%, Twin-shear criterion and Drucker-Prager criterion take second place, Uniaxial-strength criterion is relatively poor. On the other hand, Uniaxial-strength criterion has the best safety threshold with a margin more than 75%, Mohr-Coulomb criterion, Twin-shear criterion and Drucker-Prager criterion follow. In a word, Mohr-Coulomb criterion can predict the apparent strength upper limit of HMX-based PBX and the lower limit of TATB-based PBX, whose upper limit can be predicted by Twin-shear criterion.
2013 Vol. 34 (6): 550-556 [
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315
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557
INFLUENCE OF SPAN ON THE RESPONSE AND DAMAGE OF COMPOSITE LAMINATE UNDER LOW-VELOCITY IMPACT INDUCED BY LARGE-MASS AND INTERMEDIATE-MASS
This paper presents the results of numerical investigation concerning span on the responses and damage of composite laminates subjected to low-velocity impact. Three full 3-D composite laminate models of different span are developed using ABAQUS finite element code. Impact responses and damage of these composite laminates under large-mass impact and intermediate-mass impact are investigated. In the large-mass impact, the response of composite laminates is quasi-static, and the influences of span on the peak contact force, the impact duration and delamination are simple and evident. While in the intermediate-mass impact, the responses of the laminate are complex, because the vibrations of the plate are significant and result in the separation of impactor and plate. Special analysis should be taken out for such problems. The influence of mass level on the impact responses are analyzed with ratio between fundamental vibration period and contact duration.
2013 Vol. 34 (6): 557-561 [
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267
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562
THE CONSTRUCTION OF OPERATOR CUSTOM-DESIGN WAVELET FINITE ELEMENTS AND ADAPTIVE ANALYSIS OF ELASTIC PLATES
A new construction method of operator custom-design wavelet finite elements is proposed for analyzing elastic plate problems. The superiority of the method is the construction of decoupling operator custom-design wavelet bases according to the requirements of engineering problems, which leads to highly sparse multiscale system stiffness matrix along diagonal line. The independence and fast computation on each level using the proposed algorithm are realized and the computational efficiency of system of equations is much improved. A multiresolution Lagrange finite element space and multiscale computation theory are constructed. The building method and decoupling condition of operator custom-design wavelet finite element are presented for the elastic plate problems based on stable completion. An adaptive operator custom-design wavelet finite element algorithm is proposed according to two-level relative error estimation. Numerical examples show that the operator custom-design wavelet finite element method is accurate and efficient for solving elastic plate problems.
2013 Vol. 34 (6): 562-570 [
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292
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571
A MODIFIED LOW CYCLE FATIGUE DAMAGE MODEL FOR METALS
Fatigue failure is one of the most common failure modes of metal materials and structures. In this paper, a modified low cycle fatigue damage law is presented, based on the continuum damage mechanics and energy principle, which considers the effects of plastic hardening and microdefects closure into damage evolution. To predict the fatigue failure of metal materials, the modified damage model is incorporated into the commercial finite element platform ABAQUS/ Explicit through a user material subroutine UMAT. In addition, the validity and applicability of this model are examined by comparing the numerical results with the experimental data of aluminum alloy 7050-T7451.
2013 Vol. 34 (6): 571-578 [
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432
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579
Dynamic Green’s function for three-dimensional concentrated loads in the interior of viscoelastic layered half-space—Modified Stiffness Matrix Method
This paper presents a new solution techniques—Modified Stiffness Matrix Method for the dynamic response under concentrated load embedded in three-dimensional viscoelastic layered half space, combined with the Hankel integral transform approach. Based on the potential function theory, this kind of three-dimensional problem can be broken down to two two-dimensional problem of in-plane response (P-SV waves) and anti-plane response( SH waves) respectively. Similar to principle of the displacement method in structural mechanics, the up and bottom surfaces of the force layer are fixed firstly, and the reaction forces at two fixed ends can be obtained by superposition of particular and homogeneous solution of the wave equation. Then loosen the two “fixed end constraint”, using direct stiffness method to get the displacement of each layer surface. In the layer imposed by the load, the Green’s function is decomposed of the particular solution, the homogeneous solution and the reaction solution, in which the particular solution can be impaled by the analytical solution in the whole space. With this method, the convergence problem of improper integral can be solved with Sources and receivers at close or same depths. Finally, this method is proved to be efficient and accurate for both low frequency and high frequency dynamic problems by numerical examples.
2013 Vol. 34 (6): 579-589 [
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289
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简报
590
A NOVEL FINITE ELEMENT ANALYSIS OF STRESSES NEAR APEX OF A BI-MATERIAL WEDGE SUBJECTED TO THERMAL LOADING
A super wedge tip element for application to bi-material wedge is develop utilizing the numerical stress and displacement field eigen-solutions based on an ad hoc finite element eigenanalysis method. Singular stresses near apex of arbitrary bi-material wedges under thermal loading can be obtained from the super wedge tip element. Different from the super wedge tip element for pure mechanical loading, the thermal-mechanical coupling behavior is considered in the expression of total potential functional, and the thermal-mechanical stress field is decomposed as singular terms and non-singular terms in which the singular terms include the homogeneous solutions of thermal and mechanical loadings. The validity and applicability of this novel element are established through existing asymptotic solutions and conventional detailed finite element analysis. All numerical examples show that the novel finite element method yields satisfactory solutions with few elements, and is applicable to the problem of multiple singular points.
