2009 Vol. 30, No. 12

Display Method:
2009, 30(12): 1387-1398. doi: 10.3879/j.issn.1000-0887.2009.12.001
Abstract(1388) PDF(942)
Abstract:
A method for computing the second-order sensitivity matrix of eigenvalues and eigenvectors of the multiple parameter structures,i.e.the Hessian matrix,was presented.The second-order perturbations of eigenvalues and eigenvectors were transformed into the multiple parameter forms, and the second-order perturbation sensitivity matrices of eigenvalues and eigenvectors were developed.Using these formulations,the efficient methods based on the second-order Taylor expansion and second-order perturbation were obtained to estimate the changes of eigenvalues and eigenvectors when design parameters changed.The method avoided direct differential operation thus reducing the difficulty for computing the second-order sensitivity matrices of eigenpairs.A numerical example was given to demonstrate the application and the accuracy of the proposed methods.
2009, 30(12): 1399-1414. doi: 10.3879/j.issn.1000-0887.2009.12.002
Abstract(1840) PDF(919)
Abstract:
Two systems of non-homogeneous linear equations in 8 unknowns were obtained by introducing two stress functions containing 16 undetermined coefficients and two real stress singularity exponents with the help of boundary conditions.By solving the above systems of non-homogeneous linear equations,the two real stress singularity exponents can be determined when the double material engineering parameters meet certain conditions.The expression of the stress function and all the coefficients were got by the unique theorem of limit.By substituting them into corresponding mechanics equations,theoretical solutions to the stress intensity factor,the stress field and the displacement field near the crack tip of each material can be obtained when the discriminants of the characteristic equations are less than zero'stress and displacement near crack tip show mixed crack characteristics but no stress oscillation or crack surfaces overlap.As an example,when the two orthotropic materials are the same,the stress singularity exponent,the stress intensity factor,the stress field and the expression for the displacement field of the orthotropic single material can be deduced.
2009, 30(12): 1415-1426. doi: 10.3879/j.issn.1000-0887.2009.12.003
Abstract(1651) PDF(704)
Abstract:
The present problem was concerned with the study of deformation of a rotating generalized thermoelastic solid with an overlying infinite thermoelastic fluid due to different forces acting along the interface under the influence of gravity.The components of displacement,force stress and temperature distribution were obtained in Laplace and Fourier domain by applying integral transforms.These components were then obtained in the physical domain by applying a numerical inversion method'some particular cases were also discussed in context of the problem.The results are also presented graphically to show the effect of rotation and gravity in the medium.
2009, 30(12): 1427-1439. doi: 10.3879/j.issn.1000-0887.2009.12.004
Abstract(1562) PDF(986)
Abstract:
Formulation and numerical evaluation of a novel QUAD4 with continuous nodal stress(Q4-CNS)were presented.And Q4-CNS can be regarded as an improved FE-LSPIM QUAD4,which is a hybrid FE-Meshless method.The derivatives of Q4-CNS are continuous at nodes,so continuous nodal stress can be obtained without any smoothing operation.It is found that,compared with standard 4-node quadrilateral element(QUAD4),Q4-CNS can achieve significantly better accuracy and higher convergence rate.It is also found that Q4-CNS exhibits high tolerance to mesh distortion. Moreover,since the derivatives of Q4-CNS shape functions are continuous at nodes,Q4-CNS is potentially useful for the problem of bending plate and shell models.
2009, 30(12): 1440-1452. doi: 10.3879/j.issn.1000-0887.2009.12.005
Abstract(1559) PDF(760)
Abstract:
The Ray leigh-Stokes problem for a heated generalized second grade fluid(RSP-HGSGF) with fractional derivative was considered.An effective numerical method for approximating RSP-HGSGF in a bounded domain was presented.And the stability and conver gence of the numerical method were analyzed.Finally,some numerical examples were presented to show the application of the present technique.
2009, 30(12): 1453-1462. doi: 10.3879/j.issn.1000-0887.2009.12.006
Abstract(1231) PDF(743)
Abstract:
Velocity field in a single plateau border of aluminum foam during drainage process was studied by a mathematic model for the flow inside a micro-channel.It is shown that the liquid/gas interface mobility,which is characterized by the Newtonian surface viscosity,has substantial effect on velocity inside single plateau border.It's found that at the same liquid/gas interfacial mobility (M)and same radius of curvature,the max velocity inside an exterior plateau border is about 6~8 times as large as that inside an interior plateau border.It's also found that a critical value of the interfacial mobility in interior plateau border,for values greater or less than which the effects of the film thickness on the velocity in plateau border show opposite tendencies.Based on the results from the microscopical model,a new macroscopical drainage model was presented for aluminum foams.Comparisons of computed results by this model with experimental data from the literature and with those from the classical drainage equation show a reasonable agreement.Furthermore,computational results reveal that the liquid holdup of foams is dependent strongly on the value of M and bubble radius.
2009, 30(12): 1463-1472. doi: 10.3879/j.issn.1000-0887.2009.12.007
Abstract(1399) PDF(943)
Abstract:
A new transition prediction model was introduced which coupled the intermittency effect into the turbulence transport equations and took the characteristics of fluid transition into consideration so as to mimic the exact process of transition.Test cases including two-dimensional incompressible plate and two-dimensional NACA0012 airfoil,and the performance of this transition model used in incompressible flow were studied.It was proved that the numerical results were well consistent with experimental data.Meanwhile the requirement of grid resolution for this transition model was also studied.
2009, 30(12): 1473-1481. doi: 10.3879/j.issn.1000-0887.2009.12.008
Abstract(1478) PDF(632)
Abstract:
The MHD flow of a viscous fluid towards a non-linear porous shrinking sheet was investigated.The governing equations were simplified by similarity transformations and then the reduced problem was solved by homotopy analysis method(HAM).The pertinent parameters appeared in the problem were discussed graphically and through the tables.It is found that the shrinking solutions in the presence of MHD exit.It is also observed from the tables that solutions for f"(0) with different values of parameters are convergent.
2009, 30(12): 1482-1492. doi: 10.3879/j.issn.1000-0887.2009.12.009
Abstract(1411) PDF(704)
Abstract:
The purpose was to solve nonselfadjoint elliptic problems with rapidly oscillatory coefficients.A two-order and two-scale approximate solution expression for nonselfadjoint elliptic problems was considered,and the error estimation of the two-order and two-scale approximate solution was derived.The numerical result shows that the approximation solution is effective.
2009, 30(12): 1493-1500. doi: 10.3879/j.issn.1000-0887.2009.12.010
Abstract(1373) PDF(733)
Abstract:
Based on a general iterative algorithm,the problem of approximating a common element in the solution set of quasi-variational inclusion problems and in the common fixed point set of an infinite family of nonexpansive mappings was considered.It is proved that the iterative sequences generated in the purposed iterative algorithm converges strongly to some common element in the framework of real Hilbert spaces.
2009, 30(12): 1501-1512. doi: 10.3879/j.issn.1000-0887.2009.12.011
Abstract(1511) PDF(815)
Abstract:
Firstly the existence of a compact uniform attractor for a family of processes corresponding to the dissipative non-autonomous Klein-Gordon-Schrêinger lattice dynamical system was proved.Then an upper bound of the Kolmogorov entropy of the compact uniform attractor was obtained.Finally an upper semicontinuity of the compact uniform attractor was established.