关于开孔薄板大挠度问题的一般数学理论(续)

本文讨论了作用在开孔薄板的各孔边上的外力自身不平衡吋的大挠度问题的应力函数的多值性,并给出了这种问题的一般数学模型,因此本文可以看成是[1]的继续和深入。     

Elastic buckling of isotropic triangular flat plates by finite elements

Although most of the plates in steel structures are rectangular, some triangular ones do occur. The number of available solutions for triangular plate buckling coefficients is small, and restricted to special triangle geometries and loading ratios. In this paper the range of available solutions is extended by the use of a plate bending finite element devised by Irons. A range of plate parameters is considered and results are tabulated and plotted. The program is available for the use of designers who wish to consider other values of parameters. The use of the procedures described in the Merrison report can extend these results to deal with the influence of initial imperfections and weld effects.     

Design of axisymmetric sandwich plates for alternative loads

The minimal-weight design of sandwich plates whose rigidplastic face sheets obey the Tresca yield condition and which are subjected to two alternative loads is systematically determined by the method of stress variation. It is shown that, when the loads are unidirectional, the general solution for a certain class of edge conditions consists of five fundamentally different designs. The totality of optimal design solutions is depicted in the form of a design chart. A comprehensive example is presented to illustrate the method.This paper is based in part upon a dissertation submitted by the first author to The University of Iowa in partial fulfillment of requirements for the PhD Degree.     

Approximation of boundary values in the boundary element method

Various techniques may be applied to the approximation of the unknown boundary functions involved in the boundary element method (BEM). Several techniques have been examined numerically to find the most efficient. Techniques considered were: Lagrangian polynomials of the zeroth, first and second orders; spline functions; and the novel weighted minimization technique used successfully in the finite difference method (FDM) for arbitrarily irregular meshes. All these approaches have been used in the BEM for the numerical analysis of plates with various boundary conditions.Both coarse and fine grids on the boundary have been assumed. Maximal errors of the deflections of each plate and the bending moments have been found and the effective computer CPU times determined.Analysis of the results showed that, for the same computer time, the greatest accuracy was obtained by the weighted FDM approach. In the case of the Lagrange approximation, higher order polynomials have proved more efficient. The spline technique yielded more accurate results, but with a higher CPU time.Two discretization approaches have been investigated: the least-squares technique and the collocation method. Despite the fact that the simultaneous algebraic equations obtained were not symmetric, the collocation approach has been confirmed as clearly superior to the least-squares technique, because of the amount of computation time used.     

A theoretical model of magnetoelastic bucking for soft ferromagnetic thin plates

As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been conducted. One of the key steps for the theoretical prediction of the critical magnetic field is how to formulate magnetic force exerted on the magnetized medium. Till today, the theoretical predictions, from theoretical models in publications, of the magnetoelastic buckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are all higher than their experimental data. Sometimes, the discrepancy between them is as high as 100%. In this paper, the macroscope formulation of the magnetic forces is strictly obtained from the microscope Amperion current model. After that, a new theoretical model is established to describe the magnetoelastic buckling phenomenon of ferromagnetic thin plates with geometrically nonlinear deformation in a nonuniform transverse magnetic field. The numerical method for quantitative analysis is employed by combining the finite elemental method for magnetic fields and the finite difference method for deformation of plates. The numerical results obtained from this new theoretical model show that the theoretical predictions of critical values of the buckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellent agreement with their experimental data. By the way, the region of applicability to the Moon-Pao's model, or the couple model, is checked by quantitative results. This project was supported in part by the National Natural Science Foundation of China and the Foundation of the SEdC of China for Returned Chinese Scholars from Abroad.     

基于半波带分析法的菲涅耳波带片衍射特性的讨论

基于半波带的分析方法简单明了地分析了平行光经菲涅耳波带片衍射后的多焦点特性以及各焦点的光强变化规律．     

Dusty effects on pulsating viscous flow of two immiscible fluids between two parallel plates

The flow of two immiscible incompressible dusty viscous fluids between two parallel plates generated by a pulsating pressure gradient is investigated. Velocity fields for the fluid-particle system along with the expressions for the skin friction drag at the plates are obtained and studied graphically. It is found that there is an immediate response to pressure fluctuations in the first stream at low frequency range 0<σ≤4 being maximum at σ=4. On the contrary, the second stream is more responsive to fluctuations at relatively higher frequencies. The maximum response in this case is shifted to σ=16.     

Transmission of sound through a pair of rectangular elastic plates

^** Email: f.leppington{at}ukonline.co.uk Two thin elastic plates, which may have different physical parameters,occupy the parallel regions 0 < x < a, 0 < y < b,z = – d and 0 < x < a, 0 < y < b, z = 0, ina Cartesian coordinate system, where the separation distanced is much less than the dimensions a and b. The plates are simplyconnected to a structure that occupies the rest of the region– d < z < 0. The side walls (x = 0 or a, 0 <y < b, – d < z < 0 and y = 0 or b, 0 < x <a, – d < z < 0) are taken to be acoustically soft;the surfaces z = – d and z = 0, outside the rectangularregions occupied by the plates, are taken to be acousticallyhard. Light compressible fluid (air) is in each of the half-spacesoutside the plates and in the rectangular region between them.A sound field is induced by a high-frequency plane wave. Allowanceis made for a small element of damping in the fluid trappedbetween the plates, as well as damping in the plates. Estimatesare derived for the transmitted power, averaged over a frequencyband and with respect to all incidence directions, in the asymptoticlimits of small fluid loading and high frequency. For the casewhere the two plates have identical physical properties, detailedasymptotic estimates are given for the form of the peaks inthe transmitted power, at a discrete set of operating frequencies,both above and below the plates' coincidence frequency.     

The particular solutions for thin plates resting on Pasternak foundations under arbitrary loadings

Analytical particular solutions of splines and monomials are obtained for problems of thin plate resting on Pasternak foundation under arbitrary loadings, which are governed by a fourth‐order partial differential equation (PDEs). These analytical particular solutions are valuable when the arbitrary loadings are approximated by augmented polyharmonic splines (APS) constructed by splines and monomials. In our derivations, the real coefficient operator in the governing equation is decomposed into two complex coefficient operators whose particular solutions are known in literature. Then, we use the difference trick to recover the analytical particular solutions of the original operator. In addition, we show that the derived particular solution of spline with its first few directional derivatives are bounded as r → 0. This solution procedure may have the potential in obtaining analytical particular solutions of higher order PDEs constructed by products of Helmholtz‐type operators. Furthermore, we demonstrate the usages of these analytical particular solutions by few numerical cases in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Smoothness properties of Newtonian potentials in the study of elastic plates

The Hölder continuity and differentiability are investigated of Newtonian potentials arising in the theory of bending of elastic plates with transverse shear deformation. These properties play an essential role in the study by means of boundary integral equation techniques of boundary value problems for the equilibrium and harmonic oscillation states, and in the construction of associated boundary element methods.