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2012 Vol. 33, No. 1
Published:
论文
0
A Meshfree Support Integration Method
DOI:
A support integration method based on the locality of meshfree methods was proposed for Petrov-Galerkin meshfree methods. Positions and weights of quadrature points were obtained through the requirements that the integral of test functions multiplied by polynomials can be evaluated exactly on the support domain. Only two quadrature points are needed in each dimension for each support domain. The computational cost is much decreased in comparison with background mesh integration. This method can calculate nodal forces exactly for linear stress field, so that the integral constraint condition is satisfied to ensure the stability. One-dimensional and two-dimensional examples show that this method has good accuracy and convergence rates.
2012 Vol. 33 (1): 0-7 [
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424
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A kinematic model and numerical algorithm for constitutive behavior of single crystal shape memory alloy
DOI:
Based on the concept that NiTi shape memory alloys (SMAs) are substantially heterogeneous and there inevitably exist residual micro-stress fields, and the superposition of the residual stress and the that induced by applied thermal-mechanical loads may cause martensitic transformation at low level of applied thermal-mechanical loads, a new transformation driving force model is proposed for an existing description for martensite variants in NiTi SMAs. The corresponding numerical algorithm is developed and the pseudoelasticity of NiTi SMAs is analyzed, and compared with experimental results and the results by Gall et al. In the proposed model the transformation driving force is considered as a continuous function of martensite volume fraction, however, the transformation as well as its rare is insignificantly small as the transformation driving force is far from its saturated magnitude. Analysis shows that the range of the transformation driving force with respect to prescribed tolerance of transformation volume fraction is much smaller that that adopted in the existing work, and vice versa, indicating higher computation accuracy. On the other hand, no assessment is needed for the occurrence of transformation and its direction in each variant a priori, which is significant in computation, especially in the case of multiaxial thermal-mechanical loading. Since the proposed approach avoids the discontinuity in the evolution of transformation driving force at the instant when transformation starts, and the additional numerical process for the identification of the variants where transformation proceeds or not, it can not only simplify the numerical process, but also enable the computation process be more stable and efficient.
2012 Vol. 33 (1): 0-16 [
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385
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Void Growth Behavior Simulation based on Crystal Plasticity
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A rate-dependent Crystal Plasticity Model has been used to establish a 3D Unit Cell Model, which is applied to study the effect of lattice orientation and grain boundary on the void growth and coalescence. By comparing the growth tendency of void in different orientations for single crystal and bicrystals, it is found that lattice orientation has noticeable influences on the void growth direction and void shape.
2012 Vol. 33 (1): 0-25 [
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402
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A Theoretical Study on the Bending Rigidity of A Honeycomb Core
DOI:
In this paper the bending rigidity of a honeycomb core consisting of right hexagonal cells was investigated. Since the moment exerted on the oblique cell walls of the right hexagonal cells under in-plane loading is quite different from the one exerted on the oblique cell walls of the right hexagonal cells under out-of-plane loading, the bending deformation cannot be directly calculated by the equivalent elastic mechanical properties based on the in-plane deformation. According to the fact that the oblique cell wall will be twisted under a condition that the rotation is zero at the junction among three adjacent cell walls of the right hexagonal cell under the bending deformation, a novel analytical method for solving the bending rigidity of the honeycomb structures was proposed. Comparisons of present analytical results with those numerical solutions from the common FEM commercial software MSC.Marc, it was shown that the present method is efficient and applicable.
2012 Vol. 33 (1): 0-31 [
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406
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UPPER-BOUND LIMIT ANALYSES BASED ON NATURAL ELEMENT METHOD
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DOI:
The natural element method is a novel numerical method based on voronoi diagram and delaunay triangulation of the scattered points in the problem domain, and its shape function is built upon the notion of the natural neighbor interpolation. Compared to the moving least square approximation which widely used in the meshless method, this interpolation method does not involve the complex matrix inversion, even without any artificial parameters and can greatly improve the computational efficiency. Further more, because of the shape function satisfies the property of delta function, the imposition of essential boundary condition is as accurate as finite element method, the treatment of discontinuous field function and its derivative are conveniently. This article applies natural element method to upper bound limit analyses, prepares the corresponding computational programs, several classic examples of limit analysis are adopted to verify the performance of these programs, the results show that utilizing natural element method to solve upper-bound limit analysis problems possess the advantage of high efficiency, good accuracy and fast convergence.
