Characteristic analysis of scattering field in two-layer media by Green's function

The problem of three-dimensional(3D) acoustic scattering in a complex medium has aroused considerable interest of researchers for many years. An ultrasonic scattered field calculating technique is proposed to study the scattering echo from strongly scattered materials in a two-layer medium in this work. Firstly, with the high frequency stationary phase method,the Green's function of two-layer fluid media is derived. And then based on the idea of integral equation discretization,the Green's function method is extended to two-layer fluid media to derive the scattering field expression of defects in a complex medium. With this method, the scattering field of 3D defect in a two-layer medium is calculated and the characteristics of received echoes are studied. The results show that this method is able to solve the scattering P wave field of 3D defect with arbitrary shape at any scattering intensity in two-layer media. Considering the circumstance of waterimmersion ultrasonic non-destructive test(NDT), the scattering sound field characteristics of different types of defects are analyzed by simulation, which will help to optimize the detection scheme and corresponding imaging method in practice so as to improve the detection quality.

Numerical Treatments and Applications of the 3D Transient Green Function

How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed. It has been demonstrated by the numerical calculation that this method can improve the precision of the time-domain Green function. Numeiical research indicates that it is efficient to solve the hydrodynamic problems.

Dynamic stiffness matrix of a poroelastic multi-layered site and its Green's functions

Few studies of wave propagation in layered saturated soils have been reported in the literature.In this paper,a general solution of the equation of wave motion in saturated soils,based on one kind of practical Blot's equation, was deduced by introducing wave potentials.Then exact dynamic-stiffness matrices for a poroelastic soil layer and half- space were derived,which extended Wolf's theory for an elastic layered site to the case of poroelasticity,thus resolving a fundamental problem in the field of wave propagation and soil-structure interaction in a poroelastic layered soil site.By using the integral transform method,Green's functions of horizontal and vertical uniformly distributed loads in a poroelastic layered soil site were given.Finally,the theory was verified by numerical examples and dynamic responses by comparing three different soil sites.This study has the following advantages:all parameters in the dynamic-stiffness matrices have explicitly physical meanings and the thickness of the sub-layers does not affect the precision of the calculation which is very convenient for engineering applications.The present theory can degenerate into Wolf's theory and yields numerical results approaching those for an ideal elastic layered site when porosity tends to zero.

Exact solution and transient behavior for torsional vibration of functionally graded finite hollow cylinders

Exact solutions are obtained for transient torsio- nal responses of a finitely long, functionally graded hollow cylinder under three different end conditions, i.e. free-free, free-fixed and fixed-fixed. The cylinder with its external surface fixed is subjected to a dynamic shearing stress at the internal surface. The material properties are assumed to vary in the radial direction in a power law form, while keep invariant in the axial direction. With expansion in the axial direction in terms of trigonometric series, the governing equations for the unknown functions about the radial coordinate r and time t are deduced. By applying the variable substitution technique, the superposition method and the separation of variables consecutively, series-form solutions of the equations are obtained. Natural frequencies and the transient torsional responses are finally discussed for a functionally graded finite hollow cylinder.

Optimization and standardization of transient expression assays for gene functional analyses in strawberry fruits

Strawberry is increasingly used as a model plant for research on fruit growth and development.The transient gene manipulation(TGM)technique is widely used to determine the function of plant genes,including those in strawberry fruits.However,its reliable application for the precise identification of gene function has been difficult owing to the lack of conditional optimization.In this study,we found that successful transient gene manipulation requires optimization,with the vector type,temperature,and fruit developmental stage being three major factors determining success.Notably,we found that transient gene manipulation was feasible only from the large green fruit stage onwards,making it especially suitable for identifying genes involved in strawberry fruit ripening.Furthermore,we established a method called percentage difference of phenotype(PDP),in which the functional effect of a gene could be precisely and efficiently identified in strawberry fruits.This method can be used to estimate the functional effect of a gene as a value from 0 to 100%,such that different genes can be quantitatively compared for their relative abilities to regulate fruit ripening.This study provides a useful tool for accelerating research on the molecular basis of strawberry fruit ripening.

