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2014 Vol. 35, No. 3
Published:
217
Singular boundary method for two dimensional elasticity problems
The singular boundary method (SBM) belongs to the family of meshless boundary collocation methods and can be viewed as one kind of modified method of fundamental solutions (MFS). This method was originally proposed in 2009, based on the notion of boundary element method (BEM) and MFS, fully inherits the merits of both and in the meantime possessing its unique advantages. The key idea is to introduce the concept of the origin intensity factor to isolate the singularity of the fundamental solutions, so that the source points can be directly placed on the real boundary. This overcomes a perplexing fictitious boundary outside physical domain in the MFS. This paper makes the first attempt to apply the method to two dimensional elasticity problems. The accuracy and stability of the proposed method are tested to three benchmark elasticity examples in which the SBM solutions are compared with the results obtained by using the MFS, traditional SBM, and the finite element method (FEM).
2014 Vol. 35 (3): 217-225 [
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220
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226
An Approach for Full-Range Uniaxial Constitutive Relationships of Ductile Materials Based on Testing and Finite Element Coupling Method
bstract: The description of constitutive relationship of materials up to failure plays important role in the large deformation analysis and fracture mechanism study. The true stress and strain curves obtained by traditional tensile test become immeasurable after necking. This paper presents a new method to determine full-range uniaxial constitutive relationship of ductile material by tensile testing on a funnel-shape specimen, and using DIC(Digital image correlate)technology which could accurately measure mechanical 3D displacement and strain and finite element analysis(FEA). This method is abbreviated TF(Test and FEA)method in this study. Taking full-range constitutive relationships as constitutive relationships in finite element software material storage. The FEA results for the funnel specimens show that, the simulated load versus displacement curve, diameter at the funnel root versus displacement curve and funnel deformation contours and simulated surface strain distribution nephogram are closed to test results. The full-range true stress and strain curves obtained by funnel specimens with different radius are good coincident with each other. In addition, the mechanical behaviors on the cross section of the funnel specimens are discussed. The parameters of constitutive relationships and breaking stress and strain for 304 stainless steel are given.
2014 Vol. 35 (3): 226-240 [
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234
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241
Failure Mode Analysis of the Structure with Hierarchical Corrugated Truss Core Based on the Theory of Plate
In this paper, the failure modes of the second order hierarchical corrugated truss structure are analyzed based on the theories of elastic plates and hoff's sandwich plates. According to the force analysis for a unit free body of core, the relationship between load and deformation is obtained. The structure would fail when the stress reaches the yield stress or the axial force reaches the critical load, and thus six competing failure modes are analyzed under the compressive load or shear load, respectively. The expressions for the compressive stress and shear stress are given. It’s defined that the critical failure mode in compression or shear is the one associated with the lowest collapse strength. Then, the failure mechanism map is constructed to illustrate the regimes of dominance of the failure modes. Comparison with the results by finite element analysis showed that the theoretical predictions based on the theory of plate proposed in this paper have satisfying accuracy.
2014 Vol. 35 (3): 241-248 [
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241
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249
COMPARATIVE STUDY ON SUBSEQUENT YIELD SURFACES TESTED BY USING SINGLE AND MULTIPLE SPECIMEN
Through tension-torsion test with thin-walled tubular specimens of 45 annealing steel, the subsequent yield surfaces under different pre-tension deformation are investigated after the prescribed pre-strain. The yielding is defined by the several levels of offset strain, the effects of the chosen plastic strain offsets and the prescribed pre-strain levels on subsequent yield surface are explored. The initial and the subsequent yield surfaces are determined by the probe methods of multiple identical specimens method and single-specimen method, the rationality and limitations are discussed by the two probe method. The experimental results of yield surface for 45 steel are as follows: (1) The shape of initial yield surface tested by using multiple specimens and single-specimen method were found to be close to the von-Mises surface; (2) The shape of yield surface is significantly affected by test sequence with single-specimen method, the first yield point tested in opposite directions of preloading, the yield surface appears "inner concave"，if the test sequence is changed, the " inner concave" will no longer appear ; (3) The shape of yield surface is affected by test amounts of yield points through the single-specimen method, when the yield surface is tested by many yield points, the subsequent yield point will deviate from the yield surface because the strain hardening is caused by the cumulative plastic strain,; (4) Subsequent yield surface shape and size have the obvious difference between using the single-specimen method and the multiple-specimen method respectively，the shape of yield surface tested with single-specimen method is affected by cumulative plastic strain, the results by the probe method of multiple identical specimens are proved to be more accurate; (5) Subsequent yield surface is defined by a smaller offset strain with multiple-specimen method, the " inner concave" will also appear, but the phenomenon is not obvious.
