BEM formulation for von Kármán plates

This work deals with nonlinear geometric plates in the context of von Kármán's theory. The formulation is written such that only the boundary in-plane displacement and deflection integral equations for boundary collocations are required. At internal points, only out-of-plane rotation, curvature and in-plane internal force representations are used. Thus, only integral representations of these values are derived. The nonlinear system of equations is derived by approximating all densities in the domain integrals as single values, which therefore reduces the computational effort needed to evaluate the domain value influences. Hyper-singular equations are avoided by approximating the domain values using only internal nodes. The solution is obtained using a Newton scheme for which a consistent tangent operator was derived.     

A justification of the Marguerre-von Kármán equations

The method of asymptotic expansions, with the thickness as the small parameter, is applied to the general three-dimensional equations for the equilibrium of nonlinearly elastic shells with specific geometries, subjected to suitable loadings and boundary conditions. Then it is shown that the leading term of the expansion is the solution of a system of equations equivalent to those of Marguerre-von Karman (the case of a clamped shell is also considered). In addition, without making any a priori assumption regarding the variation of the unknowns across the thickness of the shell, it is found that the displacement field is of Kirchhoff-Love type, and that the stresses have polynomial variations with respect to the thickness.This approach clearly delineates the types of three-dimensional loadings, boundary conditions, and shallowness, for which a three-dimensional problem may be deemed asymptotically equivalent to a two-dimensional shallow shell model.Dedicated to Professor Joachim A. Nitsche on the occasion of his sixtieth birthday     

Hybrid control of vibrations of a smart von Kármán plate

The suppression of large vibrations of a smart thin elastic rectangular von Kármán’s plate is considered. The plate is subjected to external disturbances and generalized control forces produced by electromechanical feedback. The considered nonlinear initial-boundary value problem is spatially discretized by means of the time spectral method. The implicit Newmark-β iterative method is employed for the time integration of the obtained system of nonlinear equations of motion. Nonlinear controllers are designed, based on a fuzzy inference system. Two numerical algorithms involving a general control of displacement/velocity and a direct control of the Fourier coefficients are proposed. The techniques have been implemented within MATLAB environment with the use of the fuzzy logic toolbox. Numerical examples are presented.     

A consistent deduction of von Kármán-type plate theories from three-dimensional nonlinear continuum mechanics

Summary Classical and refined plate theories derived from linear continuum mechanics lead to correct results only if the transverse deflection of the plate is small compared to its thickness. In the case of large deflections, geometrical nonlinearities have to be incorporated. For the classical Kirchhoff plate theory, a suitable extension for moderate rotations has been presented by von Kármán in 1911.Starting from the three-dimensional equations of nonlinear continuum mechanics, a family of von Kármán-type plate theories is deduced. For the derivation, the kinematical variables are replaced by a series representation and the principle of virtual displacements is used. It can be shown that most plate theories can be obtained from this type of theory and that the kinematical assumptions must fulfill certain conditions to obtain a solvable system of equations.     

修正Szász算子线性组合的逼近

给出了修正 Szász算子线性组合点态逼近的正逆定理     

Application of the boundary-domain element method to the pre/post-buckling problem of von Kármán plates

Based on the BEM formulations for the finite deflection problem of von-Kármán-type plates, this paper presents an incremental boundary-domain element method for the pre/post-buckling problem of thin elastic plates. As the governing equations involve the coupled in-plane and out-of-plane deformations as the nonlinear terms, the boundary integral equations are formulated in terms of the increment by using the fundamental solutions for the linear parts of the differential operators. Some of the innovations are made in order to improve the accuracy and accelerate the convergence of the solution procedure. The load-incrementation method and also the arc-length-incrementation method are employed for each incremental step. Numerical analysis is carried out and the results are compared with the available analytical solutions to demonstrate the effectiveness of the proposed method.     

Manuel González Salazar,the Peruvian Atget

The Lima-born photographer Manuel González Salazar documented the colonial architectural heritage of his native city, as well as other major Peruvian cities such as Cusco, Arequipa, Ayacucho, Cajamarca and Trujillo. Just as Eugène Atget had documented the old Paris that he saw gradually disappearing, González Salazar chose to photograph the architectural and artistic heritage of the colonial era, which dominated the urban environment of the Peru of his day, but which was threatened by modernisation and social change. Like Atget in the French context, González Salazar is an anomaly in the history of Peruvian twentieth-century photography, which is best known on the international stage for indigenismo and the depiction of pre-Hispanic customs. The rediscovery of González Salazar’s work invites scholars to pay greater attention to the cultural heritage of the colonial era, as well as to the archives that documented it in all its splendour.     

A perturbation solution of von-Kármán circular plates with different moduli in tension and compression under concentrated force

By modifying classical von-Kármán equations, we established bimodular von-Kármán equations of thin plates with different moduli in tension and compression. Adopting central deflection as a perturbation parameter, we used a perturbation method to solve the equations under various boundary conditions, including rigidly clamped, loosely clamped, simply hinged, and simply supported. The relation of load versus central deflection and stress formulas were derived via the perturbation solution obtained. The numerical simulation also shows that the perturbation solution based on central deflection is overall valid. The results indicate that when the compressive modulus of materials is greater than the tensile one, the bearing capacity of the plate will be further strengthened, which should be considered in the analysis and design of plate-like structures with obvious bimodular effect. Moreover, by comparing with the case under uniformly distributed load, the plate-membrane transition under centrally concentrated force presents discontinuity to some extent.     

