Analytical Solution for Thermo-Electro-Elastic Problems of an Orthotropic Piezoelectric Hollow Cylinder Subjected to Various Loading

An interpolation method was used to solve the Volterra integral equation of the second kind caused by interaction among thermal, electric and mechanical fields. The exact expressions for the transient responses of stresses, electric displacement and electric potential in an orthotropic piezoelectric hollow cylinder were obtained by means of the finite integral transforms. From the sample numerical calculations, it is seen that the present method is suitable for an orthotropic piezoelectric hollow cylinder subjected to arbitrary thermal shock, mechanical load and transient electric excitation. The result can be used as a reference to solve other transient coupled problems of thermo-electro-elasticit y.     

THE EDDY LOSSES OF A MAGNETIC THRUST BEARING

Accurate calculations of losses associated with the operation of magnetic bearings are particularly important for high speed applications where the rotor losses are expected to be large and for some particular applications where even low power losses will be critical. Power losses in the magnetic thrust bearing is often neglected, but if there is misaligned in the rotor and bearing, the magnetic field in the thrust bearing is no longer axisymmetric one, or the dynamic control current in the winding is time dependent one, eddy currents are caused to flow inside the conducting material, then the power losses are very important for magnetic bearing design. This paper presents an analytical model of a thrust magnetic bearing, and the magnetic fields, forces and losses of thrust magnetic bearing are calculated. In the calculations the frequency of dynamic control current is up to 1 000 Hz, rotating speed is from 60 rpm to 1 200 rpm, and the non-linearity of material is also taken into consideration. The results shows that if the magnetic field is not saturation, the eddy losses is proportional to dynamic control current frequency and a square function of dynamic control current, and also 5/2 power function of shafts speed.     

Numerical Study of Quasi-Static Crack Growth Problems Based on Extended Finite Element Method

The extended finite element method（XFEM） is a numerical method for modeling discontinuities within a classical finite element framework. Based on the algorithm of XFEM, the major factors such as integral domain factor and mesh density which all influence the calculation accuracy of stress intensity factor（SIF） are discussed,and the proper parameters to calculate the SIF are given. The results from the case analysis demonstrate that the crack path is the most sensitive to the crack growth increment size, and the crack path is not mesh-sensitive. A reanalysis method for the XFEM has been introduced. The example presented shows that there is a significantly reduced computational cost for each iteration of crack growth achieved by using the reanalysis method and the reanalysis approach has increasing benefits as the mesh density increases or the value of crack growth increments size decreases.     

Near Crack Line Elastic-Plastic Analysis for an Infinite Plate Loaded by a Pair of Point Shear Forces

The near crack line analysis method was used to investigate a crack loaded by a pair of point shear forces in an infinite plate in an elastic-perfectly plastic solid. The analytical solution was obtained, that is the elastic-plastic fields near crack line and law that the length of the plastic zone along the crack line is varied with external loads. The results are sufficiently precise near the crack line and are not confined by small scale yielding conditions.     

Theoretical Maxwelrs Equations, Gauge Field and Their Universality Based on One Conservation Law

The notion of the inner product of vectors is extended to tensors of different orders, which may replace the vector product usually. The essences of the differential and the codiffcrential forms are pointed out： they represent the tangent surface and the normal surface fluxes of a tensor, reslpetivcly. The definitions of the divergence and the curl of a 2D surface flux of a tensor arc obtained. Maxwell＇s equations, namely, the constraction law of field, which were usually established based on two conservation laws of electric charge and imaginary magnetic charge, are derived by the author only by using one conservation law （ mass or fluid flux quantity and so on） and the feature of central field （or its composition）. By the feature of central field （or its composition）, the curl of 2D flux is zero. Both universality of gauge field and the difficulty of magnetic monopole theory （ a magnetic monopole has no effect on electric current just like a couple hasing no effect on the sum of forces） axe presented： magnetic monopole has no the feature of magnet. Finally it is pointed out that the base of relation of mass and energy is already involved in Maxwell＇s equations.     

Parallel Distributed Implementation of Truss Optimization on a Local Area Network

A two-level optimization method for the design of complex truss and parallel distributed implementation on a LAN is presented using parallel virtual machine (PVM) for Win 32 as message passing between PCs. The volumes of truss are minimized by decomposing the original optimization problem into a number of bar optimization problems executed concurrently and a coordinate optimization problem, subject to constraints on nodal displacements, and stresses, buckling and crippling of bars, etc. The system sensitivity analysis that derives the partial derivatives of displacements and stresses with respect to areas are also performed in parallel so as to shorten the analysis time. The convergence and the speedup performances as well as parallel computing efficiency of the method are investigated by the optimization examples of a 52-bar planar truss and a 3 126-bar three-diraensional truss. The results show that the ideal speedup is obtained in the cases of 2 PCs for the 3 126-bar space truss optimization, while no speedup is observed for the 52-bar truss. It is concluded that (1) the parallel distributed algorithm proposed is efficient on the PC-based LAN for the coarsegrained large optimization problem; (2) to get a high speedup, the problem granularity should match with the network granularity;and (3) the larger the problem size is, the higher the parallel efficiency is.     

