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51.
本文用样条边界元法分析轴对称圆形基础板的非线性非光滑接触。除事先给出外力与地基表面位移的对应关系外,地基的模型、板的厚薄(Reissner/Kirchhoff型)和外荷载沿径向的分布均可是任意的。文中将地基反力看作板的外载,对变量沿径向采用不等距祥条插值,并用无地基效应的板基本解。算例表明本文方法只要用少量自由度,便可得到令人满意的结果。 相似文献
52.
从虚功原理出发,证明了薄板小挠度弯曲问题的功的互等定理,并由此推出了求解矩形薄板自然频率的公式.算例表明,该公式计算简便,精度较高. 相似文献
53.
A customary, heuristic, method, by which the Poisson integral formula for the Dirichlet problem, for the half space, for Laplace's equation is obtained, involves Green's function, and Kelvin's method of images. Although this heuristic method leads one to guess the correct result, this Poisson formula still has to be verified directly, independently of the method by which it was arrived at, in order to be absolutely certain that a solution of the Dirichlet problem for the half space, for Laplace's equation, has been actually obtained. A similar heuristic method, as seems to be generally known, could be followed in solving the Dirichlet problem, for the half space, for the equation where is a real constant. However, in Part 1, a different, labor-saving, method is used to study Dirichlet problems for the equation. This method is essentially based on what Hadamard called the method of descent. Indeed, it is shown that he who has solved the half space Dirichlet problem for Laplace's equation has already solved the half space Dirichlet problem for the equation In Part 2, the solution formula for the quarter space Dirichlet problem for Laplace's equation is obtained from the Poisson integral formula for the half space Dirichlet problem for Laplace's equation. A representation theorem for harmonic functions in the quarter space is deduced. The method of descent is used, in Part 3, to obtain the solution formula for the quarter space Dirichlet problem for the equation by means of the solution formula for the quarter space Dirichlet problem for Laplace's equation. So that, indeed, it is also shown that he who has solved the quarter space Dirichlet problem for Laplace's equation has already solved the quarter space Dirichlet problem for the " equation" For the sake of completeness and clarity, and for the convenience of the reader, the appendix, at the end of Part 3, contains a detailed proof that the Poisson integral formula solves the half space Dirichlet problem for Laplace's equation. The Bibliography for Parts 1,2, 3 is to be found at the end of Part 1. 相似文献
54.
55.
F. J. Garcia‐Garcia T. Y. Chiu P. Skeldon G. E. Thompson 《Surface and interface analysis : SIA》2015,47(1):30-36
Cathodic polarization of aluminium and Al–0.18 wt.% Mg and Al–0.08 wt.% Ti alloys in 0.24 mol dm?3 nitric acid solution at 38 °C has been employed to assist understanding of the roles of alloying elements in electrograining. The findings indicate that additions of magnesium and titanium to aluminium accelerate the corrosion of the substrate under the alkalization caused by the cathodic reactions. The accelerated dissolution and the consequent formation of hydrated alumina result in a decreased net cathodic current density in potentiostatic and potentiodynamic polarization conditions relative to the behaviour of aluminium. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
56.
A three-dimensional, explicit and exact, equilibrium solution is derived for transversely isotropic, linearly elastic bodies
in the form of a right cylinder simply supported over its lateral boundary and loaded over its end faces. This solution, which
generalizes an earlier proposal of Levinson in various respects, is to serve as a benchmark for the corresponding plate theories.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
57.
The Poincaré sphere representation of polarization states is used to derive two auxiliary equations for phase retardance measurements. These equations, in addition to another two previously derived equations, allow for extending the range of validity of a model for calibrating phase plates in pairs. In another application, the sphere is used to explain a new method for identifying the principal axes of two birefringent phase plates during their calibration. 相似文献
58.
Aliki D. Muradova 《Advances in Computational Mathematics》2008,29(2):179-206
In this paper a spectral method and a numerical continuation algorithm for solving eigenvalue problems for the rectangular
von Kármán plate with different boundary conditions (simply supported, partially or totally clamped) and physical parameters
are introduced. The solution of these problems has a postbuckling behaviour. The spectral method is based on a variational
principle (Galerkin’s approach) with a choice of global basis functions which are combinations of trigonometric functions.
Convergence results of this method are proved and the rate of convergence is estimated. The discretized nonlinear model is
treated by Newton’s iterative scheme and numerical continuation. Branches of eigenfunctions found by the algorithm are traced.
Numerical results of solving the problems for polygonal and ferroconcrete plates are presented.
Communicated by A. Zhou. 相似文献
59.
A. H. England 《Journal of Elasticity》2006,82(2):129-173
A procedure has been developed in previous papers for constructing exact solutions of the equations of linear elasticity in a thick plate of inhomogeneous isotropic linearly elastic material in which the elastic moduli depend in any specified manner on a coordinate normal to the plane of the plate. The essential idea is that any solution of the classical thin plate or classical laminate theory equations (which are two-dimensional theories) generates, by straightforward substitutions, a solution of the three-dimensional elasticity equations for the homogeneous material. Recently this theory has been formulated in terms of functions of a complex variable. It was shown that the displacement and stress fields in the inhomogeneous material could be expressed in terms of four complex potentials that are analytic functions of the complex variable ζ = x + iy in the mid-plane of the plate. However, the analysis performed so far applies only to the case of a plate with traction-free upper and lower faces. The present paper extends these solutions to the case where the plate is bent by a pressure distribution applied to a face. 相似文献
60.
A recently developed coupled third-order zigzag theory for the statics of piezoelectric hybrid cross-ply plates is extended
to dynamics. The theory combines a third-order zigzag approximation for the in-plane displacements and a sub-layerwise linear
approximation for the electric potential, considering all components of the electric field. The nonuniform variation of the
transverse displacement due to the piezoelectric field is accounted for. The conditions for the absence of shear traction
at the top and bottom surfaces and continuity of transverse shear stresses in the presence of electromechanical loading are
satisfied exactly, thereby reducing the number of displacement variables to five, which is the same as in a first- or third-order
equivalent single-layer theory. The governing equations of motion are derived from the extended Hamilton's principle. The
theory is assessed by comparing the Navier solutions for the free and forced harmonic vibration response of simply supported
plates with the exact three-dimensional piezoelasticity solutions. Comparisons for hybrid test, composite and sandwich plates
establish that the present theory is quite accurate for the dynamic response of moderately thick plates. 相似文献