Lattice Green's Function for Infinite Square Lattice in the Second Nearest-Neighbour Interaction Approximation

In dealing with the square lattice model,we replace the traditionally needed Born-Von Karmann periodic boundary condition with additional Hamiltonian terms to make up a ring lattice.In doing so,the lattice Green's function of an infinite square lattice in the second nearest-neighbour interaction approximation can be derived by means of the matrix Green's function method.It is shown that the density of states may change when the second nearest-neighbour interaction is turned on.

Hybrid graded element model for transient heat conduction in functionally graded materials

This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials （FGMs）. First, a Laplace transform approach is used to handle the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, a hybrid graded element is formulated based on the obtained fundamental solution and a frame field. As a result, the graded properties of FGMs are naturally reflected by using the fundamental solution to interpolate the intra-element field. Further, Stefest＇s algorithm is employed to convert the results in Laplace space back into the time-space domain. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method.

COUPLED THERMAL/MECHANICAL ANALYSIS FOR THE FRACTURE OF FUNCTIONALLY GRADED MATERIALS UNDER TRANSIENT THERMAL LOADING

A comprehensive treatment of fracture of functionally gradedmaterials (FGMs) is provided. It is assumed that the materialproperties depend only on the coordinate perpendicular to the cracksurface And vary continuously along the crack faces. By using alaminated composite plate model to simulate the ma- Terialnon-homogeneity, an algorithm for solving the system based on Laplacetransform and Fourier transform Techniques is presented. Unlikeearlier studies that considered certain assumed propertydistributions and a Single crack problem, the current investigationstudies multiple crack problem in the FGMs with arbitrarily Varyingmaterial properties. Transient thermal stresses are presented.

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.

NEW TYPE OF DUAL BEM AND GREEN'S-FUNCTION-LIBRARY STRATEGY FOR FRACTURE ANALYSIS IN COMPLEX STRUCTURES

A new type of dual boundary integral equations(DBIE)is presented first,through which,a smaller system of equations needs to be solved in fracture analysis.Then a non-conforming crack tip element in two-dimensional problems is proposed.The exact formula for the hypersingular integral over the non-con- forming crack tip element is given next.By virtue of Green's-function-library strategy,a series of stress in- tensity factors(SIF)of different crack orientations,locations and/or sizes in a complicated structure can be obtained easily and efficiently.Finally,several examples of fracture analysis in two dimensions are given to demonstrate the accuracy and efficiency of the method proposed.

Solutions of Green's function for Lamb's problem of a two-phase saturated medium

The solutions of Green’s function are significant for simplification of problem on a two-phase saturated medium.Using transformation of axisymmetric cylindrical coordinate and Sommerfeld’s integral,superposition of the influence field on a free surface,authors obtained the solutions of a two-phase saturated medium subjected to a concentrated force on the semi-space.

GREEN'S FUNCTIONS OF INTERNAL ELECTRODES BETWEEN TWO DISSIMILAR PIEZOELECTRIC MEDIA

The generalized 2-D problem of a half-infinite interfacial electrode layer between two arbitrary piezoelectric half-spaces is studied. Based on the Stroh formalism, exact expressions for the (Green's) functions of a line force, a line charge and a line electric dipole applied at an arbitrary point near the electrode edge,were presented, respectively. The corresponding solutions for the intensity factors of fields were also obtained in an explicit form. These results can be used as the foundational solutions in boundary element method (BEM) to solve more complicated fracture problems of piezoelectric composites.

THE NUMERICAL SOLUTIONS OF GREEN'S FUNCTIONS FOR TRANSVERSELY ISOTROPIC ELASTIC STRATA

In this paper, a model of transversely isotropic elastic strata is used to simulate the soil layers situated on a half space. Instead of the half space, an artificial transmitting boundary is used to absorb the vibration energy. The displacement formulas at any soil layer interface under vertical or horizontal harmonic ring loads are obtained by using the thin layer element method. From these formulas, the explicit solutions of Green's functions_the displacement responses at any interface of these strata under vertical and horizon harmonic point loads_are derived. The examples show that the method presented in this paper is close to the theoretical method and the transversely isotropic property has evident influence on the Green's functions.