2013 Vol. 34 (6): 590-597 [
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289
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598
Refined Theory of Axisymmetric Circular Cylinder in One-dimensional Hexagonal Quasicrystals
The refined theory of axisymmetric cylinder was extended to axisymmetric cylinder in one-dimensional (1D) hexagonal quasicrystals (QCs). The refined theory of axisymmetric cylinder is derived without ad hoc assumptions,which yields Bessel’s function and the general solution of 1D hexagonal QCs. First, According to the Bessel’s function , we can get the expressions of all the phonon and phason displacements and stress components by the three functions with single independent variable. Based on the nonhomogeneous boundary conditions, the refined equation for the cylinder is derived directly. And we can get the approximate solutions which burdened by a circular cylinder under radial direction surface through dropping terms of high order.
2013 Vol. 34 (6): 598-601 [
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256
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602
The effects of the internal pressure on the evolution of microcracks by multi-physical fields induced surface diffusion
Based on the theory of surface diffusion, a finite element method is developed to simulate shape evolutions of intragranular microcracks in metal materials due to internal pressure, stress field, electric field and thermal gradient induced surface diffusion. The results show that there is a critical value for a given aspect ratio . When , the microcrack will evolve into a cylinder directly. When , the microcrack will be divided into two right-and-left or lower-and-upper microcracks. The cylinderization time of the microcrack increases with the internal pressure increasing, while the splitting time decreases. Besides, the internal pressure is conducive to the microcrack splitting. There is a critical value of pressure for when , and are given. If , the microcrack propagation firstly appears at its lower-and-upper side with the increasing of and . The internal pressure has little influence on critical value when MPa.
2013 Vol. 34 (6): 602-606 [
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291
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511
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607
Effects of initial stresses on circumferential waves in unidirectional cylindrical curved plates
In the context of “Mechanics of Incremental Deformations”, the circumferential wave characteristics in unidirectional cylindrical curved plates under uniform initial stresses in the radial and axial directions are investigated. The Legendre polynomial series method is used to solve the coupled wave equation. Two different fiber directions, the circumferential direction and the axial direction, are discussed respectively. The effects of the initial stresses on the circumferential Lamb-like waves and on the circumferential SH waves are investigated, respectively. Numerical results show they are quite distinct. Moreover, the effects of the initial stress in the axial direction are very different from those in the radial direction, both on the dispersion curves and on the displacement and stress distributions.
2013 Vol. 34 (6): 607-613 [
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242
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568
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614
Uncertainty Calculation in Frequency Spatial Domain Decomposition Modal Parameters Identi?cation Method
Operational modal parameters identification is output only modal analysis method. The modal parameters obtained from ambient vibration are subject to statistical uncertainty. The uncertainty can be evaluated by its statistical characteristics. Variance calculation in frequency spatial domain decomposition is illustrated based on sensitivity analysis of the algorithm. The calculation flow includes four steps: (1) Estimating covariance of power spectrum density (2) Calculating variance of enhanced power spectrum density. (3) Calculating poles covariance (4) Calculating modal parameters variance. Finally, a simulated case of four DOFs system and a measurement case of Zhang Jia Gang bridge are used to validate the accuracy and practicability of the presented calculation method.
2013 Vol. 34 (6): 614-619 [
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279
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620
Viscoelastic analysis of the stress and displacement in tunnel surrounding rock and support during the process of tunnel construction
Li Zhida
In this paper, combined with the design and construction of a tunnel, and using viscoelasticity, time-dependence stress and displacement in tunnel surrounding rock and support have been studied. Firstly, to stress analysis of the surrounding rock and support as a boundary value problem with the initial stress under the action of the displacement in the tunnel surrounding rock after tunnel excavation, the time-dependence stress and displacement in tunnel surrounding rock and support have been derived, these depend on the interaction between tunnel surrounding rock and support. Then, the interaction between tunnel surrounding and support has been derived by compatibility of deformation, the interaction is not only dependence on material property and size of tunnel surrounding and support, but also the time of making supports. Finally, combined with the design and construction of a special tunnel, and using the time-dependence stress in this paper, the stress release of the tunnel surrounding rock and load distribution ratio and the stress in support have been calculated, and the displacement and stress in the second lining under different load distribution ratio have been given. These can be provided a reference for the construction and design of the tunnel.
2013 Vol. 34 (6): 620-627 [
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268
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628
Meaning and Rationality of Guide-weight Criterion For Structural Optimization
The Guide-weight criterion is a rational criterion for structural optimization, which strictly derived from Kuhn-Tucker extremum condition. The criterion is expressed as: in an optimum structure, the weight of a component group should be proportionally distributed by its Guide-weight. Guide-weight criterion is clear in meaning, simple in form and easy to employ. Guide-weight criterion had conquered drawback of virtual work criterion method that neglecting derivative of load changing with variable change. In many application examples, it is shown that Guide-weight criterion took advantages of fast convergence and excellent result. During the iterative computations in structural optimization, it is the function of Guide-weight criterion to guide rational distribution of design resources, such as structure weight or cost etc., to cause this distribution to achieve an optimal status that the weights of component groups are proportional to their Guide-weights. The mathematical meaning and mechanical meaning of Guide-weight and Guide-weight criterion are explained, rationality of the Guide-weight criterion and the supervise sense of Guide-weight criterion for optimization iterative are discussed, and an index measuring the optimization degree of structures is proposed.
2013 Vol. 34 (6): 628-638 [
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270
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523
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