Techniques for improving computational speed in numerical simulation of casting thermal stress based on finite difference method

Finite difference method (FDM) was applied to simulate thermal stress recently, which normally needs a long computational time and big computer storage. This study presents two techniques for improving computational speed in numerical simulation of casting thermal stress based on FDM, one for handling of nonconstant material properties and the other for dealing with the various coefficients in discretization equations. The use of the two techniques has been discussed and an application in wave-guide casting is given. The results show that the computational speed is almost tripled and the computer storage needed is reduced nearly half compared with those of the original method without the new technologies. The stress results for the casting domain obtained by both methods that set the temperature steps to 0.1 ℃ and 10 ℃, respectively are nearly the same and in good agreement with actual casting situation. It can be concluded that both handling the material properties as an assumption of stepwise profile and eliminating the repeated calculation are reliable and effective to improve computational speed, and applicable in heat transfer and fluid flow simulation.

Using finite difference method to simulate casting thermal stress

Thermal stress simulation can provide a scientific reference to eliminate defects such as crack,residual stress centralization and deformation etc.,caused by thermal stress during casting solidification.To study the thermal stress distribution during casting process,a unilateral thermal-stress coupling model was employed to simulate 3D casting stress using Finite Difference Method(FDM),namely all the traditional thermal-elastic-plastic equations are numerically and differentially discrete.A FDM/FDM numerical simulation system was developed to analyze temperature and stress fields during casting solidification process.Two practical verifications were carried out,and the results from simulation basically coincided with practical cases.The results indicated that the FDM/FDM stress simulation system can be used to simulate the formation of residual stress,and to predict the occurrence of hot tearing.Because heat transfer and stress analysis are all based on FDM,they can use the same FD model,which can avoid the matching process between different models,and hence reduce temperature-load transferring errors.This approach makes the simulation of fluid flow,heat transfer and stress analysis unify into one single model.

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.

On the Construction of Mohr Stress Circle and a Graphic Method in Representing the Stress Components on Different Oblique Planes

The Mohr stress circle for three-dimensional stress is usually determined by equations,which is lack of intuitionistic meanings and difficult to understand. In this paper, the construction of Mohr stress circle is illustrated directly by numerical method. The shortcoming of Mohr stress circle in representing the stress components on different oblique planes for three-dimensional stress is analyzed. A three-dimensional figure is given to describe the variation of normal and shear stress on different oblique planes at one point for the first time.

COMPUTATION OF SUPER-CONVERGENT NODAL STRESSES OF TIMOSHENKO BEAM ELEMENTS BY EEP METHOD

The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given.Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions.The EEP method gives super_convergent nodal stresses,which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude.And in addition,it can overcome the “shear locking” difficulty for stresses even when the displacements are badly affected.This research paves the way for application of the EEP method to general one_dimensional systems of ordinary differential equations.

The Effect of Near-Wall Vortices on Wall Shear Stress in Turbulent Boundary Layers

The objective of the present study is to explore the relation between the near-wall vortices and the shear stress on the wall in two-dimensional channel flows. A direct numerical simulation of an incompressible two-dimensional turbulent channel flow is performed with spectral method and the results are used to examine the relation between wall shear stress and near-wall vortices. The two-point correlation results indicate that the wall shear stress is associated with the vortices near the wall and the maximum correlation-value location of the near-wall vortices is obtained. The analysis of the instantaneous diagrams of fluctuation velocity vectors provides a further expression for the above conclusions. The results of this research provide a useful supplement for the control of turbulent boundary layers.

Characteristics of the Mesozoic and Cenozoic Tectonic Stress Fields of the Urumqi-Usu Region, Xinjiang

Based on the study of folds and related conjugate shear joints, the tectonic stress fields of the Urumqi-Usu region to the north of the North Tianshan Mountains have been reconstructed. Furthermore the author discussed the tectonic movements and their dynamic features. The early tectonic movement in the investigated region occurred from the end of the Late Jurassic to the initial stage of the Early Cretaceous, with the maximum (tensile) and minimum (compressional) principal stress trajectories in the tectonic stress field being in E-W and S-N directions respectively; the late tectogenesis took place from the end of the Early Pleistocene to the initial Middle Pleistocene, with the maximum and minimum principal stress trajectories in the late stress field striking in WNW and NE-NNE directions respectively. Through computer-aided simulated calculation by the finite element method and analysis of geological structure, it has been ascertained that the early tectogenesis is a nearly N-S compressive movement and the late one a NE to nearly N-S compressive movement with reverse shear. The dynamic force which caused the tectogeneses came from the movement of the southern major fault, i.e. the North Tianshan Mountains.

Design of Measuring Instrument with Whole Direct Method for Bed Shear Stress Under Two-Dimensional Water-Flow Co-action

The present study aims at the design and making of measuring instrument of whole direct method for bed shear stress under two-dimensional water-flow co-action. The instrument combines the traditional strain gauge with a precise pressure gauge, and adopts the method directly measuring the difference between the lateral hydrodynamic pressure and different head pressures on both sides of the force plate. As a result, such an instrument solves a technical puzzle of the past strain gauge, i.e. the difficulty to set apart shear stress and lateral force. Static force test and sink test both prove that the instrument is precise, stable and applicable to the measurement of rough beds with different shear stresses.

