开孔薄板的变分原理及屈曲和过屈曲分析的有限元方法

本文以开孔薄板大挠度问题的一般理论为基础,建立了以挠度 w 和应力函数F为未知量的变分原理,并由此建立了用于分析开孔薄板屈曲和过屈曲问题的有限单元法可以看到由于区域的多连通性,单元性质是较为复杂的。     

Buckling and post-buckling of annular plates under non-axisymmetric plane edge forces

On the basis of both the general theory [1,2] and the finite element method [4] of perforated thin plates with large deflection,the buckling and post-buckling of annular plates under non-axisymmetric plane edge forces are studied.The Project supported by the State Education Commission of the People's Republic of China     

A rectangular element of thin plates based upon the generalized variational principles

Based on generalized variational principles, an element called M R-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible element converges very rapidly and has good accuracy. It was demonstrated that generalized variational principles are useful and effective in founding incompatible element. Moreover, element MR-12 is easy for implementation since it does not differ very much from the common rectangular element R-12 of thin plate.     

THE MATHEMATICAL MODELS AND GENERALIZED VARIATIONAL PRINCIPLES OF NONLINEAR ANALYSIS FOR PERFORATED THIN PLATES

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BUCKLING AND POST-BUCKLING OF ANNULAR PLATES UNDER xNON-AXISYMMETRIC PLANE EDGE FORCES

On the basis of both the general theory[1,2]and the finite element method[4]ofperforated thin plates with large deflection,the buckling and post-buckling of annular platesunder non-axisymmetric plane edge forces are studied.     

开孔粘弹性薄板的非线性数学模型

应力函数的多值性和位移单值性要求，是开孔薄板大挠度问题中必须注意的两个方面。本文利用线粘性力学中的Ｂｏｌｔｚｍａｎｎ蠕变律，把开孔弹性薄板大挠度问题的一般数学理论推广到开孔弹性薄板。在考察应力函数的多值性和位移单值性条件的基础上，提出了开孔粘弹性薄板的控制方程和初、边值条件，系统地建立了开也粘弹性薄板非线性分析的三类初一边值问题。     

Optimizing formulation of hybrid model for thin and moderately thick plates

A 20 — DOF hybrid stress element based upon Mindlin plate theory is developed using the optimization design method for thin and moderately thick plates. Numerical tests consist of the convergency and performance to the plates with arbitrary thickness and shape and of the ultimate thin plate problems.Projects Supported by the National Natural Science Foundation of China.     

Elastic buckling of rectangular plates under linearly varying in-plane normal load with a circular cutout

The elastic buckling behavior of rectangular perforated plates was studied by using the finite element method in this study. Circular cutout was chosen at different locations along the principal x-axis of plates subjected to linearly varying loading in order to evaluate the effect of cutout location on the buckling behavior of plates. The results show that the center of a circular hole should not be placed at the end half of the outer panel for all loading patterns. Furthermore, the presence of a circular hole always causes a decrease in the elastic buckling load of plates subjected to bending, even if the circular hole is not in the outer panel.     

The existence of buckled states on a perforated thin plate

On the basis of the generalized yon Kàrmàn theory for perforated thin plates established in [1, 2], the existence of buckled states for perforated plates subjected to self-equilibrating inplane forces along each edge systematically is investigated. This work completely generalizes the results in [3, 4].     

复合材料层合厚板锯齿理论及有限元分析

对于较厚复合材料弯曲问题,已有锯齿型厚板理论最大误差超过35%。为了合理地分析较厚复合材料弯曲问题,发展了准确高效的锯齿型厚板理论。此理论位移变量个数独立于层合板层数,其面内位移不含有横向位移一阶导数,构造有限元时仅需C0插值函数,故称此理论为C0型锯齿厚板理论。基于发展的锯齿理论,构造了六节点三角形单元并推导了复合材料层合/夹层板弯曲问题有限元列式。为验证C0型锯齿厚板理论性能,分析了复合材料层合/夹层厚板弯曲问题,并与已有C1型锯齿理论对比。结果表明,本文的C0型锯齿厚板理论最大误差15%,比已有锯齿型厚板理论准确高效。     

孔结构金属复合夹芯板抗爆炸冲击响应及吸能特性研究

采用有限元方法研究爆炸载荷下四边固支孔结构金属复合夹芯板的动力响应及吸能特性,给出了孔结构金属复合夹芯板的动力响应过程,得到夹芯板的变形模式,比较了孔结构金属复合夹芯板与非孔结构金属复合夹芯板的抗爆炸冲击性能,同时讨论了孔大小、间距、排布方式和面板质量分布等因素对孔结构金属复合夹芯板抗爆炸冲击性能的影响。研究结果表明,迎爆面外面板的孔设计使爆炸冲击波穿过孔洞直接作用在芯材上,增强了芯材的压缩,从而提高了夹芯板的能量吸收能力。同等面密度情况下,内外面板厚度比大于1的孔结构金属复合夹芯板变形挠度小于内外面板厚度比小于1的孔结构金属复合夹芯板。进一步研究发现,通过合理设计内外面板的质量分布,可以使孔结构金属复合夹芯板的抗爆炸冲击性能最优。     

