The magnetic field of an arbitrary shaped defect in a plane-parallel plate

The problem of an arbitrarily shaped defect in a ferromagnetic half-space and a plane-parallel plate plate is solved. The solution is expressed as an integral equation in which the integration was performed only over the defect surface. This integral equation is solved by the iteration method, which allows one to represent the solution as a series in powers of the small parameter \(\lambda /2\pi \left( {\lambda = \frac{{\mu - 1}}{{\mu + 1}}} \right)\). The numerical results are obtained for a defect in the form of an ellipsoid.     

热流道板的热平衡及温度场的有限元分析

热平衡是热流道系统的核心问题之一,热流道板的主要任务是恒温地将熔体从主流道送入各个单独喷嘴.热流道板必须处于热平衡状态,热损失必须通过加热来补偿.通过分析热流道板的热损失,进行加热器功率的计算,并利用ANSYS软件分析热流道板的温度场.     

一种快速计算二维缺陷漏磁场的有限元建模和求解方法

漏磁检测的速度快,灵敏度高,检测过程操作简单,是一种常用的铁磁材料无损检测方法,其中有限元模型被广泛用于漏磁检测中。有限元模型的求解精度高但是计算时间较长,因此,本文提出了一种快速计算二维缺陷漏磁场的有限元建模和求解方法,在保证精度的同时缩短计算时间。通过对有限元数值计算的理论推导,建立了漏磁场的有限元模型,首先采用六节点三角形单元划分网格,其次使用稀疏矩阵的形式求解方程组,再利用边界条件矩阵零空间的正交基求解出磁势。与COMSOL仿真软件的计算结果进行比较,表明本文所建模型是正确可行的。经过实测数据验证,该模型相比于传统有限元模型有明显的性能提升,精度上最大提高83.49%,计算时间能减少95.43%,为研究不规则缺陷的漏磁重构提供了快速有效的正演模型。     

The finite expansion of a circular hole in an infinite plate: A dynamic solution

The problem of dynamic expansion of a finite circular hole in an infinite plate, of uniform initial thickness, in a state of plane stress is worked out by solving the equation of motion. A numerical solution is obtained for a strain-hardening material using (i) a continuous three-parameter stress-strain relation and (ii) Nadai's J₂-deformation theory of plasticity. The solution is obtained by the method of characteristics for both ramp velocity and ramp pressure prescribed at the hole boundary.     

Mindlin plate finite elements by a modified transverse displacement

The formulation of 4-node plate bending elements to eliminate the shear locking is presented. The kinematic variables in the Mindlin plate are related through the equilibrium equations; and then the transverse displacement, rotations, and shear strain are expressed in terms of the curvature sum. The elements are formulated by using the modified transverse displacement defined as the transverse displacement subtracted by the curvature sum times the ratio of flexural to shear rigidity. It is shown that the elements describe plate behavior quite correctly without any locking and also that they are applicable to the analysis of both thin and thick plates.     

含特异材料缺陷层一维光子晶体多缺陷现象及其内部场分布

通过数值模拟和理论分析含特异材料缺陷层一维光子晶体中特异材料折射率与缺陷模式的关系,从而发现调节特异材料折射率可以得到不同状态的振荡透射模。同时还分析了保持特异材料折射率不变的情况下其它材料折射率改变对缺陷模式的影响,理论模拟了含特异材料缺陷层一维光子晶体内部场分布,从而可以非常清晰地再现缺陷模式的局域特性。     

The forced convection flow over a flat plate with finite length with a constant convective boundary condition

The flow of a fluid past a flat plate of finite length and infinite width (two-dimensional flow) is considered. The plate is heated by convection from a fluid with constant temperature T _f with a constant heat transfer coefficient h _f . In all previous works, the problem was considered using boundary layer theory whereas, in the present work, the solution is based on the full Navier-Stokes equations. The problem is investigated numerically with a finite volume method using the commercial code ANSYS FLUENT. The governing parameters are the Reynolds number, the new heat transfer parameter, and the Prandtl number. In addition, the influence of these three parameters on the temperature field is investigated. It is found that high Reynolds and high Prandtl numbers the wall temperature increases along the plate. They reach a maximum near the trailing edge then decrease. The same occurs as the heat transfer parameter increases. When the Reynolds and Prandtl numbers are low, the plate temperature tends to become symmetric, with a maximum at the middle of the plate. The temperature profiles become thicker as the Reynolds number and the Prandtl number is reduced while the temperature profiles become thicker as the heat transfer parameter increases.     

Boundary layer flow over a finite flat plate with a constant slip velocity

Two-dimensional incompressible laminar flow induced by a constant slip velocity on the surface of a finite flat plate is studied both analytically and numerically for large Reynolds numbers. It turned out that the thickness of the thin layer downstream of the trailing edge increases in square root of the distance from the trailing edge. Numerical integration of the boundary layer equations for the whole flow field confirmed two asymptotic natures of the flow field; near the trailing edge the analytic result is approached, and far downstream of the plate the jet flow solution is attained.     

离合器摩擦片热变形有限元分析

建立了摩擦离合器接合过程热分析数学模型,并利用有限元技术对离合器外摩擦片进行了热变形分析,结果显示离合器外摩擦片在一定工况条件下会发生翘曲变形,与实际外摩擦片变形情况一致,证明了热变形分析的正确性.该分析也为摩擦离合器安全工作提供了一定的理论依据.     

A three-dimensional finite element method for plate bending

A three-dimensional finite element method is proposed for plate bending. The displacement function is assumed to have a particular form with respect to the thickness variable.The assumed displacement function is substituted into the three-dimensional potential energy functional and a two-dimensional variational problem emerges.The two-dimensional problem is treated by the finite element method and it is seen that for conforming solutions the only requirement is continuity of the basis functions.The method includes transverse shear and thickness effects and may be used for both thin and moderately thick shells.To illustrate the method and to compare it with other results, the problems of a square plate under point and distributed loads and with simply supported and clamped boundary are treated numerically.     