Absolute instability of the von Kármán, Bödewadt and Ekman flows between a rotating disc and a stationary lid

The stability of a family of boundary-layer flows, which includes the von Kármán, B?dewadt and Ekman flows for a rotating incompressible fluid between a rotating disc and a stationary lid, is investigated. Numerical computations with the use of a spectral method are carried out to analyse absolute and convective instability. It is shown that the stability of the system is enhanced with a decrease in distance between the disc and the lid.     

Results of outdoor radon monitoring in Bratislava and Nováky

Measurements of radon activity concentration (RAC) were made in two localities of Slovakia. The first one is located on the campus of Comenius University in Bratislava, where radon has been monitored since 1991. The second area is situated in the city of Nováky (midwest Slovakia, ～150 km from Bratislava). The localities have a different orography. RAC was measured continuously by large-volume scintillation chambers. The outdoor air was sampled at a height of 1.5 m above the ground. Time courses of RAC in both localities have a similar character. The correlation coefficients between RAC in Bratislava and Nováky was quite high (R(2) = 0.45). However, RACs in Nováky were found out to be about two times higher (～12.1 Bq m(-3)) than in Bratislava.     

关于Szász-Durrmeyer-Bézier算子的点态逼近

Bézier型算子是一些著名算子的推广,已有研究成果主要是对有界变差函数的逼近,而对于应用光滑模研究其中心逼近定理的结果很少.本文利用一阶Ditzian-Totik模得到了Szász-Durrmeyer-Bézier算子点态逼近的正、逆定理及等价定理这一完美的逼近结果.     

Prof. Tibor Jávor, M. Sc., PhD. DrSc

RILEM Bulletin

Prof. Tibor Jávor, M. Sc., PhD. DrSc     

A general method for analyzing moderately large deflections of a non-uniform beam: an infinite Bernoulli–Euler–von Kármán beam on a nonlinear elastic foundation

The present paper concerns a semi-analytical procedure for moderately large deflections of an infinite non-uniform static beam resting on a nonlinear elastic foundation. To construct the procedure, we first derive a nonlinear differential equation of a Bernoulli–Euler–von Kármán “non-uniform” beam on a “nonlinear” elastic foundation, where geometrical nonlinearities due to moderately large deflection and beam non-uniformity are effectively taken into account. The nonlinear differential equation is transformed into an equivalent system of nonlinear integral equations by a canonical representation. Based on the equivalent system, we propose a method for the moderately large deflection analysis as a general approach to an infinite non-uniform beam having a variable flexural rigidity and a variable axial rigidity. The method proposed here is a functional iterative procedure, not only fairly simple but straightforward to apply. Here, a parameter, called a base point of the method, is also newly introduced, which controls its convergence rate. An illustrative example is presented to investigate the validity of the method, which shows that just a few iterations are only demanded for a reasonable solution.     

Photothermal Radiometry Characterization of Limestone Rocks from the Península of Yucatán

Limestone is a sedimentary rock composed of calcium carbonate with minor amounts of silica, iron oxide, clay, dolomite, and organic material. These types of stones have been used extensively as building materials. Due to this, determination of their thermal properties is of the utmost importance. These properties depend on the microstructure and composition of each type of rock. In this study, the effect of the thermal treatment of three different limestone rocks from the Peninsula of Yucatán were studied, in the range from 100?°C up to 600?°C, using photothermal radiometry. These studies were complemented by the characterization of the crystalline phases using X-ray diffraction and effective porosity measurements performed by the saturation technique. It is shown that the thermal diffusivity, thermal conductivity, and specific heat of the limestone decrease as the temperature increases. This behavior can be related to increases in microcracks and effective porosity due to thermal treatments.     

修正的Szász算子同时逼近的点态估计(英文)

证明了定义在 [0 ,∞ )上的具有 s阶连续有界导数的函数可以用修正的 Sza′sz算子线性组合的 s阶导数逼近 ,得到了点态逼近的正定理和逆定理 .     

Optimal defocus distance for testing the 2.1 m telescope at San Pedro Mártir

Within the preliminary development of a low-cost active optics system (AOS), computer simulations have been performed. The general purpose of simulations is to find an optimal scheme for the wavefront control of the primary mirror. We present results for the wavefront sensor of the AOS proposed for the 2.1 m telescope at San Pedro Mártir. The method presented here can be used for any other telescopes as well.     

二维直方图斜分Tsallis–Havrda–Charvát熵图像阈值分割

本文指出了现有二维直方图区域直分法中存在明显的错分,提出了二维直方图区域斜分方法,即通过与主对角线平行的四条斜线将直方图分成内点区、边界点区和噪声点区,并按灰度级与邻域平均灰度级之和的大小进行分割.该方法可以运用于所有的基于二维直方图的阈值分割.文中导出了基于二维直方图区域斜分的Tsallis–Havrda–Charvát 熵阈值选取公式及其快速递推算法,给出了分割结果和运行时间.与基于二维直方图直分的Tsallis–Havrda–Charvát 熵原始算法相比,本文提出的基于二维直方图斜分的Tsallis–Havrda–Charvát 熵阈值分割算法,使分割后的图像内部区域均匀,边界形状准确,更有稳健的抗噪性,其运行时间减少了五个数量级.     

Active primary mirror support for the 2.1-m telescope at the San Pedro Mártir Observatory

We have designed and installed a new set of actuators for the suspension of the primary mirror of the 2.1-m telescope at San Pedro Mártir. This active optics system has allowed us to correct low-order aberrations identified by several wave-front analysis techniques.