Scaling analysis of thermal-hydraulics for steam generator passive heat removal system

Steam generator passive heat removal system （SG-PHRS） is used as a passively safe mode to provide decay heat removal in some advanced pressurized water reactors. Due to the structure characteristics of steam generator （SG）, there are two natural circulation loops coupling in SG-PHRS in case of a safety-related event. The existing natural circulation scaling criteria could be used to simulate the natural circulation inside SG. Two-phase natural circulation loop is studied carefully, and the dominant effects of SG on behaviors of natural circulation in passive heat removal system are presented. Based on the understanding of SG-PHRS operation, system pressure transient scaling and two-phase natural circulation scaling are analyzed by establishing the relevant continuity, integral momentum and energy equations in one-dimensional area-averaged forms. With modified equations, similarity criteria for SG-PHRS are obtained for engineering application. In addition, equal height simulation and reduced height simulation are studied.     

Analysis of interaction factors between two piles

A rigorous analytical method is presented for calculating the interaction factor between two identical piles subjected to vertical loads. Following the technique proposed by Muki and Sternberg, the problem is decomposed into an extended soil mass and two fictitious piles characterized respectively by Young＇s modulus of the soil and that of the difference between the pile and soil. The unknown axial forces along fictitious piles are determined by solving a Fredholm integral equation of the second kind, which imposes the compatibility condition that the axial strains of the fictitious piles are equal to those corresponding to the centroidal axes of the extended soil. The real pile forces and displacements can subequally be calculated based on the determined fictitious pile forces, and finally, the validity of the proposed approach and desired pile interaction factors may be obtained. Results confirm the portray the influence of the governing parameters on the pile interaction.     

Free vibration analysis of cylindrical and rectangular sandwich panels with a functionally graded core

Based on the Reissner assumptions, the free vibration analysis of simply supported cylindrical and rectangular sandwich panels with isotropic face sheets and a functionally graded core is concerned. Firstly, the expressions of the displacements, stresses and internal forces are presented according to the constitutive relations and stress states of the core and face sheets. Then, the dynamic stability and compatibility equations are given for cylindrical sandwich panels with functionally graded core, elastic modulus and density in which vary continuously in the thickness direction. Finally, the proposed solutions are validated by comparing the results of degenerate example with classical solutions, and a numerical analysis is performed on the example of simply supported cylindrical and rectangular sandwich panels. The elastic modulus and density of the functionally graded core are assumed to be graded by a power law distribution of volume fractions of the constituents, and the Poisson ratio is held constant. The effects of the distribution of functionally graded core's properties, the thickness-side ratios and ratio of radius(R) to length(l) κ = R/l are also examined.     

ASYMPTOTIC ELASTIC STRESS FIELD NEAR A BLUNT CRACK TIP IN AN ANISOTROPIC MATERIAL

IntroductionThe Williams' [1] approximate solution ob-tained with the characteristic expansion method isused for the calculation of stress distribution of anideal crack.The idealcrack is regarded as a mathe-matical line,so the crack tip becomes a singularpoint in this method. The applicability ofWilliams' solution is limited to a small annular re-gion after the elimination of a small region contain-ing the crack tip.However,in real situations,acrack tip generally has a curvature to some exten…     

CAE-Based Robust Optimization for Deep-Drawing Process of Sheet Metal Forming Using Grey Relational Analysis Method

The theory of grey systems is a new technique for performing prediction, relational analysis and decision making in many areas. The grey relational analysis was used to optimize the deep-drawing process parameters with considerations of the multiple response (the wrinkle, crack and thinning variation). The deep-drawing parameters, such as the blank holding force (F_ bh ), the radii of punch and die (R_1,R_2), the coefficients of friction (μ_1,μ_2,μ_3) are considered. An orthogonal array is used for the experimental design. The multiple response values are obtained making use of finite element analysis (FEA). Optimal process parameters are determined by the grey relational grade obtained from the grey relational analysis for multi-performance characteristics (the wrinkle, crack and the thinning). The analysis of variance (ANOVA) for the grey relational grade is implemented. The results show that the quality of stamped parts can be improved effectively through the new approach. The grey relational analysis can be applied in sheet metal forming.     

