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11.
Fracture of a rectangular piezoelectromagnetic body 总被引:5,自引:0,他引:5
The singular stress, electric fields and magnetic fields in a rectangular piezoelectromagnetic body containing a center Griffith crack under longitudinal shear are obtained. Fourier transforms and Fourier sine series are used to reduce the mixed boundary value problems of the crack, which is assumed to be impermeable, to dual integral equations. The solution of the dual integral equations is then expressed in terms of Fredholm integral equations of the second kind. Expressions for stresses, electric displacements and magnetic inductions in the vicinity of the crack tip are derived. Also obtained are the field intensity factors and the energy release rates. Numerical results obtained show that the geometry of the rectangular body have significant influence on the field intensity factors and the energy release rates. 相似文献
12.
We propose an efficient approach to the problem of multi-degree reduction of rectangular Bézier patches, with prescribed boundary control points. We observe that the solution can be given in terms of constrained bivariate dual Bernstein polynomials. The complexity of the method is O(mn1n2) with m ? min(m1, m2), where (n1, n2) and (m1, m2) is the degree of the input and output Bézier surface, respectively. If the approximation—with appropriate boundary constraints—is performed for each patch of several smoothly joined rectangular Bézier surfaces, the result is a composite surface of global Cr continuity with a prescribed r ? 0. In the detailed discussion, we restrict ourselves to r ∈ {0, 1}, which is the most important case in practical application. Some illustrative examples are given. 相似文献
13.
Shahrokh Hosseini-Hashemi Mohammad Fadaee Hossein Rokni Damavandi Taher 《Applied Mathematical Modelling》2011
In this paper, exact closed-form solutions in explicit forms are presented for transverse vibration analysis of rectangular thick plates having two opposite edges hard simply supported (i.e., Lévy-type rectangular plates) based on the Reddy’s third-order shear deformation plate theory. Two other edges may be restrained by different combinations of free, soft simply supported, hard simply supported or clamped boundary conditions. Hamilton’s principle is used to derive the equations of motion and natural boundary conditions of the plate. Several comparison studies with analytical and numerical techniques reported in literature are carried out to demonstrate accuracy of the present new formulation. Comprehensive benchmark results for natural frequencies of rectangular plates with different combinations of boundary conditions are tabulated in dimensionless form for various values of aspect ratios and thickness to length ratios. A set of three-dimensional (3-D) vibration mode shapes along with their corresponding contour plots are plotted by using exact transverse displacements of Lévy-type rectangular Reddy plates. Due to the inherent features of the present exact closed-form solution, the present findings will be a useful benchmark for evaluating the accuracy of other analytical and numerical methods, which will be developed by researchers in the future. 相似文献
14.
A.M.Zenkour 《Acta Mechanica Sinica》2011,27(6):956-962
The mixed first-order shear deformation plate theory(MFPT) is employed to study the bending response of simply-supported orthotropic plates.The present plate is subjected to a mechanical load and resting on Pasternak’s model or Winkler’s model of elastic foundation or without any elastic foundation.Several examples are presented to verify the accuracy of the present theory.Numerical results for deflection and stresses are presented.The proposed MFPT is shown simplely to implement and capable of giving satisfactory results for shear deformable plates under static loads and resting on two-parameter elastic foundation.The results presented here show that the characteristics of deflection and stresses are significantly influenced by the elastic foundation stiffness,plate aspect ratio and side-to-thickness ratio. 相似文献
15.
