An extended displacement discontinuity method for analysis of stress wave propagation in viscoelastic rock mass

An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as 'macro-joints',while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as 'micro-defects'.The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass (ERM) from the conventional displacement discontinuity method (CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.

The Stress Combination Method for the Fatigue Assessment of the Hatch Corner of a Bulk Carrier Based on Equivalent Waves

The stress combination method for the fatigue assessment of the hatch comer of a bulk carrier was investigated based on equivalent waves. The principles of the equivalent waves of ship structures were given, including the determination of the dominant load parameter, heading, frequency, and amplitude of the equivalent regular waves. The dominant load parameters of the hatch comer of a bulk carrier were identified by the structural stress response analysis, and then a series of equivalent regular waves were defined based on these parameters. A combination method of the structural stress ranges under the different equivalent waves was developed for the fatigue analysis. The combination factors were obtained by least square regression analysis with the stress ranges derived from spectral fatigue analysis as the target value. The proposed method was applied to the hatch comer of another bulk carrier as an example. This shows that the results from the equivalent wave approach agree well with those from the spectral fatigue analysis. The workload is reduced substantially. This method can be referenced in the fatigue assessment of the hatch comer of a bulk carrier.

SCATTERING OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN MINDLIN'S THICK PLATES WITH A CUTOUT

Using the complex variable method and conformal mapping,scat- tering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout have been studied.The general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique,the dynamic stress problem can be reduced into the solution of a set of infinite algebraic equations.As examples, numerical results for the dynamic stress concentration factor in Mindlin's plates with a circular,elliptic cutout are graphically presented in sequence.

AN ANALYSIS FOR DIFFRACTION OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN THICK PLATES WITH A CAVITY

By using the complex variable method and conformal mapping, the diffraction of flexural waves and dynamic stress concentrations in thick plates with a cavity have been studied. A general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of an arbitrary cavity is obtained. By employing the orthogonal function expansion technique, the dynamic stress problem can be reduced to the solution of an infinite algebraic equation series. As an example, the numerical results for the dynamic stress concentration factor in thick plates with a circular, elliptic cavity are graphically presented. The numerical results are discussed.

BEM for Diffraction of Elastic Wave and Dynamic Stress Concentrations in Thin Plate with a Circular Hole

Boundary Element Method (BEM) is employed to run theoretical analsis and numerical calculation of dif-fraction of elastic wave and dynamic stress concentration in an infinite then plate with a cireular hole. Based on the work equivalent law of dynamics,boundary integral equation is established for flexural waves of thin plate. Calculation formulas of influence coefficients are derived using Mathematica software and numerical results are obtained for dynam-ic stress conoentration factors in a then plate with a circular hole.

AN EXPERIMENTAL-NUMERICAL METHOD FOR MEASURING CRACK PROPAGATING VELOCITIES UNDER STRESS WAVE LOADING

An experimental-numerical method for measuring dynamic crack propagatingvelocities under stress wave loading is established in this paper. The experiments of thethree-point bend specimen are done on the improved Hopkinson bar. Deflection of loading point,dynamic load and instantaneous crack length are measured, then crack propagating velocities arecalculated. Experiments on 40Cr steel show that the results given by this method have a goodagreement with that obtained by the resistance fracture gage method. Therefore this method isfeasible for measuring crack propagating velocities under high loading rate and will have wideapplication.

Numerical Simulation of Elastic Stress Wave Refraction at Air-Solid Interfaces

Elastic wave refraction at the air-solid interface and wave propagations in the vicinity of the air-solid interface are numerically studied.The modified ghost fluid method(MGFM)and isobaric fix methods are combined to solve the fluid and solid statuses at the air-solid interface and construct a continuous boundary condition for the air-solid interface.The states in the ghost domain are evaluated by the MGFM-algorithm.The solid governing equations are solved with second order spatial discretization.Numerical tests verify the correctness of the presented continuous boundary condition and show that the combined method is convergent in the vicinity of the air-solid interface.The 3D numerical results by the combined method are close to those of the ArbitraryLagrangian-Eulerian(ALE)method.The combined method is robust when applied for multi-dimensional problems.A compression stress wave impacting on the air-solid interface result in a compression wave in air.A tension stress wave impacting on the air-solid interface result in an expansion wave in air.