Energy Separation and Explicit Dynamic Analysis of Low Temperature Impact Toughness of Transmission Tower Material Q420B

To determine the physical significance of the impact toughness parameters and accurately characterize the low temperature impact toughness of transmission tower material Q420 B,the finite element model of Charpy impact test is established on the basis of experiment.The simulation and test results are verified,and the specimen fracture is analyzed by scanning electron microscope.The formation and growth mechanism of the crack are dynamically analyzed.On this basis,energy separation method is used to investigate the effect of low temperature on impact toughness.The results show that the simulation and test results are in good agreement,and the ductile-brittle transition temperature of Q420 B is about-50 ℃.The breaking process of the specimen is divided into the crack formation and propagation.When temperature drops from 20 to-60 ℃,the crack propagation energy decreases from 51.0 to 11.9 J,the crack formation energy reduces from 39.9 to 15.8 J,and the fracture time of the material drops from 1.8 to 0.6 ms.     

Surge Response of a Compliant Offshore Structure by Time Domain Simulation

A single-degree-of-freedom equation of motion was used for modeling a compliant offshore structure exposed to viscous hydrodynamic loads. The equation of motion contains nonlinearities in the forms of both Duffing stiffness and Morison drag force with current. The water particle velocity and acceleration for calculating the Morison inertia and drag forces are modeled as Gaussian processes based on a Pierson-Moskowitz (P-M) elevation spectrum. The single-degree-of-freedom equation of motion containing different ocean current values are then numerically integrated via a fourth-order Runge-Kutta scheme. Time trajectories of the surge response displacements of the offshore structure and the response probability density curves are obtained. Furthermore, the ocean current influences on the response central moments up to the fourth order are studied. A literature review reveals that this is the first treatment of such a pair of nonlinearities in time domain. The simulation results are analyzed, and some conclusions valuable for engineering design are pointed out.     

Analysis of through-the-thickness stress distribution in thick laminate multi-bolt joints using global-local method

The stress distribution surrounding the fastener hole in thick laminate mechanical joints is complex. It is time-consuming to analyze the distribution using finite element method. To accurately and efficiently obtain the stress state around the fastener hole in multi-bolt thick laminate joints, a global-local approach is introduced. In the method, the most seriously damaged zone is 3D modeled by taking the displacement field got from the 2D global model as boundary conditions. Through comparison and analysis there are the following findings: the global-local finite element method is a reliable and efficient way to solve the stress distribution problem; the stress distribution around the fastener hole is quite uneven in through-the-thickness direction, and the stresses of the elements close to the shearing plane are much higher than the stresses of the elements far away from the shearing plane; the out-of-plane stresses introduced by the single-lap joint cannot be ignored due to the delamination failure; the stress state is a useful criterion for further more complex studies involving failure analysis.     

The Tip Leakage Flow Structure of an Axial Fan with Tip Clearance

Experiment and numerical simulation technique are used to investigate the tip leakage flow in an axial fan with tip clearance at the design condition. The flow field in the tip region of fan is measured using a PDA (Particle Dynamics Analysis) system. The flow is surveyed across the whole passage at fifteen axial locations (from the 100% axial chord in front of the leading edge to the 100% axial chord behind the trailing edge), mainly focusing on the outer 90% blade span. Both experiment measurement and numerical simulation indicates the leakage flow orig-inated from the tip clearance along the chord rolls-up into three-dimensional spiral structure to form leakage flow vortex. The interaction of leakage flow and main flow will produce the low velocity zone, and block the flow. The leakage flow almost occupies the most part of flow passage behind the trailing edge.     

Free-Surface Wave Interaction with a Very Large Floating Structure

The free-surface wave interaction with a pontoon-type very large floating structure（VLFS） is analyzed by utilizing a modal expansion method. The modal expansion method consists of separating the hydrodynamic analysis and the dynamic response analysis of the structure. In the dynamic response analysis of the structure,the deflection of the structure with various edge conditions is decomposed into vibration modes that can be arbitrarily chosen. Free-free beam model, pinned-free beam model and fixed-free beam model are three different types of edge conditions considered in this study. For each of these beam models, the detailed mathematical formulations for calculating the corresponding eigenvalues and eigenmodes have been given, and the mathematical formulations corresponding to the beam models of pinned-free beam and fixed-free beam are novel. For the hydrodynamic analysis of the structure, the boundary value problem（BVP） equations in terms of plate modes have been established, and the BVP equations corresponding to the beam models of pinned-free beam and fixedfree beam are also novel. When these BVP equations are solved numerically, the structure deflections and the wave reflection and transmission coefficients can be obtained. These calculation results point out some findings valuable for engineering design.     