2012 Vol. 33 (1): 0-47 [
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383
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STATIC CHARACTERISTICS AND COHESIVE ZONE MODEL OF JOINT SURFACES IN MACHINE TOOLS
DOI:
To satisfy the functional, process and design requirements, each type of machine tool is assembled by various parts or components at certain order instead of a complete and continuous structure, and hence a variety of joint surfaces exist between different parts or components. As the joint surfaces are discrete surfaces, their stiffness and damping affect considerably the static and dynamic performance of the machine tool. In the present paper, model experiments were firstly carried out to characterize the relationship between contact pressure and deformation of nominally plain joint surfaces. The contact behavior of the joint was then simulated using the method of finite elements by simplifying the measured morphology of the joint surfaces as semi-circular or sinusoidal. It was demonstrated that the numerical simulations agreed better with the experimental measurements if the joint surface morphology was taken as semi-circular. Finally, by assuming that the interaction between a pair of joint surfaces is equivalent to cohesion effects, the classical cohesive zone model (CZM) was adopted to analyze the mechanical behavior of the joint. It was established that the model predictions agree well with the experimental results.
2012 Vol. 33 (1): 0-57 [
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386
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A MULTIAXIAL FATIGUE LIFE PREDICTED MODEL WITH SHEAR FORM BASED ON THE CRITICAL PLANE APPROACH
DOI:
Based on the critical plane approach, a new multiaxial fatigue damage parameter with shear form is proposed by means of the von-Mises criterion. This proposed damage parameter is suitable for both proportional and non-proportional loading. Besides, this damage parameter considers the maximum shear strain range and the normal strain range on the critical plane. The effect of the non-proportional cyclic hardening on the fatigue life is taken into account by an introduced stress-correlated factor. It is convenient for engineering application because of no empirical constants in this parameter. The predicted multiaxial fatigue lives of the considered materials (1045HR Steel, S45C Steel, Inconel718 Steel and 16MnR Steel) using the proposed model are found in good agreement with the experimental results.
2012 Vol. 33 (1): 0-62 [
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426
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简报
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Study on Scale Effects for Free-vibrating of Four edges Simply Supported Micro-plate Based on the Cosserat Theory
DOI:
The mechanical properties of a certain material depend on its internal structure, and study on scale effects of microstructure dynamics is greatly significant. It is well know most of the micro/nano devices are typically plate-structured. The lack of literature on study on the scale effect for micro-plates has significantly limited the designing and application of micro/nano devices. The free vibrating differential equation of four edges simply supported (SSSS) micro-plate is presented using the modified Cosserat theory in this paper. Consequently, we obtain the formula of natural frequencies that meet SSSS boundary conditions and analyze the scale effects for natural frequencies of micro-plates with different dimensions. The results show that scale effects is highly significant on the free vibrating natural frequency when characteristic length and micro-plates thickness are close, and the natural frequencies increase along with the increase of characteristic length. Additionally, the scale effects depend on thickness of micro-plate. The theory we presented is of fundament importance for the application of microstructure system.
2012 Vol. 33 (1): 0-68 [
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474
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Micromechanism of affecting the shear banding behaviors in metallic glasses
DOI:
Shear banding behaviors in metallic glasses(MGs) are studied in the present paper. Based on the band-like solution and the critical wavelength of shear banding instability, the critical free volume concentration of shear banding instability and the thickness of shear band in MGs are predicted. The results agree well with experimental observations and simulations. We also demonstrates that the prediction of shear band thickness, which is based on the critical wavelength, is only valid for a short time after shear instability and the diffusion of defects should be included in the mature shear band in MGs. The physical factors governing the thickness of shear bands are also illustrated. The results indicate that the thickness of shear bands is insensitive to the Poison’s ratio and is governed by the features and evolution of the defects (STZs).
2012 Vol. 33 (1): 0-74 [
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447
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Yuanwen Gao
DOI:
The propagation of elastic waves in one-dimensional phononic crystals(PCs) which are composed of both functionally graded materials(FGM) and isotropic material has been studied by using the plane wave expansion method. The material properties of FGM are varied according to a well-known rule, such as the exponential function. The influences of the exponential factor of FGM , filling fraction of two kinds of materials and length of materials on the first four normalize frequency gaps location and width are discussed, respectively. These results provide the theoretical basis and guidance for PCs with FGM widely using in engineering practice.
2012 Vol. 33 (1): 0-80 [
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410
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Topological Optimization of Plant and Shell Structure with Displacement Constraints under Multiple Load Cases Based on ICM Method
DOI:
An approximately explicit topological optimization model of plant and shell structure is established using ICM method to minimize the weight with displacement constraints under multiple load cases. The model is solved by a sequential quadratic programming (SQP) based on exact dual mapping and the optimal topology is finally obtained, which demonstrates that ICM method is effective in dealing with the topological optimization of plant and shell structure. Several numerical examples show that: 1.the optimal force-transfer path of the structure is related with its boundary conditions; 2.the variety of displacement constraint values result in different optimal topologies; 3. the force-transfer path in multiple load cases is not a simple superposition of those in each single load case.
