Stochastic transient analysis of thermal stresses in solids by explicit time-domain method

Stochastic heat conduction and thermal stress analysis of structures has received considerable attention in recent years.The propagation of uncertain thermal environments will lead to stochastic variations in temperature fields and thermal stresses.Therefore,it is reasonable to consider the variability of thermal environments while conducting thermal analysis.However,for ambient thermal excitations,only stationary random processes have been investigated thus far.In this study,the highly efficient explicit time-domain method(ETDM)is proposed for the analysis of non-stationary stochastic transient heat conduction and thermal stress problems.The explicit time-domain expressions of thermal responses are first constructed for a thermoelastic body.Then the statistical moments of thermal displacements and stresses can be directly obtained based on the explicit expressions of thermal responses.A numerical example involving non-stationary stochastic internal heat generation rate is investigated.The accuracy and efficiency of the proposed method are validated by comparison with the Monte-Carlo simulation.

Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time （HB-AFT） do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

A time domain induced polarization relaxation time spectrum inversion method based on a damping factor and residual correction

Relaxation time spectra （RTS） derived from time domain induced polarization data （TDIP） are helpful to assess oil reservoir pore structures. However, due to the sensitivity to the signal-to-noise ratio （SNR）, the inversion accuracy of the traditional singular value decomposition （SVD） inversion method reduces with a decrease of SNR. In order to enhance the inversion accuracy and improve robustness of the inversion method to the SNR, an improved inversion method, based on damping factor and spectrum component residual correction, is proposed in this study. The numerical inversion results show that the oscillation of the RTS derived from the SVD method increased with a decrease of SNR, which makes it impossible to get accurate inversion components. However, the SNR has little influence on inversion components of the improved method, and the RTS has high inversion accuracy and robustness. Moreover, RTS derived from core sample data is basically in accord with the pore-size distribution curve, and the RTS derived from the actual induced polarization logging data is smooth and continuous, which indicates that the improved method is practicable.

Dynamic interaction numerical models in the time domain based on the high performance scaled boundary finite element method

Consideration of structure-foundation-soil dynamic interaction is a basic requirement in the evaluation of the seismic safety of nuclear power facilities. An efficient and accurate dynamic interaction numerical model in the time domain has become an important topic of current research. In this study, the scaled boundary finite element method （SBFEM） is improved for use as an effective numerical approach with good application prospects. This method has several advantages, including dimensionality reduction, accuracy of the radial analytical solution, and unlike other boundary element methods, it does not require a fundamental solution. This study focuses on establishing a high performance scaled boundary finite element interaction analysis model in the time domain based on the acceleration unit-impulse response matrix, in which several new solution techniques, such as a dimensionless method to solve the interaction force, are applied to improve the numerical stability of the actual soil parameters and reduce the amount of calculation. Finally, the feasibility of the time domain methods are illustrated by the response of the nuclear power structure and the accuracy of the algorithms are dynamically verified by comparison with the refinement of a large-scale viscoelastic soil model.

Finite difference time domain method forward simulation of complex geoelectricity ground penetrating radar model

The ground penetrating radar(GPR) forward simulation all aims at the singular and regular models, such as sandwich model, round cavity, square cavity, and so on, which are comparably simple. But as to the forward of curl interface underground or “v” figure complex model, it is difficult to realize. So it is important to forward the complex geoelectricity model. This paper takes two Maxwell’s vorticity equations as departure point, makes use of the principles of Yee’s space grid model theory and the basic principle finite difference time domain method, and deduces a GPR forward system of equation of two dimensional spaces. The Mur super absorbed boundary condition is adopted to solve the super strong reflection on the interceptive boundary when there is the forward simulation. And a self-made program is used to process forward simulation to two typical geoelectricity model.

A 1D time-domain method for in-plane wave motions in a layered half-space

A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the layered half-space is discretized on the basis of the propagation characteristic of elastic wave according to the Snell law. Then, the finite element method with lumped mass and the central difference method are incorporated to establish 2D wave motion equations, which can be transformed into 1D equations by discretization principle and explicit finite element method. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained, and the wave motions in layered half-space are finally determined based on the characteristic of traveling wave. Both the theoretical analysis and the numerical results demonstrate that the proposed method has high accuracy and good stability.

Second-Order Wave Diffraction Around 3-D Bodies by A Time-Domain Method

A time-domain method is applied to simulate nonlinear wave diffraction around a surface piercing 3-D arbitrary body. The method involves the application of Taylor series expansions and the use of perturbation procedure to establish the corresponding boundary value problems with respect to a time-independent fluid domain. A boundary element method based on B-spline expansion is used to calculate the wave field at each time step, and the free surface boundary condition is satisfied to the second order of wave steepness by a numerical integration in time. An artificial damping layer is adopted on the free surface for the removal of wave reflection from the outer boundary. As an illustration, the method is used to compute the second-order wave forces and run-up on a surface-piercing circular cylinder. The present method is found to be accurate, computationally efficient, and numerically stable.

Comparison of delay compensation methods for real-time hybrid simulation using frequency-domain evaluation index

The delay compensation method plays an essential role in maintaining the stability and achieving accurate real-time hybrid simulation results. The effectiveness of various compensation methods in different test scenarios, however, needs to be quantitatively evaluated. In this study, four compensation methods （i.e., the polynomial extrapolation, the linear acceleration extrapolation, the inverse compensation and the adaptive inverse compensation） are selected and compared experimentally using a frequency evaluation index （FEI） method. The effectiveness of the FEI method is first verified through comparison with the discrete transfer fimction approach for compensation methods assuming constant delay. Incomparable advantage is further demonstrated for the FEI method when applied to adaptive compensation methods, where the discrete transfer function approach is difficult to implement. Both numerical simulation and laboratory tests with predefined displacements are conducted using sinusoidal signals and random signals as inputs. Findings from numerical simulation and experimental results demonstrate that the FEI method is an efficient and effective approach to compare the performance of different compensation methods, especially for those requiring adaptation of compensation parameters.

