DERIVATION OF THE GENERAL FORM OF ELASTICITY TENSOR OF THE TRANSVERSE ISOTROPIC MATERIAL BY TENSOR DERIVATE

In the paper the elasticity tensor and the relation between stress and strain of transverse isotropic material and isotropic material are deduced by tensor derivate. From the derivation the reason why there are two independent elasticity coefficients for isotropic elastic material and five for transverse isotropic elastic material can be seen more clearly.

TORSIONAL OSCILLATION OF RIGID DISK IN INFINITE TRANSVERSELY ISOTROPIC ELASTIC CYLINDER

In the present analysis torsional oscillation of a rigid disk in an infinite transversely isotropic elastic cylinder is considered. The effects of anisotropy in the stress intensity factor are shown graphically.

Dynamic response in two-dimensional transversely isotropic thick plate with spatially varying heat sources and body forces

This paper deals with a two-dimensional （2D） problem for a transverselyisotropic thick plate having heat sources and body forces. The upper surface of the plate is stress free with the prescribed surface temperature, while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of the generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in the Laplace-Fourier transform domain by applying the Laplace and Fourier transforms. The inversion of the double transform is done numerically. Numerical inversion of the Laplace transform is done based on the Fourier series expansion. Numerical computations are carried out for magnesium （Mg）, and the results are presented graphically. The results for an isotropic material （Cu） are obtained numerically and presented graphically to be compared with those of a transversely isotropic material （Mg）. The effect of the body forces is also studied.

A PENNY-SHAPED CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SOLID:MODES Ⅱ AND Ⅲ PROBLEMS

An exact analysis of the modes Ⅱ and Ⅲ problems of a penny- shaped crack in a transversely isotropic piezoelectric medium is performed in this paper.The potential theory method is employed based on the general solution of three-dimensional piezoelasticity and the four harmonics involved are represented by one complex potential.Previous results in potential theory are then utilized to obtain the exact solution that is expressed in terms of elementary functions.Comparison is made between the current results with those published and good agreement is obtained.

Thermal stresses in infinite circular cylinder subjected to rotation

The present investigation is concerned with the effect of rotation on an infi- nite circular cylinder subjected to certain boundary conditions. An analytical procedure for evaluation of thermal stresses, displacements, and temperature in rotating cylinder subjected to thermal load along the radius is presented. The dynamic thermal stresses in an infinite elastic cylinder of radius a due to a constant temperature applied to a variable portion of the curved surface while the rest of surface is maintained at zero temperature are discussed. Such situation can arise due to melting of insulating material deposited on the surface cylinder. A solution and numerical results are obtained for the stress components, displacement components, and temperature. The results obtained from the present semi-analytical method are in good agreement with those obtained by using the previously developed methods.

Evaluation of stress intensity factors of thin AZ31B magnesium alloy plate under biaxial tensile loading

Stress intensity factors of thin AZ31B magnesium alloy sheet under biaxial tension loading were analyzed by modified Dugdale model. K-values with crack angle of 90° obviously show that there is no influence of the loading condition in Mode-I. In the 45° case, K1 values are obtained within 10% errors when they are calculated by modified Dugdale model under biaxial loading. It is concluded that the modified Dugdale model is one of effective ways to evaluate stress intensity factor of AZ31 magnesium alloy sheet appropriately.

A Cell-Based Linear Smoothed Finite Element Method for Polygonal Topology Optimization

The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.

Design of small-scale gradient coils in magnetic resonance imaging by using the topology optimization method

A topology optimization method based on the solid isotropic material with penalization interpolation scheme is utilized for designing gradient coils for use in magnetic resonance microscopy.Unlike the popular stream function method,the proposed method has design variables that are the distribution of conductive material.A voltage-driven transverse gradient coil is proposed to be used as micro-scale magnetic resonance imaging(MRI)gradient coils,thus avoiding introducing a coil-winding pattern and simplifying the coil configuration.The proposed method avoids post-processing errors that occur when the continuous current density is approximated by discrete wires in the stream function approach.The feasibility and accuracy of the method are verified through designing the z-gradient and y-gradient coils on a cylindrical surface.Numerical design results show that the proposed method can provide a new coil layout in a compact design space.

Isotropic Cloak Materials Design Based on the Numerical Optimization Method of the Inverse Medium Problem

In recent years,various kinds of cloak devices were designed by transforma-tion optics,but these cloak metamaterials are anisotropic and difficult to manufacture.In this paper,we designed the isotropic cloak metamaterials based on the numeri-cal method of the optimization theory to the inverse medium problem.This method has universality,and it is not limited by the shape and type of the cloak device.This isotropic material is easier to manufacture in practice than anisotropic material.A large number of numerical results show the effectiveness of the method.

An engineering analysis of penetration of metal ball into fibre-reinforced composite targets

An engineering analysis of computing the penetration problem of a steel ball penetrating into fibre-reinforced composite targets is presented. Assume the metal ball is a rigid body, and the composite target is a transversely isotropic elasto-plastic material. In the analysis, a spherical cavity dilatation model is incorporated in the cylindrical cavity penetration method. Simulation results based on the modified model are in good agreement with the results for 3-D Kevlar woven （3DKW） composite anti-penetration experiments. Effects of the target material parameters and impact parameters on the penetration problem are also studied.

Using modified Mach-Zehnder interferometer to get better nonlinear correction term of an isotropic nonlinear material

Nonlinear materials have been well established as photo refractive switching material. Important applica- tions of isotropic nonlinear materials are seen in self-focusing, defocusing phenomena, switching systems, etc. The nonlinear correction term is basically responsible for the optical switches. Mach-Zehnder inter- ferometer （MZI） is a well-known arrangement for determining the above correction term, but there are some major problems for finding out the term by MZI. We propose a new method of finding the nonlinear correction term as well as the second order nonlinear susceptibility of the materials by using a modified MZI system. This method may be used to find out the above parameters for any unknown nonlinear material.

Layered and isotropic acoustic cloak design based on conformal transformation acoustics

The acoustic cloak can manipulate sound waves in surprising ways and enable us to guide the trajectories of waves at will.In contrast to the existing approaches for designing such devices that need exotic material parameters,here we demonstrate how to design a layered and isotropic acoustic cloak based on conformal transformation acoustics.A petal-shaped layered acoustic cloak is designed from the reduction of material parameters of an approximate rectangular cloak.The resultant material parameters span a narrow range,thus strongly facilitating the implementation.The invisibility performance of the cloak for different shapes of acoustic wavefront is verified using a full-wave finite-element analysis.

Topology optimization of transient problem with maximum dynamic response constraint using SOAR scheme

This paper proposes a novel method for the continuum topology optimization of transient vibration problem with maximum dynamic response constraint.An aggregated index in the form of an integral function is presented to cope with the maximum response constraint in the time domain.The density filter solid isotropic material with penalization method combined with threshold projection is developed.The sensitivities of the proposed index with respect to design variables are conducted.To reduce computational cost,the second-order Amoldi reduction(SOAR)scheme is employed in transient analysis.Influences of aggregate parameter,duration of loading period,interval time,and number of basis vectors in the SOAR scheme on the final designs are discussed through typical examples while unambiguous configuration can be achieved.Through comparison with the corresponding static response from the final designs,the optimized results clearly demonstrate that the transient effects cannot be ignored in structural topology optimization.