2012 Vol. 33 (1): 0-90 [
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402
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SYMPLECTIC ANALYSIS FOR BAND GAPS IN ONE DIMENSIONAL PHONON CRYSTAL BASED ON NONLOCAL ELASTIC THEORY
DOI:
The elastic wave propagation in periodic composite structure (Phonon crystal) appears especial dispersion relations: the wave can only propagate in some frequency ranges (called pass-band) without dissipation. The dispersion relations of one dimensional phonon crystal can be analysed as the eigen-value problems of elastic wave propagation in layered media. In this paper, we investigate the nonlocal effect on the band gaps in phonon crystal. The two dimensional nonlocal linear elastic theory presented by Eringen is derived to the Hamilton system. The precise integration method and external Wittrick-Williams algorithm are used to calculate the eigen-solutions in arbitrary frequency ranges. The numerical results of typical problems and the comparison between nonlocal theory and classical local theory are given out and discussed. The advantages and applicability of the approach are also presented.
2012 Vol. 33 (1): 0-97 [
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393
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Large Deflection Analysis of a Saturated Poroelastic Timoshenko Beam
DOI:
Based on the theory of microscopic incompressible saturated porous media and the hypothesis of large deflection deformation of the elastic beam, with the effect of shear deformation of the beam, a nonlinear mathematical model is presented for large deflection bending of saturated poroelastic Timoshenko beams under constraints of the inextensibility of the axial line and the diffusion of the pore fluid only in the axial direction of beams. Then, the nonlinear quasi-static bending of a simply supported saturated poroelastic Timoshenko beam with two ends permeable, subjected to a step constant transverse load, is investigated with the Galerkin truncation method. The curves of deflections, bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure are shown in figures. The results of the nonlinear large deflection and the linear small deflection theories of the saturated poroelastic Timoshenko beam as well as the nonlinear large deflection theory of the saturated poroelastic Euler-Bernoulli beam are compared, and the differences among them are revealed. It is shown that, when the dimensionless load parameter , the nonlinear large deflection mathematical model of the saturated poroelastic Timoshenko beam or Euler-Bernoulli beam should be employed for analysis of the bending of the saturated poroelastic beams, and especially, the large deflection mathematical model of the saturated poroelastic Timoshenko beam be employed when the slenderness ratio of the beam .
2012 Vol. 33 (1): 0-111 [
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508
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Analysis of Non-linear Flap Vibration of Wind Turbine Blades
DOI:
The nonlinear governing equation of flap vibration is established by considering the blade as a rotating Euler-Bernoulli cantilever beam with variable sections on the hub. The unsteady aerodynamic forces acting on the blade are derived by using the Greenberg’s expressions. The assumed-modes method is introduced to compute modes functions since bending rigidity and line density are variable alone the elastic axis and expressions of modes can’t be derived directly. By using these modes functions as a functional base, the Galerkin procedure is applied to the governing equation to discrete the continuum Model. The dynamic response is analyzed by decomposing the flap vibration as static displacements and dynamic displacements. Influences of the rotating speed, the wind velocity, and the rotating angle to flap characteristics are discussed. The study shows that: 1) the influence of the rotating speed to vibration characteristic is dramatic, but those of the wind velocity and the rotating angle are inapparent; 2) the static displacement increases proportionally with the wind velocity, but the aerodynamic damping decreases with the wind velocity; 3) the nonlinear flap vibration under lower wind velocity is attenuating, and it becomes a quasi-periodic vibration through a periodic vibration with increase of the wind velocity.
2012 Vol. 33 (1): 0-102 [
Abstract
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448
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Structural damage detection by an improved sensitivity technique
DOI:
In this paper, an improved sensitivity technique is presented for structural damage detection. The drawback of the existing sensitivity methods is discussed firstly and then an improved method is proposed. The most significant contribution of this work is in the development of a simple accelerated formula used in the iteration process. With the introduction of the accelerated formula, the proposed method is able to quantify large damages without any high-order analysis on the eigenparameters or multi-iterations. The effectiveness of the proposed method is illustrated using simulated data with measurement noise on two numerical examples in references [8] and [10]. The results show that the proposed procedure is economical in computation and is simple to implement. Regardless of whether the damage is small or large, the proposed method can identify both locations and extents of structural damages accurately only using the first iteration. It has been shown that the presented scheme may be useful for structural damage identification.
2012 Vol. 33 (1): 0-118 [
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394
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