On calculating the secondary field of a finite hard cylindrical shell

Using an analytical method, a formula was obtained to calculate the acoustic pressure of the secondary hydroacoustic field reradiated by a perfectly hard finite cylindrical shell in the far-field region.     

用于有限元分析的板壳模型的特征造型

为满足板壳结构有限元分析的需要，将板壳结构特征化，以平面特征和曲面特征表示几何特性，以网格特征表示离散特性，厚度、载荷和约束特征表示计算特性，从而形成了造型和有限元网格划分一体化的板壳模型特征造型方案。     

A magnetostatic problem for a semispace with a spherical defect in an inhomogeneous external field

Formulas for calculating the resulting field from a magnetic semispace containing a spherical cavity in an arbitrary field are derived. The results of calculations for an external field created by a turn with a current are presented as an example.     

Vibration analysis of a ferromagnetic plate subjected to an inclined magnetic field

The magnetic traction on a deformable ferromagnetic material is deduced based on the classical magnetoelastic model. The vibration frequency of a ferromagnetic beam subjected to an inclined magnetic field is analyzed by employing formulations of the magnetic force. The result for the condition of longitudinal magnetic field is the same trend as that of the previous experiment carried out by Takagi et al. [Analysis and experiment of dynamic deflection of a thin plate with a coupling effect. IEEE Transactions on Magnetics 1992;28(2):1259–62]. Moreover, experimental tests have been carried out to study the free vibration of a magnetic plate subjected to an inclined magnetic field.     

Prediction of actuating displacement in a piezoelectric composite actuator with a thin sandwiched PZT plate by a finite element simulation

This paper presents the evaluation of a plate-type piezoelectric composite actuator (PCA) with a thin sandwiched plate having four kinds of lay-up configurations by analyzing the flexural displacement For this, a three-dimensional finite element simulation considering the thermal deformation effect of PCA during manufacturing is conducted based on a thermal analogy model. The distribution of residual thermal stresses and the dome height caused by the mismatch in coefficient of thermal expansion (CTE) between the layers of PCA are predicted with the aid of a classical laminated plate theory (CLPT). Results of finite element analyses have revealed that the flexural displacement of PCA subjected to electric fields is considerably affected by the variation of lay-up configuration, the thickness of an embedded PZT wafer and boundary conditions. In particular, as the thickness of the PZT ceramic increases, the bending stiffhess of PCA increases faster than the actuation distance does, which leads to the overall reduction in flexural displacement. It is therefore suggested that the electrically induced flexural displacement of unimorph-type PCA depends more on the bending stiffhess than on the actuation distance.     

Non-linear analysis of skew thin plate by finite difference method

This paper deals with a discrete analysis capability for predicting the geometrically nonlinear behavior of skew thin plate subjected to uniform pressure. The differential equations are discretized by means of the finite difference method which are used to determine the deflections and the in-plane stress functions of plates and reduced to several sets of linear algebraic simultaneous equations. For the geometrically non-linear, large deflection behavior of the plate, the non-linear plate theory is used for the analysis. An iterative scheme is employed to solve these quasi-linear algebraic equations. Several problems are solved which illustrate the potential of the method for predicting the finite deflection and stress. For increasing lateral pressures, the maximum principal tensile stress occurs at the center of the plate and migrates toward the corners as the load increases. It was deemed important to describe the locations of the maximum principal tensile stress as it occurs. The load-deflection relations and the maximum bending and membrane stresses for each case are presented and discussed.     

Further results on non-Newtonian power-law flows past a two-dimensional flat plate with finite length

The flow of a non-Newtonian, power-law fluid directed either tangentially or normally to a flat plate of finite length and infinite width (two-dimensional flow) is considered. The problem is investigated numerically using the code ANSYS FLUENT. This problem has been investigated in the past but only for shear-thinning fluids (n < 1). We extend the investigation for the case of shear-thinning, Newtonian and shear-thickening fluids, covering a wide range of Reynolds numbers (from very low to very high). For low Reynolds numbers and low power-law index (n < 0.6) the drag coefficient obeys the relationship c _D = A/Re, both for tangential and normal flow. Equations for the quantity A have been derived as functions of the power-law index. For normal flow, the drag coefficient tends to become independent of the power-law index, both for shear-thinning and shear-thickening fluids at high Reynolds numbers.     

Application of modified mapping-collocation method to cracks emanating from a circular hole in an orthotropic finite plate

A modified mapping-collocation method is applied to the analysis of cracks emanating from a circular hole in an orthotropic finite plate under uniform stress. To check the effectiveness of this procedure, we present the various results for comparison with references. Then, the stress intensity factors are presented for several plate configurations of [0 _n /90 _m ] _s laminates. The results show that the modified mapping-collocation method is effectively applicable to analyzing such cracks in an orthotropic finite plate. The results also show that the stress intensity factors depend on the material orthotropy and geometry.     

A three-dimensional or penalty finite element method for plate bending

This paper, a sequel to an earlier paper by the same authors, uses a three dimensional or penalty function approach to obtain finite element solutions for plate bending problems. The advantage in using this approach is that the finite element subspaces need only be continuous; the disadvantages are that more functions are needed.In our previous paper, we used piecewise quadratic and linear functions, in the present paper we use piecewise cubic and quadratic functions with a resultant reduction of the discretization error. We also suggest an interpolation method or an a priori choice of the thickness to length ratio which are appropriate for thin or moderately thick plates. Numerical results are given for clamped and simply supported plates with point and distributed loads.