Longitudinal integral response deformation method for the seismic analysis of a tunnel structure

For the longitudinal seismic response analysis of a tunnel structure under asynchronous earthquake excitations,a longitudinal integral response deformation method classified as a practical approach is proposed in this paper.The determinations of the structural critical moments when maximal deformations and internal forces in the longitudinal direction occur are deduced as well.When applying the proposed method,the static analysis of the free-field computation model subjected to the least favorable free-field deformation at the tunnel buried depth is performed first to calculate the equivalent input seismic loads.Then,the equivalent input seismic loads are imposed on the integral tunnel-foundation computation model to conduct the static calculation.Afterwards,the critical longitudinal seismic responses of the tunnel are obtained.The applicability of the new method is verified by comparing the seismic responses of a shield tunnel structure in Beijing,determined by the proposed procedure and by a dynamic time-history analysis under a series of obliquely incident out-of-plane and in-plane waves.The results show that the proposed method has a clear concept with high accuracy and simple progress.Meanwhile,this method provides a feasible way to determine the critical moments of the longitudinal seismic responses of a tunnel structure.Therefore,the proposed method can be effectively applied to analyze the seismic response of a long-line underground structure subjected to non-uniform excitations.

QUASI-PRINCIPAL AXIS METHOD IN FINITE DEFORMATION

A quasi-quasi-principal axis frame means a unit orthogonal frame in which the shear strains are small. As an extension of Hill's principal axis method we establish the approximate representations for various strains. the.finite rotation tensor, spins, strain rates. conjugate stresses and their rates with respect to quasi-principal axes. The quasiprincipal axis method may function as a new basis of numerically analyzing finite deformation problems.

Plastic Deformation of Nano-TiO_2 Ceramics Prepared by Different Methods

The comparative study of the tensile plastic deformation of nano(n)-TiO2 ceramic prepared byphysical gas condensation (P) and chemical hydrolysis precipitation (C) methods was conductedby a gas pressure forming technique at 750~800℃. The results show that n-TiO2 (P) possessesexcellent property of tensile pIastic deformation comparing with n-TiO2(C). The reason for thisis attributed to the surface cleanness and soft agglomeration of n-TiO2 (P) particfe prepared inreIatively cIean vacuum condition.

AN ANALYTICAL METHOD FOR SOLVING INTERNAL FORCES AND DEFORMATIONS OF BAR-SYSTEM STRUCTURE IN SPACE

In this paper, based on the idea of finite element method, the initial parametric method in bending, problem of a beam is extended to analyse the bar-system structure by employing Dirac function and llcavisidc step function.Then a new method for analysing the internal forces and deformations of bar-system structure in space is suggested by improving the mixed method in statically indeterminate structure.The inferred process and obtained answer will be more succinct and accurate when the problem of internal forces and deformations of bar-system structure is analysed by using the new method provided in this paper.

An eigenelement method and two homogenization conditions

Under inspiration from the structure-preserving property of symplectic difference schemes for Hamiltonian systems, two homogenization conditions for a representative unit cell of the periodical composites are proposed, one condition is the equivalence of strain energy, and the other is the deformation similarity. Based on these two homogenization conditions, an eigenelement method is presented, which is characteristic of structure-preserving property. It follows from the frequency comparisons that the eigenelement method is more accurate than the stiffness average method and the compliance average method.

Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method

Abstract A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport （SST） k-w turbulence model to predict the transition region for a laminar-turbulent boundary layer. The non-uniform free-form deformation （NFFD） method based on the non-uniform rational B-spline （NURBS） basis function is introduced to the airfoil parameterization. The non-dominated sorting genetic algorithm-II （NSGA-II） is used as the search algo- rithm, and the surrogate model based on the Kriging models is introduced to improve the efficiency of the optimization system. The optimization system is set up based on the above technologies, and the robust design about the uncertainty of the Mach number is carried out for NASA0412 airfoil. The optimized airfoil is analyzed and compared with the original airfoil. The results show that natural laminar flow can be achieved on a supercritical airfoil to improve the aerodynamic characteristic of airfoils.