Characteristic-Based Time Domain Method for Cylindrically Conformal Microstrip Patch Antennas

The characteristics of a cylindrical conformal microstrip patch antenna are analyzed by using the characteristic-based time domain （CBTD） method. A governing equation in the cylindrical coordinate system is formulated directly to facilitate the analysis of cylindrically conformal microstrip patch antennas. The algorithm has second-order accuracy both in time and space domain and has the potential to eliminate the spurious wave reflection from the numerical boundaries of the computational domain, Numerical results demonstrate the important merits and accuracy of the proposed technique in computational electromagnetics,

Investigation of three-pulse photon echo in thick crystal using finite-difference time-domain method

This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works.The influence of thickness on the three-pulse photon echo＇s amplitude and efficiency is analyzed with the Maxwell-Bloch equations solved by finite-difference timedomain method.We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm^（3＋）：YAG when the attenuation of the input pulse is taken into account.Meanwhile,we find the expression 0.09 exp（α＇L）,which is previously employed to describe the relationship between echo＇s efficiency and thickness,should be modified as 1.3 · 0.09 exp（2.4 ·α＇L） with the propagation of echo considered.

A TIME DOMAIN BOUNDARY ELEMENT METHOD FOR WATER-SOLID IMPACT ANALYSIS

A reciprocal theorem of dynamics for potential flow problems is first derived by means of the Laplace transform in which the compressibility of water is taken into account. Based on this theorem, the corresponding time-space boundary integral equation: is obtained. Then, a set of time domain boundary element equations with recurrence form is immediately formulated through discretization in both time and boundary. After having carried out the numerical calculation two solutions are found in which a rigid semicircular cylinder and a rigid wedge with infinite length suffer normal impact on the surface of a half-space fluid. The results show that the present method is more efficient than the previous ones.

A Krylov Space-Based Finite Element Time Domain Method for Broadband Frequency Domain Solutions

A Krylov space based time domain method for wave propagation problems is introduced. The proposed method uses the Arnoldi algorithm to obtain broad-band frequency domain solutions. This method is especially advantageous in cases where slow convergence is observed when using traditional time domain methods. The efficiency of the method is examined in several test cases to show its fast convergence in such problems.

Optical simulation of in-plane-switching blue phase liquid crystal display using the finite-difference time-domain method

The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.

Numerical Solutions of Finite Well in Two Dimensions Using the Finite Difference Time Domain Method

The higher excited states for two dimensional finite rectangular well potential are calculated numerically,by solving the Schrödinger equation using the finite difference time domain method.Although,this method is suitable to calculate the ground state of the quantum systems,it has been improved to calculate the higher excited states directly.The improvement is based on modifying the iterative process involved in this method to include two procedures.The first is known as cooling steps and the second is known as a heating step.By determining the required length of the cooling iteration steps using suitable excitation energy estimate,and repeating these two procedures using suitable initial guess function for sufficient times.This modified iteration will lead automatically to the desired excited state.In the two dimensional finite rectangular well potential problem both of the suitable excitation energy and the suitable initial guess wave function are calculated analytically using the separation of variables technique.

An Implicit-Explicit Computational Method Based on Time Semi-Discretization for Pricing Financial Derivatives with Jumps

This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys the SVJ model. This equation is numerically solved by using the implicit- explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.

An efficient locally one-dimensional finite-difference time-domain method based on the conformal scheme

An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D transverse-electric（TE） case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit（ADI） CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field（TF/SF） boundary and the perfectly matched layer（PML）, the radar cross section（RCS） of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.

Study on generalized magneto-thermoelastic problems by FEM in time domain

This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times （i.e., the G-L theory） are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced front and the magnitude of magnetic field at the heat wave the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.

Time Domain Simulation of Transient Responses of Very Large Floating Structures Under Unsteady External Loads

A time domain finite element method （FEM） for the analysis of transient elastic response of a very large floating structure （VLFS） subjected to arbitrary time-dependent external loads is presented. This method is developed directly in time domain and the hydrodynamic problem is formulated based on linear, inviscid and slightly compressible fluid theory and the structural response is analyzed on the thin plate assumption. The time domain finite element procedure herein is validated by comparing numerical results with available experimental data. Finally, the transient elastic response of a pontoon-type VLFS under the landing of an airplane is computed by the proposed time domain FEM. The time histories of the applied force and the position and velocity of an airplane during landing are modeled with data from a Boeing 747-400 jumbo jet.

An Approximation to Energy Dissipation in Time Domain Simulation of Sloshing Waves Based on Linear Potential Theory

This paper proposes a new approximation to energy dissipation in time domain simulation of sloshing waves by use of a linear potential theory. The boundary value problem is solved by the NURBS （non-uniform rational B-spline） higher-order panel method, in which a time-domain Green function is employed. The energy dissipation is modeled by changing the boundary condition on solid boundaries. Model experiments are carried out in a partially filled rectangular tank with forced horizontal motion. Sloshing-induced internal pressures and horizontal force obtained numerically and experimentally are compared with each other. It is observed that the present energy dissipation approximation can help produce a fair agreement between experimental forces and those of numerical simulations.