In the paper,the origin,exploitative flow,current status of material design and prospect of functionally graded materials (FGM) are introduced.The adopting method of FGM design,FGM synthesizing and thermal and mechanical evaluation are discussed in detail.Finally,the developing directions of FGM are analysed.

Functionally Graded Materials

By virtue of the separation of variables and orthogonal expansion technique, the plane strain dynamic problem of a magneto-electro-elastic hollow cylinder is reduced to two integral equations of two time functions. Then, by means of the interpolation method, the integral equations are solved successfully. As a result, all the transient responses of displacements, stresses, electric potentials, electric displacements, magnetic potentials and magnetic inductions are completely obtained. The present method is suitable for the analysis of hollow cylinders with arbitrary thickness and subjected to arbitrary mechanical and electromagnetic loads. Numerical results are also presented.

The transient responses of magneto-electro-elastic hollow cylinders

http://www.umsl.edu/~dibooglus/personal/cevik%26dibooglu%26kutan13.pdf

Measuring financial stress in transition economies

Elongated cylindrical structures like rods, pipes, cable strands or fibers, support the propagation of mechanical waves at ultrasonic frequencies along their axes. This waveguide behaviour is used in a number of scientific and engineering applications: the Non Destructive Evaluation (NDE) of the structural health of civil engineering elements for safety purposes (Rose, 2000), in linear displacement sensors (Seco et al., 2009) for high accuracy absolute linear position estimation, in the evaluation of material properties of metal wires, optical fibers or composites (Nayfeh & Nagy, 1996), and as fluid sensors in pipes transporting liquids (Ma et al., 2007). These applications demand exact quantitative models of the processes of wave generation, propagation and reception of the ultrasonic signals in the waveguides.

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Modelling the Generation and Propagation of Ultrasonic Signals in Cylindrical Waveguides

Free vibration of multi-layered spherically isotropic hollow spheres

Studies on the static and dynamic deformation of isotropic and anisotropic elastic shell-like bodies of complex shape performed using classical and refined problem statements are reviewed. To solve two-dimensional boundary-value problems and eigenvalue problems, use is made of a nontraditional discrete-continuum approach based on the spline-approximation of the unknown functions of partial differential equations with variable coefficients. This enables reducing the original problem to a system of one-dimensional problems solved with the discrete-orthogonalization method. An analysis is made of numerical results on the distribution of stress and displacement fields and dynamic characteristics depending on the loading and boundary conditions, geometrical and mechanical parameters of elastic bodies. Emphasis is placed on the accuracy of the results

Static and Dynamic Problems for Anisotropic Inhomogeneous Shells with Variable Parameters and Their Numerical Solution (Review)

Axisymmetric electroelastic waves in a hollow piezoelectric ceramic cylinder

The natural vibrations of anisotropic rectangular plates of varying thickness with complex boundary conditions are studied using the spline-collocation and discrete-orthogonalization methods. The basic principles of the approach are outlined. The natural vibrations of orthotropic plates with parabolically varying thickness are calculated. The results (natural frequencies and modes) obtained with different boundary conditions are analyzed

Spline-Approximation Method Applied to Solve Natural-Vibration Problems for Rectangular Plates of Varying Thickness

The three-dimensional theory of elasticity is used to study the free vibrations of an anisotropic hollow cylinder with different boundary conditions at the ends. The relevant problem is solved by a numerical-and-analytic method. Spline approximation and collocation is used to reduce the partial differential equations of elasticity to a boundary-value problem for a system of ordinary differential equations of high order for the radial coordinate, which is solved using the stable discrete-orthogonalization and incremental-search methods. The calculated results for an orthotropic inhomogeneous cylinder with boundary conditions of several types are presented

Using spline-approximation to solve problems of axisymmetric free vibration of thick-walled orthotropic cylinders

The stress–strain state of open and closed variable-thickness elliptic cylindrical shells is studied. To solve the problem, the Mushtari–Donell–Vlasov shell model and numerical-analytical approach based on the spline-collocation and discrete-orthogonalization methods are used. Various types of boundary conditions and variable loadings are considered. The influence of the type of variable loading and thickness on the distribution of displacements and stresses in the shells is analyzed.

A. Ya. Grigorenko

Papers

Static and Dynamic Problems for Anisotropic Inhomogeneous Shells with Variable Parameters and Their Numerical Solution (Review)

Axisymmetric electroelastic waves in a hollow piezoelectric ceramic cylinder

Spline-Approximation Method Applied to Solve Natural-Vibration Problems for Rectangular Plates of Varying Thickness

Using spline-approximation to solve problems of axisymmetric free vibration of thick-walled orthotropic cylinders

Analysis of Influence of the Geometrical Parameters of Elliptic Cylindrical Shells with Variable Thickness on their Stress-Strain State