Non-destructive Evaluation of Absolute Stress in Steel Members Using Shear-Wave Spectroscopy

Non-destructive measurement of absolute stress in steel members can provide useful information to optimize the design of steel structures and allow the safety of existing structures to be evaluated.This paper investigates the non-destructive capability of ultrasonic shear-wave spectroscopy in absolute stress evaluation of steel members.The effect of steel-member stress on the shear-wave amplitude spectrum is investigated,and a method of absolute stress measurement is proposed.Specifically,the process for evaluating absolute stress using shear-wave spectroscopy is summarized.Two steel members are employed to investigate the relationship between the stress and the frequency in shear-wave echo amplitude spectrum.The H-beam loaded by the universal testing machine is evaluated by the proposed method and the traditional strain gauge method for verification.The results show that the proposed method is effective and accurate for determining absolute stress in steel members.

THE APPLICATION OF DISCRETE ELEMENT METHOD IN SOLVING THREE-DIMENTIONAL IMPACT DYNAMICS PROBLEMS

A three-dimensional discrete element model of the connective type is presented. Moreover,a three-dimensional numerical analysis code,which can carry out the transitional pro- cess from connective model(for continuum)to contact model(for non-continuum),is developed for simulating the mechanical process from continuum to non-continuum.The wave propagation process in a concrete block(as continuum)made of cement grout under impact loading is numer- ically simulated with this code.By comparing its numerical results with those by LS-DYNA,the calculation accuracy of the model and algorithm is proved.Furthermore,the failure process of the concrete block under quasi-static loading is demonstrated,showing the basic dynamic tran- sitional process from continuum to non-continuum.The results of calculation can be displayed by animation.The damage modes are similar to the experimental results.The two numerical examples above prove that our model and its code are powerful and efficient in simulating the dynamic failure problems accompanying the transition from continuum to non-continuum.It also shows that the discrete element method(DEM)will have broad prospects for development and application.

Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

On the Foundations of the Ultrasonic Non-Destructive Determination of Stresses in Near-the-Surface Layers of Materials： Review

The foundation of the ultrasonic non-destructive determination of stresses in near-the-surface layers of solids is presented. The method is based on the regularities of Rayleigh wave propagation in solids with initial （residual） stresses. A description of the above mentioned method and examples of stress determination are presented. Examples are considered as applied to the residual stresses arising at electric welding and the operating stresses arising at loading.

On the stress–strain states of cellular materials under high loading rates

A virtual Taylor impact of cellular materials is analyzed with a wave propagation technique, i.e. the Lagrangian analysis method, of which the main advantage is that no pre-assumed constitutive relationship is required. Time histories of particle velocity, local strain, and stress profiles are calculated to present the local stress-strain history curves, from which the dynamic stress-strain states are obtained. The present results reveal that the dynamic-rigid-plastic hardening （D-R-PH） material model introduced in a previous study of our group is in good agreement with the dynamic stress-strain states under high loading rates obtained by the Lagrangian analysis method. It directly reflects the effectiveness and feasibility of the D-R-PH material model for the cellular materials under high loading rates.

An IBEM solution to the scattering of plane SH-waves by a lined tunnel in elastic wedge space

The indirect boundary element method （IBEM） is developed to solve the scattering of plane SH-waves by a lined tunnel in elastic wedge space. According to the theory of single-layer potential, the scattered-wave field can be constructed by applying virtual uniform loads on the surface of lined tunnel and the nearby wedge surface. The densities of virtual loads can be solved by establishing equations through the continuity conditions on the interface and zero-traction conditions on free surfaces. The total wave field is obtained by the superposition of free field and scattered-wave field in elastic wedge space. Numerical results indicate that the IBEM can solve the diffraction of elastic wave in elastic wedge space accurately and effi- ciently. The wave motion feature strongly depends on the wedge angle, the angle of incidence, incident frequency, the location of lined tunnel, and material parameters. The waves interference and amplification effect around the tunnel in wedge space is more significant, causing the dynamic stress concentration factor on rigid tunnel and the displacement amplitude of flexible tunnel up to 50.0 and 17.0, respectively, more than double that of the case of half-space. Hence, considerable attention should be paid to seismic resistant or anti-explosion design of the tunnel built on a slope or hillside.

INTERACTION OF ELASTIC WAVES WITH A PERIODIC ARRAY OF COLLINEAR INPLANE CRACKS

A boundary integral equation method is applied to the study of the interaction of plane elastic waves with a periodic array of collinear inplane cracks.Numerical results are presented for the dynamic stress in- tensity factors.The effects of the wave type,wave frequency,wave incidence angle,and crack spacing on the dynamic stress intensity factors are analyzed in detail.