2014 Vol. 35 (3): 249-258 [
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258
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259
TENSILE DYNAMIC CONSTITUTIVE MODEL OF 5083H111 ALUMINUM ALLOY AT A WIDE RANGE OF STRAIN RATES
Combined with tensile experimental data of 5083H111 aluminum alloy at a wide range of strain rates from 2×10-4 to 4×102s-1, the V-typed strain-rate effect of this aluminum alloy is analyzed. The strain-rate and strain dependence of the logarithmic strain rate sensitivity coefficient λ and tangent modulus Et are discussed. Then, a dynamic constitutive model is established to describe the dynamic tensile behavior of 5083H111 aluminum alloy at a range of lower and middle strain-rates by modifying the Johnson-Cook model. The model reflects the V-typed strain-rate effect of tensile deformation of the aluminum alloy at researching strain-rates, and the predicted results of the proposed model are in good agreement with the experimental ones. Furthermore, based on the logarithmic strain-rate sensitivity coefficient β of failure strain, a new equation to predict the tensile failure strain of the alloy is formulated, and the predicted results are basically consistent with the experimental ones.
2014 Vol. 35 (3): 259-265 [
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182
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266
A MULTI-SCALE MODEL FOR NONLOCAL EFFECTS AND ITS APPLICATION ON BENDING ANALYSIS OF MICRO-BEAMS
Exact nonlocal stress field is derived via a successive approximation approach based on Eringen’s nonlocal elasticity theory. The explicit solution of nonlocal stress is provided and it can be expressed as an infinite series. Subsequently, the transverse bending and pure bending deformations of micro-beams are taken as examples to exhibit the effect of nonlocal small scale parameter on static deflection. The equilibrium equations are solved and the results are analyzed and discussed in detail. It shows that with different nonlocal small scale parameters, nonlocal bending deflection is lower or higher than that predicted by the classical continuum mechanics, or nonlocal effect increases or decreases structural stiffness of micro-beams. Two opposite nonlocal models proposed respectively by Wang et al and Lim et al are both existence and acceptable. It is demonstrated firstly that deflection fluctuates up and down with increasing the scale parameters, and the existence of some discontinuity points is also observed. The deflection is a non-monotone function with respect to nonlocal small scale parameter. The present study also suggests a possible approach to determine the nonlocal material parameter.
2014 Vol. 35 (3): 266-271 [
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153
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272
A Theoretical Study of Dynamic Thermal Stress Distribution on the Surface of Channel Filled by Flow Medium
Throught translation and rotation method of coordinational axil, a problem of the dynamical thermal stress distribution on the surface of a channel filled by flow medium was studied theoretically. A general analytic solution with a computional process was described in detailed. As an illustration sample, some numberical results are shown in the figures about the dynamical thermal stress distribution on the surface of an elliptic channel filled by flow medium.
2014 Vol. 35 (3): 272-276 [
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178
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277
Investigation on the Stress/Force Enhancement in Cellular Metallic Materials
Cellular metallic materials possess high specific stiffness, high specific strength and strong energy-absorbing capability, and have been used significantly as packaging material and crash material. In this paper, through numerical simulation and experimental study, four kinds of stress/force enhancement of cellular metallic materials under impact loads were researched as follows: 1) under small impact load, stress enhancement appears in cellular material and the reason is related to the irregularity of cell shape; 2) when cellular material is fully consolidated, stress enhancement happens because the material has been a dense solid and its property has changed completely; 3) stress enhancement happens before the cellular material is fully consolidated, and the reason lies in that when cellular material is undergoing plastic deformation, the plastic wave propagates increasingly fast with increasing strain and when the propagation velocity of high amplitude perturbation is greater than that of low amplitude perturbation in the front, stress enhancement forms over a period of time; 4) stress enhancement appears at impact end, because according to the well known shock-wave propagation theory, stresses at impact end continuously increase with increasing impact velocities. In these situations, the third one is of great significant to be noted because this kind of stress enhancement may severely damage the substance under protection. This paper will provide a valuable reference for the crashworthiness design of cellular materials.
2014 Vol. 35 (3): 277-284 [
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312
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285
Analytical Modeling of Lamb Waves based on Transfer Function Method
This paper studies the analytical modeling of Lamb wave propagation excited by wafer type piezoelectric sensors (PZT). The PZT excitation is modeled by the distributed point sources at the PZT edge. By using the Fourier transform, the three dimensional wave equation is solved in frequency-wavenumber domain. For the unit harmonic excitation, the frequency response of the Lamb wave propagation is achieved. For any type of excitation, the Lamb wave response is obtained with the help of transfer function method. Using inverse Fourier transform, the time-space wavefield is obtained from the frequency response. In order to verify the analytical modeling, the analytical results are compared with experimental measurements. The comparisons show the analytical results are in a good accordance with the experimental measurements.
