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## A new hybrid quadrilateral finite element for mindlin plate

### Applied Mathematics and Mechanics (1994-02-01) 15: 189-199 , February 01, 1994

In this paper a new quadrilateral plate element concerning the effect of transverse shear strain has been presented. It is derived from the hybrid finite element model based on the principles of virtual work. The outstanding advantage of this element is to use more rational trial functions of the displacements. For this reason, every variety of plate deformation can be simulated really while the least degrces of freedom is employed. A wide range of numerical tests was conducted and the results illustrate that this element has a very wide application scape to the thickness of plates and satisfactory accuracy can be obtained by coarse mesh for all kinds of examples.

## The linear bi-spatial tensor equation φi j AiXBj= C

### Applied Mathematics and Mechanics (1996-10-01) 17: 979-986 , October 01, 1996

A linear bi-spatial tensor equation which contains many often encountered equations as particular cases is thoroughly studied. Explicit solutions are obtained. No conditions on eigenvalues of coefficient tensors are imposed.

## Unsteady three-dimensional boundary layer flow due to a permeable shrinking sheet

### Applied Mathematics and Mechanics (2010-11-01) 31: 1421-1428 , November 01, 2010

The unsteady viscous flow over a continuously permeable shrinking surface is studied. Similarity equations are obtained through the application of similar transformation techniques. Numerical techniques are used to solve the similarity equations for different values of the unsteadiness parameter, the mass suction parameter, the shrinking parameter and the Prandtl number on the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. It is found that, different from an unsteady stretching sheet, dual solutions exist in a certain range of mass suction and unsteadiness parameters.

## Degenerate scale problem in antiplane elasticity or Laplace equation for contour shapes of triangles or quadrilaterals

### Applied Mathematics and Mechanics (2012-04-01) 33: 525-538 , April 01, 2012

This paper provides several solutions to the degenerate scale for the shapes of triangles or quadrilaterals in an exterior boundary value problem (BVP) of the antiplane elasticity or the Laplace equation. The Schwarz-Christoffel mapping is used throughout. It is found that a complex potential with a simple form in the mapping plane satisfies the vanishing displacement condition (or *w*=0) along the boundary of the unit circle when the dimension *R* reaches its critical value 1. This means that the degenerate size in the physical plane is also achieved. The degenerate scales can be evaluated from the particular integrals depending on certain parameters in the mapping function. The numerical results of degenerate sizes for the shapes of triangles or quadrilaterals are provided.

## The plane piston problem in a weak gravitational field

### Applied Mathematics and Mechanics (1985-01-01) 6: 75-85 , January 01, 1985

We analyze a gasdynamical process in the stellar atmosphere that is driven by a “piston” moving with constant velocity in a weak gravitational field. Ahead of the piston, the gas is compressed, and this compressed gas uses part of its internal energy and somewhere its kinetic energy to overcome the applied gravity.

If we expand the quantities as a series of a small parameter, which is the ratio of a typical escape velocity to the plasma velocity, the basic state gives a uniform flow, as shown by the case of gasdynamical theory without gravity. The first-order relationships show the influence of the applied gravity on the flow fields, that is, the strength of the shock wave changes slightly, the internal energy of the gas exhausts. For the cases of strong shock wave and near the piston, an analytical solution may be approximately obtained and has the similar features.

Because of the importance of the applied gravity in the astrophysical and atmospheric physical processes, these results may shed light on the mechanics of transient process in the stellar and planetary atmosphere.

## Interval analysis of fuzzy-random heat conduction in composite tubes

### Applied Mathematics and Mechanics (2005-10-01) 26: 1312-1318 , October 01, 2005

During the analysis of stability heat conduction in the composite tubes, firstly, when the temperature boundary conditions are the random conditions, equations of the mean values and variances of the random thermal function are transformed. Secondly, when the heat conduct parameters are the fuzzy numbers and the temperature boundary conditions are the random numbers, interval equations of the heat conduction are presented. Thirdly, by comparison of the interval results, the result in the interval analysis is larger than that in the confidence interval. Moreover the error expecting equation is presented. Finally, with upper (lower) approximation in rough set theory, a new method of the interval analysis to deal with the stability heat conduction is presented.