The efect of the couple stress parameter and Prandtl number on the transient natural convection flow over a vertical cylinder

An analysis is performed to study transient free convective boundary layer flow of a couple stress fluid over a vertical cylinder, in the absence of body couples. The solution of the time-dependent non-linear and coupled governing equations is carried out with the aid of an unconditionally stable Crank-Nicolson type of numerical scheme. Numerical results for the steady-state velocity, temperature as well as the time histories of the skin-friction coefficient and Nus- selt number are presented graphically and discussed. It is seen that for all flow variables as the couple stress control parameter, Co, is amplified, the time required for reaching the temporal maximum increases but the steady-state decreases.

Couple stress nanofluid flow through a bifurcated artery—Application of catheterization process

In this article,we are exploring the hemodynamics of nanofluid,flowing through a bifurcated artery with atherosclerosis in the presence of a catheter.For treating obstruction in the artery,one can use the catheter whose outer surface is carrying the drug coated with nano-particles.The resultant solvent is considered as blood nano-fluid.Blood being a complex fluid,is modeled by couple stress fluid.In the presence of nano-particles,the temperature and the concentration distribution are understood in a bifurcated stenotic artery.The concluded mathematical model is governed by coupled non-linear equations,and are solved by using the homotopy perturbation method.Consequently,we have explored is the effects of fluid and the embedded geometric parameters on the hemodynamics characteristics.It is also realized that high wall shear stress exists for couple stress nano-fluid when compared to Newtonian nano-fluid.which is computed at a location corresponding to maximum constriction(z=12.5)of the artery.

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE Ⅰ CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅱ)--THE ANALYSES OF THE STRESS STRUCTURE

Based on[1],the stress structures of the smooth region and shear lip of the specimens have been investigated in the paper.The characteristics of the stress structure in the smooth region have been found that the variable z can separated out;the stresses in the midsection can be obtained by the plane strain FEM results or HRR structure modified by the stress triaxiality.The effects of load level and thickness on the stress structure can be reflected by the distribution of CTOD along the thickness direction.The obtained expressions of the stresses are very simple and visualized.The analyses of the stress structure in the shear lip show that the stresses can be obtained by different methods of interpolation to a certain precise degree.A new degree parameter of the plane strain state has been put forward and studied.The parameter can reflect relatively well the variation of the kind and thickness of the specimen as well as the load level.The fracture parameter has also been investigated to be sure that it can be obtained by modified CTOD with the stress triaxiality.

Cohesive Strength and Seismogenic Stress Pattern along the Active Basement Faults of the Precordillera-Sierras Pampeanas Ranges,Western Argentina:An Experimental Analysis by Means of Numerical Model

A two-dimensional finite element method （FEM） model that incorporates faults, elastic rock physical properties, topographical load due to gravity and far-field plate velocity boundary conditions was used to recognize the seismogenic stress state along the fold-and-thrust belt of the Precordillera-Sierras Pampeanas ranges of western Argentina. A plane strain model with nine experiments was presented here to examine the fault strength with two major rock phyical properties： cohesion and angle of internal friction. Mohr-Coulomb failure criterion with bulk rock properties were applied to analyse faults. The stress field at any point of the model was assumed to be comprised of gravitational and tectonic components. The analysis was focused to recognize the seismogenic shear strain concentrated in the internal-cristaline domain of the orogene shown by the modeling. Modeling results are presented in terms of four parameters, i. e., （i） distributions, orientations, and magnitudes of principal stresses （σ1 and σ3）, （ii） displacement vector1 （iii） strain distribution, and （iv） maximum shear stress （τmax） contour line within the model. The simulation results show that the compressive stress is distributed in and around the fault systems. The overall orientation of of σ1 is in horizontal directions, although reorientations do occur within some stress weaker parts, especially subsequent to the faults. A large-scale shear stress is accumulating along the active faults of Tapias-Villicum Fault （TVF）, Salinas-Berros Fault （SBF）, Ampacama-Niquizanga Fault （ANF） and Las Charas Fault （CF）, which could act as local stress and strain modulators to localize the earthquakesoccurrence.

ANALYSIS OF SHEAR STRESS DISTRIBUTION IN HONEYCOMB AIRCRAFT WING STRUCTURE SUBJECTED TO (S.T.) TORQUE

Using the method of elasticity, an analytical approach is developed to analyze the shear stress in a honeycomb wing structure with a large aspect ratio under the condition of free torsion. The formulas of shear stress, warping and angle of twist are derived. These formulas are both useful and convenient from the point of view in the structure design.

Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder

The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.

ANALYSIS OF INTER-LAMINAR STRESSES FOR COMPOSITE LAMINATED PLATE WITH INTERFACIAL DAMAGE

A constitutive model for composite laminated plates with the damage effect of the intra-layers and inter-laminar interface is presented. The model is based on the general six-degrees-of-freedom plate theory, the discontinuity of displacement on the interfaces are depicted by three shape functions, which are formulated according to solutions satisfying three equilibrium equations, By using the variation principle, the three-dimensional non-linear equilibrium differential equations of the laminated plates with two different damage models are derived. Then, considering a simply supported laminated plate with damage, an analytical solution is presented using finite difference method to obtain the inter-laminar stresses.