Compressional Deformation in Indentation Process for Microlens Array Mold

The structure of a microlens array（ MLA） can be formed on copper by an indentation process which is a new manufacture approach we applied here instead of a traditional method to test the material property,thereby work time can be saved. Single-indentation and multi-indentation are both conducted to generate a single dimple and dimples array,namely micro lens and MLA. Based on finite element simulation method,factors affecting the form accuracy,such as springback at the compressed area of one single dimple and compressional deformation at the adjacent area of dimples arrays,are determined,and the results are verified by experiments under the same conditions. Meanwhile,indenter compensation method is proposed to improve form accuracy of single dimple,and the relationship between pitch and compressional deformation is investigated by modelling seven sets of multi-indentations at different pitches to identify the critical pitch for the MLA＇s indentation processing. Loads and cross-sectional profiles are measured and analyzed to reveal the compressional deformation mechanism. Finally,it is found that MLA at pitches higher than 1. 47 times of its diameter can be manufactured precisely by indentation using a compensated indenter.

Thermo-hydro-mechanical-air coupling finite element method and its application to multi-phase problems

In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.

Numerical simulation of influences of the earth medium's lateral heterogeneity on co- and post-seismic deformation

Many studies revealed that the Earth medium＇s lateral heterogeneity can cause considerable effects on the co- and post-seismic deformation field. In this study, the threedimensional finite element numerical method are adopted to quantify the effects of lateral heterogeneity caused by material parameters and fault dip angle on the co- and postseismic deformation in the near- and far-field. Our results show that： 1） the medium＇s lateral heterogeneity does affect the co-seismic deformation, with the effects increasing with the medium＇s lateral heterogeneity caused by material parameters; 2） the Lame parameters play a more dominant role than density in the effects caused by lateral heterogeneity; 3） when a fault＇s dip angle is smaller than 90, the effects of the medium＇s lateral heterogeneity on the hanging wall are greater than on the footwall; 4） the impact of lateral heterogeneity caused by the viscosity coefficient on the post-seismic deformation can affect a large area, including the near- and far-field.

Extrusion deformation process of ground surface during the Lushan earthquake in China

Based on finite element method, the extrusion deformation process of ground surface during the Lushan earthquake （April 20, 2013） is investigated in this work. In order to construct the finite element model of Lushan earthquake structure, the geophysical layer model of Lushan area, the frictional characteristic of slip-weaken along the fault surface, and the Coulomb failure criterion are considered. Through the computation and the comparison with achievement on the Lushan focal dynamics, our researches indicate that： （1） The most extrusion deformation of ground surface occurred in the initial phase of earthquake procession, i.e., between the fourth and sixth seconds after the earthquake occurred. （2） Between the first and sixth seconds after the earthquake, the extrusion deformation concentrates on the surface projection of earthquake fault. （3） Between the first and third seconds after the earthquake, the extrusion deformation of ground surface is very tiny. Meanwhile, the extrusion deformation reaches maximum at the sixth second after earthquake. （4） After 6 s of Lushan earthquake, the extrusion deformation spread out of earthquake structure projection. （5） During the earthquake, the maximum of extrusion deformation on ground surface is larger than the final deformation of the post-earthquake, in other words, the ground extrusion deformation will lastly reach a relatively small value after the Lushan earthquake occurred.

NON-SYMMETRICAL LARGE DEFORMATION OF A SHALLOW THIN SPHERICAL SHELL

By the modified iteration method,in this paper,non=symmetrical large deflectionof a shallow spherical shell is discussed. We solve the second-order approximate analytical solution of the deflection of a shallow spherical shell subjected to linearliquid loads. and portray the characteristic curves of load-deflection on a perturbing point. With this paper's method, the similar questions of other kind of shell can bediscussed. Through the examples.we discuss the large defection of a plane and shallow spherical shells with different initial deflections.

