Finite element piezothermoelasticity analysis and the active control of FGM plates with integrated piezoelectric sensors and actuators

 An efficient finite element model is presented for the static and dynamic piezothermoelastic analysis and control of FGM plates under temperature gradient environments using integrated piezoelectric sensor/actuator layers. The properties of an FGM plate are functionally graded in the thickness direction according to a volume fraction power law distribution. A constant displacement-cum-velocity feedback control algorithm that couples the direct and inverse piezoelectric effects is applied to provide active feedback control of the integrated FGM plate in a closed loop system. Numerical results for the static and dynamic control are presented for the FGM plate, which consists of zirconia and aluminum. The effects of the constituent volume fractions and the influence of feedback control gain on the static and dynamic responses of the FGM plates are examined. Received: 13 March 2002 / Accepted: 5 March 2003 The work described in this paper was supported by a grant awarded by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1024/01E).     

Network topology and the theory of rubber elasticity

The earliest investigations on rubber elasticity, commencing in the 19th century, were necessarily limited to phenomenological interpretations. The realisation that polymers consist of very long molecular chains. commencing c. 1930, gave impetus to the molecular theory of rubber elasticity (1932-). according to which the high deformability of an elastomer, and the elastic force generated by deformation, stem from the configurations accessible to long molecular chains. Theories of rubber elasticity put forward from 1934-1946 relied on the assumption that the junctions of the rubber network undergo displacements that are affine in macroscopic strain. The theory of James and Guth (1947) dispensed with this premise, and demonstrated instead that the mean positions of the junctions of a ‘phantom’ network consisting of Gaussian chains devoid of material properties are affine in the strain. The vital significance of the distinction between the actual distribution of chain vectors in a network and their distribution if the junctions would be fixed at their mean positions went unnoticed for nearly 30 years. Experimental investigations, commencing with the incisive work of Gee in 1946. revealed large departures from the relationship of stress to strain predicted by the theories cited. This discrepancy prompted extensive studies, theoretical and experimental, during succeeding years. Inquiry into the fundamentals of polymer networks, formed for example by interlinking very long polymer molecules, exposed the need to take account of network imperfections, typically consisting of chains attached at only one end to a network junction. Various means were advocated to make corrections for these imperfections. The cycle rank ζ of the network has been shown (1976) to be the fundamental measure of its connectivity, regardless of the junction functionality and pattern of imperfections. Often overlooked is the copious interpenetration of the chains comprising typical elastomeric networks. Theories that attempt to represent such networks on a lattice are incompatible with this universal feature. Moreover, the dense interpenetration of chains may limit the ability of junctions in real networks to accommodate the fluctuations envisaged in the theory of phantom networks. It was suggested in 1975 that departures from the form predicted for the elastic equation of state are due to constraints on the fluctuations of junctions whose effect diminishes with deformation and with dilation. Formulation of a self-consistent theory based on this suggestion required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Implementation of the idea was achieved through postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions. This led in due course to a theory that accounts for the relationship of stress to strain virtually throughout the ranges of strain accessible to measurement. The theory establishes connections between structure and elastic properties. This is achieved with utmost frugality in arbitrary parameters.     

纵横波测井资料在储层评价中的应用

将弹性波基础理论，Gasman理论，Biot理论和实验研究结果相结合，探讨了沉积岩地层中速度和弹性模量，弹性模量和孔隙度，剪切模量和孔隙度，速度和孔隙度，孔隙度和Biot系数之间的关系，利用从各种声学测井资料中提取出的P波和S波时差（或速度）定量评价地层孔隙度和骨架物质，辅以泥质指示测井曲线，可以计算地层孔隙度，饱和度，岩性等参数，在M，Krief方法的基础上，采用优化算法寻求适合于任何岩性地层的孔隙度与Biot系数之间的关系式，提高了Biot系数的计算精度，该评价方法有坚实的实验基础和理论基础，评价结果与实验室岩心分析数据吻合。     

Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications

Part 2 of this series of two papers presents the applications of the discrete singular convolution (DSC) algorithm. The main purpose of this paper is to explore the utility, test the accuracy and examine the convergence of the proposed approach for the vibration analysis of rectangular plates with internal supports. Both partial internal line supports and complex internal supports are considered for 21 square plates of various combinations of edge support conditions. The effects of different size, shape and topology of the internal supports and different boundary conditions on the vibration response of plates are investigated. The partial internal line supports may vary from a central point support to a full range of cross or diagonal line supports. Several closed‐loop supports, such as ring, square and rhombus, and their combinations are studied for complex internal supports. Convergence and comparison studies are carried out to establish the correctness and accuracy of the DSC algorithm. The DSC results are compared with those in the available literature obtained by using other methods. Numerical results indicate that the DSC algorithm exhibits controllable accuracy for plate analysis and shows excellent flexibility in handling complex geometries, boundary conditions and support conditions. Copyright © 2002 John Wiley & Sons, Ltd.     

Axial vibrations of U-shaped bellows with elastically restrained end conditions

Previous work by Li et al. in the area of axial vibrations of bellows dealt with fixed end conditions. However, it is seen on several occasions that bellow ends are welded to a small pipe spool that has a lumped mass such as a valve or an instrument. Hence, the present paper aims at finding out the effect of elastically restrained ends on the axial natural frequencies. The analysis considers finite stiffness axial restraints on the bellows, i.e. solving the set of equations with non-homogeneous boundary conditions. Two bellow specimens are considered for comparison having the same dimensions as taken by Li in his analysis. The transcendental frequency equation deduced is accurate as the first, second and third mode frequencies computed are in close agreement to the ones obtained by Li.     

A direct stiffness analysis of a composite beam with partial interaction

The use of the conventional semi-analytical stiffness method in finite element analysis, in which interpolation polynomials are used to develop the stiffness relationships, leads to problems of curvature locking when beam-type elements are developed for composite members with partial interaction between the materials of which it is comprised. The curvature locking phenomenon that occurs for composite steel–concrete members is quite well reported, and the general approach to minimizing the undesirable ramifications of curvature locking has been to use higher-order polynomials with increasing numbers of internal nodes. This paper presents an alternate formulation based on a direct stiffness approach rather than starting from pre-defined interpolation polynomials, and which does not possess the undesirable locking characteristics. The formulation is based on a more general approach for a bi-material composite flexural member, whose constituent materials are joined by elastic shear connection so as to provide partial interaction. The stiffness relationships are derived, and these are applied to a simply supported and a continuous steel–concrete composite beam to demonstrate the efficacy of the method, and in particular its ability to model accurately both very flexible and very stiff shear connection that causes difficulties when implemented in competitive semi-analytical algorithms. Copyright © 2004 John Wiley & Sons, Ltd.     

Application of piece‐wise linear weight functions for 2D 8‐node quadrilateral element in contact problems

The present study is a continuation of our previous work with the aim to reduce problems caused by standard higher order elements in contact problems. The difficulties can be attributed to the inherent property of the Galerkin method which gives uneven distributions of nodal forces resulting in oscillating contact pressures. The proposed remedy is use of piece‐wise linear weight functions. The methods to establish stiffness and/or mass matrix for 8‐node quadrilateral element in 2D are presented, i.e. the condensing and direct procedures. The energy and nodal displacement error norms are also checked to establish the convergence ratio. Interpretation of calculated contact pressures is discussed. Two new 2D 8‐node quadrilateral elements, QUAD8C and QUAD8D, are derived and tested in many examples, which show their good performance in contact problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Experimental and numerical investigation of fracture in double-edge notched steel plates

Double-edge notched (DENT) steel plates were pulled until complete fracture and several experimental observations were made (using profilometry and scanning electron microscopy). The essential work of fracture (EWF) model was found to be well verified. Numerical simulations—up to the maximum load only—of some experiments were performed using the finite element method (FEM), and incorporating geometric and material non-linearities (large deformation elasto-plasticity). Some experimental measurements were compared with the corresponding numerical computations and excellent agreement was found.     

筒体结构连续化模型的弹性动力时程分析

本文用连续化模型对高层筒体结构在地震作用下的动力时程反应进行分析．     

Analytical Calculation of Large-Scale Deflection of Pulse-Loaded Elliptic Plates

Large deflections of pulse-loaded elliptic and round plates made of hardenable elastoplastic materials are investigated analytically using an energy-based approach. Formulas that are convenient for engineering design have been derived.