GREEN'S FUNCTIONS FOR A 2D ANISOTROPIC MEDIUM WITH A HYPERBOLIC BOUNDARY

By using Stroh's formalism and the conformal mapping technique,this paper derives simple exphcit Green's functions of a piezoelectric anisotropic body with a free or fixed hyperbolic boundary.The corresponding elastic fields in the medium are obtained,too.In particular,degenerated solutions of an ex- ternal crack from those of a hyperbolic problem are analysed in detail.Then the singular stress fields and the fracture mechanics parameters are found.The solutions obtained are valid not only for plane and antiplane problems but also for the coupled ones between inplane and outplane deformations.

Complex fitting 3D closed-form Green's function and its application for silicon RF IC's

An approximate three-dimensional closed-form Green's function with the type of exponential function is derived over a lossy multilayered substrate by means of the Fourier transforms and a novel complex fitting approach. This Green's function is used to extract the capacitance matrix for an arbitrary three-dimensional arrangement of conductors located anywhere in the silicon IC substrate. Using this technique, the substrate loss in silicon integrated circuits can be analyzed. An example of inductor modeling is presented to show that the technique is quite effective.

GREEN'S FUNCTIONS FOR 2D PROBLEMS OF ANISOTROPIC PIEZOELECTRIC MATERIAL WITH A STRIP REGION

By using Stroh's formalism and the conformal mapping technique,we derive the simple ex- plicit elastic fields of a generalized line dislocation and a generalized line force in a general anisotropic piezo- electric strip with fixed surfaces,which are two fixed conductor electrodes.The solutions obtained are usually considered as Green's functions which play important roles in the boundary element methods.The Coulomb forces of the distributed charges along the region boundaries on the line charge q at z^0 are analysed in detail. The results are valid not only for plane and antiplane problems but also for the coupled problems between in- plane and outplane deformations.

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

Green's function Monte Carlo method combined with restricted Boltzmann machine approach to the frustrated J_(1)–J_(2)Heisenberg model

Restricted Boltzmann machine(RBM)has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system.On the other hand,as a shallow neural network,it is found that the RBM is still hardly able to capture the characteristics of systems with large sizes or complicated interactions.In order to find a way out of the dilemma,here,we propose to adopt the Green's function Monte Carlo(GFMC)method for which the RBM is used as a guiding wave function.To demonstrate the implementation and effectiveness of the proposal,we have applied the proposal to study the frustrated J_(1)-J_(2)Heisenberg model on a square lattice,which is considered as a typical model with sign problem for quantum Monte Carlo simulations.The calculation results demonstrate that the GFMC method can significantly further reduce the relative error of the ground-state energy on the basis of the RBM variational results.This encourages to combine the GFMC method with other neural networks like convolutional neural networks for dealing with more models with sign problem in the future.

A Real-Time Transient Analysis of a Functionally Graded Material Plate Using Reduced-Basis Methods

Based on the hybrid numerical method (HNM) combining with a reduced-basis method (RBM), the real-time transient response of a functionally graded material (FGM) plates is obtained. The large eigenvalue problem in wavenumber domain has been solved through real-time off-line/on-line calculation. At off-line stage, a reduced-basis space is constructed in sample wavenumbers according to the solved eigenvalue problems. The matrices independent of parameters are projected onto the reduced-basis spaces. At on-line stage, the reduced eigenvalue problems of the arbitrary wavenumbers are built. Subsequently, the responses in wavenumber domain are obtained by the approximated eigen-pairs. Because of the application of RBM, the computational cost of transient displacement analysis of FGM plate is decreased significantly, while the accuracy of the solution and the physics of the structure are still retained. The efficiency and validity of the proposed method are demonstrated through a numerical example.

ELECTRO-ELASTIC GREEN'S FUNCTIONS FOR APIEZOELECTRIC HALF-SPACE ANDTHEIR APPLICATION

In this paper, as is studied are the electro-elastic solutions for a piezoelectric halfspace subjected Io a line force, a line charge and a line dislocation, i. e.. Green sfunclions on the basis of Stroh formalism and the concept of analytical continuation,explicit expressions for Green's functions are derived. As a direct application of theresults obtained, an infinite piezoelectric solid containing a semi-infinite crack isexammed. Attention iffocused on the stress and electric displacement fields of a cracktip. The stress and electric displacement intensity .factors are given explicitly.