2014 Vol. 35 (3): 285-291 [
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355
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292
The IBEM solution for the scattering of plane SH-Waves by a cavity of arbitrary shape embedded in a wedge-shaped space
The scattering of plane SH waves by a cavity of arbitrary shape in a wedge-shaped space is investigated by using the indirect boundary element method (IBEM).According to the theory of single-layer potential, the scattering wave field can be constructed by applying virtual uniform load on the free surface of cavity and the wedge-shape space. The density of virtual load can be solved by establishing equation through the condition which is the free surface of the zero-stress. The total wave field is obtained by the superposition of free-wave field and scattering-wave field in wedge-shaped space. It is shown that the IBEM can solve the diffraction of elastic wave in wedge-shaped space accurately and efficiently. The scattering of waves depends on the angle of incidence, the frequency of the incident wave, the shape and location of cavity and the angle of the wedge. The waves interface effect around the cavity in wedge space seems more significant, and the wedge space surface displacement amplitude and stress concentration factor on cavity surface can reach 8.5 and 10.0 respectively, more than doubled that of the case of half space. This study will lay a foundation for the analysis of the scattering of P and SV waves in wedge-shaped space.
2014 Vol. 35 (3): 292-301 [
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198
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302
Research on the Mechanical Property of High Strength Steel Corrugated Core Sandwich Structure
The three-point bending and in-plane compression of the high strength steel corrugated core sandwich structure was simulated by using the finite element software—ABAQUS. The calculated results were compared to the experimental values and the theoretical values. Then the responses of the sandwich structure under different core materials (high strength steel and carbon steel) and different direction were analyzed. The results showed that the bending strength of the corrugated core sandwich structure of DP900 high strength steel was 2.39 times than that of DC01 low carbon steel. And the compression strength was 1.40 times than that of DC01 low carbon steel. The bending stiffness of the structure in the machine direction was 11.63 times than that in the cross- machine direction.
2014 Vol. 35 (3): 302-307 [
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308
Modeling and In-plane Dynamics Analysis of the Cable-stayed Beam
Using the Hamilton principle and the effects of the dynamic and static configuration of the cable and beam, the equations of motion of the cable-stayed beam can be obtained. Considering the boundary and continuity conditions, the in-plane eigenvalue problem is investigated. By introducing the piecewise function, the mode shapes can be obtained. Then, the effects of the sag-to-span ratio f, stiffness ratio K and mass ratio m on the in-plane natural frequencies of the cable-stayed beam are studied. It is shown that the curve veering phenomenon can be observed in the natural frequency spectrum of the system. The frequency crossover phenomenon is obvious. Considering the local mode and global mode, the mode shapes of the cable-stayed beam are discussed. Finally, the possible internal resonances such as 1:1 and 1:2 are discussed. Researches show that the static configuration of the beam influences not only the force continuity conditions, but also the natural frequency of the cable-stayed beam.
2014 Vol. 35 (3): 308-312 [
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313
Nonlinear bending analysis of FGM beams resting on two-parameter elastic foundations based on physical neutral surface and high order shear deformation theory
In this paper, nonlinear bending approximate solutions are given by Ritz method based on physical neutral surface and high-order shear deformation theory, and influences played by different supported boundaries, elastic foundations, thermal environmental conditions and volume fraction index are discussed in detail. It is worth noting that the deflections of the beams resting on Winkler elastic foundation are between those of foundationless beams and the beams resting on Pasternak elastic foundation in room temperature fields, and the deflections of the beams with immovable clamped ends in heat conduction fields are between those of beams in room and uniform temperature fields, while it is not always true for the beams with immovable simply supported ends due to initial thermal deflections.
2014 Vol. 35 (3): 313-318 [
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243
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319
Free vibration analysis of discontinuous beams under axial force using generalized functions
Abstract：The general governing differential equation of the vibration of Euler-Bernoulli beams with multiple discontinuities subjected to axial force presented by using generalized functions. The equation is then solved based on Laplace transformation. Unlike the classical solutions of discontinuous beams, the proposed scheme is valid in arbitrary miscellaneous discontinuities conditions, the generalized solutions are expressed in the terms of a single expression on the entire beam. As the specified discontinuities type, eigenvalue matrices are simplified by the degenerated continuity conditions. Final, the accuracy and efficiency of the proposed method is verified with an example of the free vibration problems for a four-span simply supported beam with three spring-mass systems subject to compressive force.Final, the free vibration problems for (a) a beam with masses and their rotatory inertias, (b) a four-span pinned-pinned beam with three spring-mass systems subject to compressive force, (c) a multiple cracked beam with axial force and elastic foundation are studied. It is shown that the present method offers an accurate and effective method of free vibration analysis of beams with arbitrary discontinuities.
2014 Vol. 35 (3): 319-324 [
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