Ulrich Soupremanien Stephane Le PersonMichel Favre-Marinet Yann Bultel 《Experimental Thermal and Fluid Science》2011,35(5):797-809
This article presents experiments conducted with two single rectangular mini-channels of same hydraulic diameter (1.4 mm) and different aspect ratios for conditions of horizontal boiling flow. The Forane® 365 HX used was subcooled (ΔTsub = 15 °C) for all the boiling curves presented in the paper. Local heat transfer coefficients were measured for heat flux ranging from 25 to 62 kW m−2 and mass flux from 200 kg m−2 s−1 to 400 kg m−2 s−1. The boiling flows were observed with two different cameras (depending on the flow velocity) through a visualization window. The flow patterns in the two channels were compared for similar conditions. The results show that the boiling heat transfer coefficient and the pressure drop values are different for the two single mini-channels. For low heat flux condition, the channel with lowest aspect ratio (H/W = 0.143) has a higher heat transfer coefficient. On the other hand, for high heat flux condition, the opposite situation occurs, namely the heat transfer coefficient becomes higher for the channel with highest aspect ratio (H/W = 0.43). This is probably due to the earlier onset of dryout in the channel with lowest aspect ratio. For the two cases of heating, the pressure drop for the two-phase flow remains lower for the channel with lowest aspect ratio. These results show that the aspect ratio plays a substantial role for boiling flows in rectangular channels. As for single-phase flows, the heat transfer characteristics are significantly influenced (even though the hydraulic diameter remains the same) by this parameter. 相似文献
16.
17.
The Complete Biorthogonal Expansion Theorem
and Its Application to a Class of Rectangular
Plate Equations 下载免费PDF全文
In this paper, we first establish the separable $Hamiltonian$ system of rectangular cantilever thin plate bending problems by choosing proper dual vectors. Then using the characteristics of off-diagonal infinite-dimensional $Hamiltonian$ operator matrix, we derive the biorthogonal relationships of the eigenfunction systems and based on it we further obtain the complete biorthogonal expansion theorem. Finally, applying this theorem we obtain the general solutions of rectangular cantilever thin plate bending problems with two opposite edges slidingly supported. 相似文献
18.
Konstantin A. Lurie 《Journal of Mathematical Analysis and Applications》2006,314(1):286-310
We consider propagation of waves through a spatio-temporal doubly periodic material structure with rectangular microgeometry in one spatial dimension and time. Both spatial and temporal periods in this dynamic material are assumed to be of the same order of magnitude. A “double Floquet” solution is obtained in the special case when the wave equation t(ρut)−z(kuz)=0 allows for the separation of variables. We also consider a checkerboard microgeometry where variables cannot be separated. The squares in a space-time checkerboard are assumed to be filled with materials having equal impedance but different phase speeds. Within certain parameter ranges, we observe numerically the formation of distinct and stable limiting characteristic paths (“limit cycles”) that attract neighbouring characteristics after a few time periods. The average speed of propagation along the limit cycles remains the same throughout certain ranges of parameters of the microgeometry (the “plateau effect”). We formulate, as a hypothesis, the statement saying that a checkerboard structure is on a plateau if and only if it yields stable limit cycles. A dynamic material is a thermodynamically open system, as it is involved in a permanent exchange of energy and momentum with the environment. Material assemblages that produce the limit cycles are special in this aspect. Specifically, to make a wave travel through such an assemblage, we find analytically that an external agent may need to supply infinite energy and this may be so regardless of the wave frequency. For spatio-temporal laminates, however, an accumulation of energy (parametric resonance) may emerge only for frequencies that are not too low relative to some characteristic frequency of the system. 相似文献
19.
矩阵的多行拟相合分类及其应用 总被引:1,自引:0,他引:1
本文把方阵的拟相合概念推广为长方阵的多行拟相合概念,并对最简情形即M2,4(Fp)给出分类结果.此概念之一应用出现在有限环的同构分类之中. 相似文献
20.
In this paper, we describe a new computer simulation technique of generating Fresnel diffraction images from rectangular apertures of arbitrary dimensions by using Fresnel integrals instead of the more common fast Fourier transform methods. The simulation can be performed in almost any PC using the software MATLAB. Diffraction images can be generated for any wavelength of light and for any aperture–screen and aperture-source distances. Images for rectangular obstacles can also be simulated. Details of the algorithm and program are presented, as well as the interesting insights than can be gained from using the program. Finally, it is shown that the simulated images reduce to the simple Fraunhofer diffraction patterns for certain limiting situations. 相似文献