Study on the subgrade deformation under high-speed train loading and water–soil interaction

It is important to study the subgrade characteristics of high-speed railways in consideration of the water–soil coupling dynamic problem,especially when high-speed trains operate in rainy regions.This study develops a nonlinear water–soil interaction dynamic model of slab track coupling with subgrade under high-speed train loading based on vehicle–track coupling dynamics.By using this model,the basic dynamic characteristics,including water–soil interaction and without water induced by the high-speed train loading,are studied.The main factors-the permeability coefficien and the porosity-influencin the subgrade deformation are investigated.The developed model can characterize the soil dynamic behaviour more realistically,especially when considering the influenc of water-rich soil.

Gravity changes and surface deformations due to faults with different geometry

Based on the formulae of the gravity changes and surface deformations raised by the dislocation of a point source,the gravity changes and deformations caused by the dislocations of fault with arbitrary geometry are computed by using numerical method. The results show that both of the dislocation and the geometry of the fault plane are the basic elements that determine the gravity and deformation effects. Gravity changes, vertical deformations and apparent vertical deformations induced by the dislocation are alike in their characteristic patterns. The similarities and differences of these patterns provide us a probability in acquiring the gravity and deformation anomalies due to faulting from the observed data. Thus the geometric and kinematic features of the earthquake-generating faults can be appropriately distinguished and evaluated.

Multiscale Isogeometric Topology Optimization with Unified Structural Skeleton

This paper proposes a multiscale isogeometric topology optimization(ITO)method where the configuration and layout of microstructures are optimized simultaneously.At micro scale,a shape deformation method is presented to transform a prototype microstructure(PM)for obtaining a series of graded microstructures(GMs),where microstructural skeleton based on the level set framework is applied to retain more topology features and improve the connectability.For the macro scale calculation,the effective mechanical properties can be estimated by means of the numerical homogenization method.By adopting identical non-uniform rational basis splines(NURBS)as basis functions for both parameterized level set model and isogeometric calculation model,the isogeometric analysis(IGA)is integrated into the level set method,which contributes to improving the accuracy and efficiency.Numerical examples demonstrate that,the proposed method is effective in improving the performance and manufacturability.

Exact periodic wave and soliton solutions in two-component Bose-Einstein condensates

We present several families of exact solutions to a system of coupled nonlinear Schrodinger equations. The model describes a binary mixture of two Bose-Einstein condensates in a magnetic trap potential. Using a mapping deformation method, we find exact periodic wave and soliton solutions, including bright and dark soliton pairs.

Accurate Solutions of the Plasma Motion Equation May be Composed with the Accurate Solutions of the Burgers Equation

The travelling solutions of the Burgers equation may be used as the seed solutions. According to the fraction-type deforming relation between the Burgers equation and the plasma motion equation, some travelling solutions of the plasma motion equation are achieved with this seed solutions as discussed in this paper.

Theoretical Research and Experimental Validation of Elastic Dynamic Load Spectra on Bogie Frame of High-speed Train

When a train runs at high speeds, the external exciting frequencies approach the natural frequencies of bogie critical components, thereby inducing strong elastic vibrations. The present international reliability test evaluation standard and design criteria of bogie frames are all based on the quasi-static deformation hypothesis. Structural fatigue damage generated by structural elastic vibrations has not yet been included. In this paper, theoretical research and experimental validation are done on elastic dynamic load spectra on bogie frame of high-speed train. The construction of the load series that correspond to elastic dynamic deformation modes is studied. The simplified form of the load series is obtained. A theory of simplified dynamic load–time histories is then deduced. Measured data from the Beijing–Shanghai Dedicated Passenger Line are introduced to derive the simplified dynamic load–time histories. The simplified dynamic discrete load spectra of bogie frame are established. Based on the damage consistency criterion and a genetic algorithm, damage consistency calibration of the simplified dynamic load spectra is finally performed. The computed result proves that the simplified load series is reasonable. The calibrated damage that corresponds to the elastic dynamic discrete load spectra can cover the actual damage at the operating conditions. The calibrated damage satisfies the safety requirement of damage consistency criterion for bogie frame. This research is helpful for investigating the standardized load spectra of bogie frame of high-speed train.