Determining Loading Field based on Required Deformation for Isotropic Hardening Material

Eringen's and Trusedell's polar decomposition are formulated by explicit formulation of displacement field, based on Chen's additive decomposition of deformation gradient. Then the strain introduced by the multiplicative decomposition and the strain introduced by the additive decomposition are formulated explicitly with displacement gradient. This formulation clears the intrinsic contents of strains defined by taking the Eringen's and Trusedell's polar decomposition. After that, Chen's strain definition was introduced to show that the plastic deformation can be understood as the irreversible local average rotation. For initial isotropic simple elastic material, the research shows that path-dependent feature of classical plasticity theory is naturally expressed in Chen's strain definition. For rate-independent plasticity, the related deformation stress was discussed. The research shows that for isotropic hardening material the relation equation between the required geometric configuration and the corresponding loading field is explicitly formulated. Hence, for metal forming, this paper explicitly formulates the related fields by displacement field and invariant elastic constants.     

Analysis of Thermal-Fluid-Structure Coupling and Resonance Forecast for Link Butterfly Valve Under Small Opening

When the link butterfly valve operates at a small opening degree in high temperature working conditions,it is prone to the problem that the valve is stuck,the strength is insufficient and the butterfly plate is violently vibrating.This paper shows simulation experiments of both thermal-fluid-structure coupling and resonance forecast about DN600 link butterfly valve in the working conditions of 250℃ and 0.5 MPa by ANSYS software.The medium is mixed with compressed air and flue gas.Flow field characteristics of the valve and stress deformation,modal and flow-induced vibration of butterfly plate are analyzed when the valve opening is less than 30%.The results indicate that,when the valve opening is less than 30%,fluid flow is relatively smooth in front of butterfly plate,a large number of vortexes are found behind the butterfly plate,and fluid flow is greatly chaotic in this position.The equivalent maximum stress and deformation of butterfly plate are relatively large when the valve locates in openings between 10% and 30%; the intensity of the butterfly plate is enough; the axial deformation does not impact opening and closing of the valve.The butterfly plate is likely resonant when the valve opening is less than 10%.The research of this paper provides a crucial reference for flow field characteristics of link butterfly valve,an analysis of intensity and rigidity of butterfly plate,and a resonance forecast of butterfly plate when the valve works in small opening.     

Shafting coupled vibration research based on wave approach

Because of propeller hydrodynamic influence, the shafting vibration is a coupled vibration which includes torsional, longitudinal and whirling vibrations. It is unsuitable to analyze different vibrations of propulsive shafting systems with development of shipbuilding technologies. To overcome the shortages of traditional marine standards, we establish a new numerical model of the shafting coupled vibration. And we put forward shafting coupled vibration calculation to ensure better reliability of main propulsion system. The shafting system is modeled into two sub-systems, a continuous one and a discrete one. Wave approach and transit matrix method are used to investigate displacement and stress fields in continuous and discrete sub-systems, respectively. And vibrations of different modes in both sub-systems are coupled by using dynamic equilibrium and continuity condition to deduce the global equations governing the motion of shafting. The coupling calculation is then used to research the reason of a very large crude carrier （VLCC） stern hull vibration. It is shown by the comparison of the results from both coupling and dependent vibration calculations that vibration in deferent directions will cause deformation in the same mode, which leads to extra stress and displacements on shafting, especially as the resonant frequencies of different vibration modes match each other. This is helpful to prevent ship stern vibration due to poor shafting vibration calculation.     

Dynamic Stress and Pore Pressure Around Circular Cavity in Saturated Porous Elastic Half-space Under Harmonic Plane Dilatational Waves

Dynamic stress concentration and pore pressure concentration around an infinitely long cylindrical cavity of circular cross-section subjected to harmonic plane dilatational waves in fluid-saturated porous elastic half-space were obtained by a complex function method based on potential function and multi-polar coordinate. The steady state Biot‘s dynamic field equations of porous elastic solid with a viscous liquid were uncoupled into Helmholtz equations via given potential functions. A circular cavity with large radius is used to replace the straight boundary of the saturated porous elastic half-space. The stresses and pore pressures were obtained by using complex functions in multi-polar coordinates with certain boundary conditions of the solid matrix and the fluid matrix. The approximate solutions were compared to existing numerical solutions. Then the variations of the coefficients of dynamic stress concentration and the pore pressures concentration on boundaries of the cavity were discussed with different parameter conditions. The results of the given numerical example indicate that the method used is useful and efficient to the scattering and dynamic stress concentration of plane dilatational waves in saturated porous elastic half-space.