A new twelve DOF quadrilateral element for analysis of thick and thin plates

A simple quadrilateral 12 DOF plate bending element based on Reissner–Mindlin theory for analysis of thick and thin plates is presented in this paper. This element is constructed by the following procedure:

• 1.the variation functions of the rotation and shear strain along each side of the element are determined using Timoshenko's beam theory; and
• 2.the rotation, curvature and shear strain fields in the domain of the element are then determined using the technique of improved interpolation.

The proposed element, denoted by ARS-Q12, is robust and free of shear locking and, thus, it can be employed to analyze very thin plate. Numerical examples show that the proposed element is a high performance element for thick and thin plates.     

Interaction of thin perforated plates and weak shock waves

The paper presents experimental results on elastic deformation of perforated thin plates made of glass-fiber laminate and subjected to weak shock waves. The characteristics of the dynamic process in the plates are determined __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 126–130, November 2006.     

Elasto-plastic buckling analysis for perforated steel plates subject to uniform compression

This study investigates the elasto-plastic buckling behaviour of simply supported square and rectangular thin steel plates having elliptic cut-outs by means of finite element method. Plates with simply supported in the out-of-plane direction are applied uniform compression in long-edge direction. A50 steel was used in the analysis and the focus was on the effect of plate aspect ratio, elliptical hole size, elliptical hole angle, elliptical hole location and slenderness ratio on buckling behaviour. It was found in the study that as the plate slenderness ratio increases, the critical buckling stress decreases for all the perforated plates.     

Effect of multiperforated plates on the acoustic modes in combustors

The analytical model derived by Howe assessing the acoustic effect of perforated plates has been implemented in a 3D Helmholtz solver. This solver allows one to compute the acoustic modes of industrial chambers taking into account the multiperforated plates present for the cooling of the walls. An academic test case consisting of two coaxial cylinders, with the inner one being perforated is used to validate the implementation in the general purpose AVSP code. This case is also used to show the effects of the presence of the plates. In particular, the sensitivity of the acoustic damping to the bias flow speed will be studied. A maximum absorption speed is shown, and the behaviour towards an infinite speed will be illustrated by the academic case. Computations are also conducted in the case of an industrial helicopter chamber. The value of the maximum absorption speed is discussed to explain why the modes are in fact not much absorbed by the perforated plates, and that the frequencies are the same as for walls. To cite this article: E. Gullaud et al., C. R. Mecanique 337 (2009).     

Formulation of a semi-analytical approach based on Gurtin variational principle for dynamic response of general thin plates

4 semi-analytical approach for the dynamic response of general thin plates which employes finite element discretization in space domain and a series of representation in time domain is developed on the basis of Gurtin variational principles. The formulation of time series is also investigated so that the dynamic response of plates with arbitrary shape and boundary constraints can be achieved with adequate accuracy.Project supported by the National Natural Science Foundation of China     

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。     

A NEW ELEMENT FOR THIN PLATE OF BENDING WITH CURVILINEAR BOUNDARY—CURVILINEAR BOUNDARY QUADRILATERAL ELEMENT

This paper presents a curvilinear boundary quadrilateral element for the problem of thin plate of bending with curvilinear boundary. A coordinate transformation of two dimensions is performed in the calculation of FEM. The introduction of an additional stiffness matrix based on the generalized variational principles results in high accuracy and less computation time. The numerical results agree with the analytical solution very well.     

Numerical prediction of turbulent flow in a conical diffuser usingk-ε model

Fully developed incompressible turbulent flow in a conical diffuser having a total divergence angle of 8° and an area ratio of 4∶1 has been simulated by ak-ε turbulence model with high Reynolds number and adverse pressure gradient. The research has been done for pipe entry Reynolds numbers of 1.16×10⁵ and 2.93×10⁵. The mean flow velocity and turbulence energy are predicted successfully and the advantage of Boundary Fit Coordinates approach is discussed. Furthermore, thek-ε turbulence model is applied to a flow in a conical diffuser having a total divergence angle of 30° with a perforated screen. A simplified mathematical model, where only the pressure drop is considered, has been used for describing the effect of the perforated screen. The optimum combination of the resistance coefficient and the location of the perforated screen is predicted for high diffuser efficiency or the uniform velocity distribution.