Analysis on Shear Deformation for High Manganese Austenite Steel during Hot Asymmetrical Rolling Process Using Finite Element Method

Based on the rigid-plastic finite element method（FEM）, the shear stress field of deformation region for high manganese austenite steel during hot asymmetrical rolling process was analyzed. The influences of rolling parameters, such as the velocity ratio of upper to lower rolls, the initial temperature of workpiece and the reduction rate, on the shear deformation of three nodes in the upper, center and lower layers were discussed. As the rolling parameters change, distinct shear deformation appears in the upper and lower layers, but the shear deformation in the center layer appears only when the velocity ratio is more than 1.00, and the absolute value of the shear stress in this layer is changed with rolling parameters. A mathematical model which reflected the change of the maximal absolute shear stress for the center layer was established, by which the maximal absolute shear stress for the center layer can be easily calculated and the appropriate rolling technology can be designed.

Numerical evaluation of strength and deformability of fractured rocks

Knowledge of the strength and deformability of fractured rocks is important for design, construction and stability evaluation of slopes, foundations and underground excavations in civil and mining engineering. However, laboratory tests of intact rock samples cannot provide information about the strength and deformation behaviors of fractured rock masses that include many fractures of varying sizes, orientations and locations. On the other hand, large-scale in situ tests of fractured rock masses are economically costly and often not practical in reality at present. Therefore, numerical modeling becomes necessary. Numerical predicting using discrete element methods(DEM) is a suitable approach for such modeling because of their advantages of explicit representations of both fractures system geometry and their constitutive behaviors of fractures, besides that of intact rock matrix. In this study, to generically determine the compressive strength of fractured rock masses, a series of numerical experiments were performed on two-dimensional discrete fracture network models based on the realistic geometrical and mechanical data of fracture systems from feld mapping. We used the UDEC code and a numerical servo-controlled program for controlling the progressive compressive loading process to avoid sudden violent failure of the models. The two loading conditions applied are similar to the standard laboratory testing for intact rock samples in order to check possible differences caused by such loading conditions. Numerical results show that the strength of fractured rocks increases with the increasing confning pressure, and that deformation behavior of fractured rocks follows elasto-plastic model with a trend of strain hardening. The stresses and strains obtained from these numerical experiments were used to ft the well-known Mohr-Coulomb(MC) and Hoek-Brown(H-B) failure criteria, represented by equivalent material properties defning these two criteria. The results show that both criteria can provide fair estimates of the compressive strengths for all tested numerical models. Parameters of the elastic deformability of fractured models during elastic deformation stages were also evaluated, and represented as equivalent Young’s modulus and Poisson’s ratio as functions of lateral confning pressure. It is the frst time that such systematic numerical predicting for strength of fractured rocks was performed considering different loading conditions, with important fndings for different behaviors of fractured rock masses, compared with testing intact rock samples under similar loading conditions.

Simulation of blast induced crater in jointed rock mass by discontinuous deformation analysis method

Rock blasting is a dynamic process accom panied with the propagations of shock waves and the dispersion of the explosion gas.This paper adopts the discontinuous deformation analysis(DDA)method to simulate the rock blasting process.A dynamic parameter adjustment and the non-reflecting boundary condition are implemented in the DDA method.The sub-block DDA method to simulate fracture problems is used.The blasting process in jointed rock mass is simulated by application of the explosion gas pressure on the expanding borehole walls and induced connected fracture surfaces around the boreholes.The blast craters with different overburdens are derived.The whole process including the explosion gas dispersion,borehole expansion,rock mass failure and cast,and the formation of the final blasting piles in rock blasting are well reproduced numerically.Parametric study for different overburdens is carried out,and the results are analyzed and discussed.