## Joule heating effect of electroosmosis in a finite-length microchannel made of different materials

### Applied Mathematics and Mechanics (2010-01-01) 31: 109-118 , January 01, 2010

This paper presents a numerical analysis of Joule heating effect of electroosmosis in a finite-length microchannel made of the glass and polydimethylsiloxane (PDMS) polymer. The Poisson-Boltzmann equation of electric double layer, the Navier-Stokes equation of liquid flow, and the liquid-solid coupled heat transfer equation are solved to investigate temperature behaviors of electroosmosis in a two-dimensional microchannel. The feedback effect of temperature variation on liquid properties (dielectric constant, viscosity, and thermal and electric conductivities) is taken into account. Numerical results indicate that there exists a heat developing length near the channel inlet where the flow velocity, temperature, pressure, and electric field rapidly vary and then approach to a steady state after the heat developing length, which may occupy a considerable portion of the microchannel in cases of thick chip and high electric field. The liquid temperature of steady state increases with the increase of the applied electric field, channel width, and chip thickness. The temperature on a PDMS wall is higher than that on a glass wall due to the difference of heat conductivities of materials. Temperature variations are found in the both longitudinal and transverse directions of the microchannel. The increase of the temperature on the wall decreases the charge density of the electric double layer. The longitudinal temperature variation induces a pressure gradient and changes the behavior of the electric field in the microchannel. The inflow liquid temperature does not change the liquid temperature of steady state and the heat developing length.

## Lagrangian cell-centered conservative scheme

### Applied Mathematics and Mechanics (2012-10-01) 33: 1329-1350 , October 01, 2012

This paper presents a Lagrangian cell-centered conservative gas dynamics scheme. The piecewise constant pressures of cells arising from the current time sub-cell densities and the current time isentropic speed of sound are introduced. Multipling the initial cell density by the initial sub-cell volumes obtains the sub-cell Lagrangian masses, and dividing the masses by the current time sub-cell volumes gets the current time subcell densities. By the current time piecewise constant pressures of cells, a scheme that conserves the momentum and total energy is constructed. The vertex velocities and the numerical fluxes through the cell interfaces are computed in a consistent manner due to an original solver located at the nodes. The numerical tests are presented, which are representative for compressible flows and demonstrate the robustness and accuracy of the Lagrangian cell-centered conservative scheme.

## Studies on stress transference mechanism of steel fibre reinforced concrete

### Applied Mathematics and Mechanics (2001-04-01) 22: 483-494 , April 01, 2001

The stress transfer mechanism of steel fibre reinforced concrete is studied. The solutions for the stress and displacement were regarded as the superposition of “the elementary solutions” and “the improved solutions”. The elementary solutions were found by using two-dimensional elastic theory and the improved solutions were found by using the Love displacement function method. The calculated results indicate that the solutions possess good convergence. By comparing the three-dimensional solutions with the shear-lag solutions, evident difference may be found.

## Improved non-singular local boundary integral equation method

### Applied Mathematics and Mechanics (2007-08-01) 28: 1093-1099 , August 01, 2007

When the source nodes are on the global boundary in the implementation of local boundary integral equation method (LBIEM), singularities in the local boundary integrals need to be treated specially. In the current paper, local integral equations are adopted for the nodes inside the domain and moving least square approximation (MLSA) for the nodes on the global boundary, thus singularities will not occur in the new algorithm. At the same time, approximation errors of boundary integrals are reduced significantly. As applications and numerical tests, Laplace equation and Helmholtz equation problems are considered and excellent numerical results are obtained. Furthermore, when solving the Helmholtz problems, the modified basis functions with wave solutions are adapted to replace the usually-used monomial basis functions. Numerical results show that this treatment is simple and effective and its application is promising in solutions for the wave propagation problem with high wave number.