A Methodology to Reduce Thermal Gradients Due to the Exothermic Reactions in Resin Transfer Molding Applications

Resin transfer molding(RTM)is among the most used manufacturing processes for composite parts.Initially,the resin cure is initiated by heat supply to the mold.The supplementary heat generated during the reaction can cause thermal gradients in the composite,potentially leading to undesired residual stresses which can cause shrinkage and warpage.In the present numerical study of these processes,a one-dimensional finite difference method is used to predict the temperature evolution and the degree of cure in the course of the resin polymerization;the effect of some parameters on the thermal gradient is then analyzed,namely:the fiber nature,the use of multiple layers of reinforcement with different thermal properties and also the temperature cycle variation.The validity of this numerical model is tested by comparison with experimental and numerical results in the existing literature.

New conception in continuum theory of constitutive equation for anisotropic crystalline polymer liquids

A new continuum theory of the constitutive equation of co-rotational derivative type is developed for anisotropic viscoelastic fluid—liquid crystalline (LC) polymers. A new concept of simple anisotropic fluid is introduced. On the basis of principles of anisotropic simple fluid, stress behaviour is described by velocity gradient tensor and spin tensor instead of the velocity gradient tensor in the classic Leslie—Ericksen continuum theory. Analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equ- ation of co-rotational type is established for the fluid. A special term of high order in the equation is introduced by author to describe the sp- ecial change of the normal stress differences which is considered as a result of director tumbling by Larson et al. Analyzing the experimental results by Larson et al., a principle of Non- oscillatory normal stress is introduced which leads to simplification of the problem with relaxation times. The special behaviour of non- symmetry of the shear stress is predicted by using the present model for LC polymer liquids. Two shear stresses in shear flow of LC polymer liquids may lead to vortex and rotation flow, i.e. director tumbling in the flow. The first and second normal stress differences are calculated by the model special behaviour of which is in agree- ment with experiments. In the research, the com- putational symbolic manipulation such as computer software Maple is used. For the anisotropic viscoelastic fluid the constitutive equation theory is of important fundamental significance.

A method for computing unsupported roof distance in roadway advancement and its in-situ application

A reasonable unsupported roof distance(URD) when advancing underground coal mine roadways can contribute greatly to safe and rapid roadway development.A mechanical model of the roof,using the relationship between the roof stress distribution and URD,obtained by the difference method,and roof stability according to the in-situ roof stress and rock mass strength was developed.We subsequently designed a proper range of URD,developed a testing method of URD with the function of mining protection,evaluated roof stability through analyzing the test data and then determined a reasonable URD.Considering the factors of the geological conditions,the immediate roof stability and the efficiency of the labor arrangement system,the URD of the advancing roadway of 9802 working face in Zhangshuanglou coal mine was determined to be 6 m using the proposed method.The results show that,when a 2 m length of roadway was reinforced by temporary support and high pre-stressed bolt support after the roadway advancement of 6 m per cycle,the speed and the security of the roadway development can be achieved and the advance rate can reach more than 400 m per month.

CALCULATION OF THE FUNDAMENTAL SOLUTION FOR THE THEORY OF SHALLOW SHELLS CONSIDERING SHEAR DEFORMATION

In this paper, some formulas are derived for the numerical computation of the fundamental solution obtained in ref. [1] and relevant computer methods are also discussed in detail. As an application of the fundamental solution, problems of a concentrated normal force acting on infinite shallow shells having positive, zero and negative Gaussian curvatures are calculated according to the numerical methods given in the paper.

Coupling characteristics of stress and strain at different layers of different sub-regions in Yunnan and its adjacent areas

In this paper, we collect 6 361 waveform data to calculate the shear wave splitting parameters from a regional seismic network of 22 digital stations in Yunnan and its adjacent area from July 1999 to June 2005. By using the cross-correlation method, 64 splitting events of 16 stations are processed. We also collect the splitting results of eight earthquake sequences to present the characteristics of shear wave splitting in Yunnan and its adjacent areas. The orientations of maximum principal compressive stress of three sub-regions in this area are derived from the CMT focal mechanism solutions of 43 moderate-strong earthquakes provided by Harvard University by the P axis azimuth-averaging method. The principal strain rate at each observatory is deduced from the observations of Crustal Movement Observation Network of China during the period from 1999 to 2004. In addition, the data of Pn aniso- tropy and SKS splitting of Yunnan and its adjacent areas are also collected. We have discovered from this study that the continental lithosphere, as a main seismogenic environment for strong earthquake, can be divided into blocks laterally; the mechanical behavior of lithosphere varies with depth and can be divided into different layers in the vertical orientation; the information of crustal deformation obtained from GPS might be affected by the type of blocks, since there are different types of active blocks in Yunnan and its adjacent areas; the shear wave splitting in this region might be affected mainly by the upper crust or even the surface tectonics.