Simulation analysis of temperature control calculation of RCC gravity dam in the cold region

In this paper, regarding the actual conditions of a roller compacted concrete dam, three-dimensional finite element relocating mesh method is utilized to simulate and calculate the temperature field of the RCC dam during the construction stage and operating period. The calculation is well consistent with the actual construction process, the thin-layer pouring process the pouring temperature and all kinds of external loads involved being taken into account, By comparing and analyzing of the impact of the cold wave on the dam stress, important references are provided for the RCCD design and the temperature control during construction.

NUMERICAL SIMULATION OF STRESS WAVE PROPAGATION WITH UNSTRUCTURED FINITE VOLUME TIME DOMAIN METHOD

An unstructured finite volume time domain method (UFVTDM) is proposed to simulate stress wave propagation. The original variables of displacement and stress are solved based on the dynamic equilibrium equations. An Euler explicit and unstructured finite volume method is used for time and spacial terms respectively. The displacements are stored on the cell vertex and a vertex based finite volume is formed with the integral surface and the stress is assumed as uniform in the cell. This is some similar with the stager grid method in computational fluid dynamics. Several cases are used to show the capability of the algorithm.

一种适应于直流微电网的全桥LLC变换器

针对传统的光伏并网隔离型变换器的变压器体积大、损耗高和半导体器件电压应力高等问题,提出一种基于LLC谐振变换器的高增益DC-DC变换器。该变换器满足了输入输出之间电气隔离的要求,将全桥LLC谐振变换器与开关电容相结合,有效地提高了变换器的增益,减少了变压器的体积和损耗,降低了半导体器件的电压应力,实现了开关管的零电压开通和二极管的零电流关断,有效地降低了开关损耗。首先对所提变换器的工作原理进行详细分析;其次用基波分析法分析其基本特性,并进行半导体器件电压、电流应力计算及电路的参数设计;最后搭建一台了800 W的实验样机,经过实验验证,该变换器实现了开关管的ZVS开通,二极管的ZCS关断;减小了变压器的体积和铜耗;转换效率最高可达94.9%。二次侧二极管的电压应力为输出电压的12,是全桥整流的0.5倍、半桥整流的0.25倍,且平均电流相同,有利于器件的选型,更适用于直流微电网的应用,证明了理论分析的准确性。

Application of stress wave theory for pyroshock isolation at spacecraft-rocket interface

A large number of pyroshock devices are employed in spacecraft and rockets to realize stage separation and appendage deployment.Release of pyroshock devices induces high-level transient shock responses which tend to cause fatal damages in electronic equipment made of crystals and brittle materials.This paper aims to provide methods to isolate pyroshock and guarantee the safety of such equipment against high-frequency shocks.Firstly,stress wave transmission mechanism in stepped rods is investigated,upon which optimal area rate for shock isolation is achieved.Then,two spacecraft-rocket interface structures for pyroshock isolation,namely isolation hole and interim segment,are proposed.Both numerical simulations and experiments are carried out to validate the two shock isolation strategies.It is revealed that the interim segment structure shows better pyroshock isolation performance at the cost of increasing the weight of launching system whereas isolation hole is an optimal choice to reduce pyroshock response without causing weight increase.

Solution of a problem of thermal stresses in a non-homogeneous thermoelastic infinite medium of isotropic material by finite difference method

The present work deals with a new problem of thermoelasticity for an infinitely long and isotropic circular cylinder of temperature dependent physical properties.The inner and outer curved surfaces of the cylinder are subjected to both the mechanical and thermal boundary conditions.A finite difference model is developed to derive the solution of the problem in which the governing equations are uncoupled linear partial differential equations.The transient solution at any time can be evaluated directly from the model.In order to demonstrate the efficiency of the present model we consider a suitable material and obtain the numerical solution of displacement,temperature,and stresses inside the cylinder for the homogeneous-dependent material properties of the medium.The results are analyzed with the help of different graphical plots.

Influence of the Radial Inertia Effect on the Propagation Law of Stress Waves in Thin-Walled Tubes

This investigation focused on the influence of the radial inertia effect on the propagation behavior of stress waves in thin-walled tubes subjected to combined longitudinal and torsional impact loads.Generalized characteristics theory was used to analyze the main features of the characteristic wave speeds and simple wave solutions in thin-walled tubes.The incremental elastic-plastic constitutive relations described by the rate-independent plasticity were adopted,and the finite difference method was used to investigate the evolution and propagation behaviors of combined elasticplastic stress waves in thin-walled tubes when the radial inertial effect was considered.The numerical results were compared with those obtained when the radial inertia effect was not considered.The results showed that the speed of the coupled stress wave increased when the radial inertia effect was considered.The hardening modulus of the material in the plastic stage had a greater impact on the coupled slow waves than on the coupled fast waves.