The efficiency of direct integration methods in elastic contact-impact problems

A comparison of direct integration methods is madeand their efficiency is investigated for impact problems.New-mark,Wilson-θ,Central Difference and Houbolt Methodsare used as direct integration methods.Impact analysisincludes that of elastic and large deformation based uponupdated Lagrangian including buckling check.The resultsshow that the direct integration methods give differentresults in different contact-impact cases.

A QUADRATURE RULE FOR HADAMARD FINITE PART INTEGRALS

Finite part integrals introduced by Hadamard in connection with hyperbolic partial differential equations,have been useful in a number of engineering applications.In this paper we investigate some numerical methods for computing finite-part integrals.

Transient heat conduction analysis using the NURBS-enhanced scaled boundary finite element method and modified precise integration method

The Non-uniform rational B-spline （NURBS） enhanced scaled boundary finite element method in combination with the modified precise integration method is proposed for the transient heat conduction problems in this paper. The scaled boundary finite element method is a semi-analytical technique, which weakens the governing differential equations along the circumferential direction and solves those analytically in the radial direction. In this method, only the boundary is discretized in the finite element sense leading to a re- duction of the spatial dimension by one with no fundamental solution required. Neverthe- less, in case of the complex geometry, a huge number of elements are generally required to properly approximate the exact shape of the domain and distorted meshes are often un- avoidable in the conventional finite element approach, which leads to huge computational efforts and loss of accuracy. NURBS are the most popular mathematical tool in CAD industry due to its flexibility to fit any free-form shape. In the proposed methodology, the arbitrary curved boundary of problem domain is exactly represented with NURBS basis functions, while the straight part of the boundary is discretized by the conventional Lagrange shape functions. Both the concepts of isogeometric analysis and scaled boundary finite element method are combined to form the governing equations of transient heat conduction analy- sis and the solution is obtained using the modified precise integration method. The stiffness matrix is obtained from a standard quadratic eigenvalue problem and the mass matrix is determined from the low-frequency expansion. Finally the governing equations become a system of first-order ordinary differential equations and the time domain response is solved numerically by the modified precise integration method. The accuracy and stability of the proposed method to deal with the transient heat conduction problems are demonstrated by numerical examples.

Numerical Simulation of Installation Process and Uplift Resistance for An Integrated Suction Foundation in Deep Ocean

A concept design, named integrated suction foundation, is proposed for a tension leg platform（TLP） in deep ocean. The most important improvement in comparing with the traditional one is that a pressure-resistant storage module is designed. It utilizes the high hydrostatic pressure in deep ocean to drive water into the module to generate negative pressure for bucket suction. This work aims to further approve the feasibility of the concept design in the aspect of penetration installation and the uplift force in-place. Seepage is generated during suction penetration, and can have both positive and negative effects on penetration process. To study the effect of seepage on the penetration process of the integrated suction foundation, finite element analysis（FEA） is carried out in this work. In particular, an improved methodology to calculate the penetration resistance is proposed for the integrated suction foundation with respect to the reduction factor of penetration resistance. The maximum allowable negative pressure during suction penetration is calculated with the critical hydraulic gradient method through FEA. The simulation results of the penetration process show that the integrated suction foundation can be installed safely. Moreover, the uplift resistance of the integrated suction foundation is calculated and the feasibility of the integrated suction foundation working on-site is verified. In all, the analysis in this work further approves the feasibility of the integrated suction foundation for TLPs in deep ocean applications.

Quasi-Homeomorphisms and Measures of Finite Energy Integrals of Generalized Dirichlet Forms

We introduce the quasi-homeomorphisms of generalized Dirichlet forms and prove that any quasi-regular generalized Dirichlet form is quasi-homeomorphic to a semi-regular generalized Dirichlet form. Moreover. we apply this quasi-homeomorphism method to study the measures of finite energy integrals of generalized Dirichlet forms. We show that any 1-coexcessive function which is dominated by a function in is associated with a measure of finite energy integral. Consequently, we prove that a Borel set B is-exceptional if and only if μ(B)=0 for any measure μ of finite energy integral.

An improved three-dimensional full-vectorial finite-difference imaginary-distance beam propagation method

A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method （3D-FV-BPM） formulation along the longitudinal direction. The cross-coupling terms （CCTs） are neglected at the first substep, and then double used at the second substep. The order of two substeps is reversed for each transverse electric field component so that the CCTs are always expressed in an implicit form, thus the calculation is efficient and stable. Based on the multinomial interpolation, a universal finite difference scheme with a high accuracy is developed to approximate the 3D-FV-BPM formulation along the transverse directions, in which the discontinuities of the normal components of the electric field across the abrupt dielectric interfaces are taken into account and can be applied to both uniform and non-uniform grids. The corresponding imaginary-distance procedure is first applied to a buried rectangular and a GaAs-based deeply-etched rib waveguide. The field patterns and the normalized propagation constants of the fundamental and the first order modes are presented and the hybrid nature of the full-vectorial guided-modes is demonstrated, which shows the validity and utility of the present approach. Then the modal characteristics of the deeply- and shallow-etched rib waveguides based on the InGaAsp/InGaAsP strained multiple quantum wells in InP substrate are investigated in detail. The results are necessary for modeling and the design of the planar lightwave circuits or photonic integrated circuits based on these waveguides.

Analytical modeling on the vibration response of a beam-stiffened Mindlin thick plate with free boundary conditions

This paper presents a new analytical solution for the vibration response of a beamstiffened Mindlin plate having a completely free boundary condition by utilizing a finite cosine integral transform.In the solution,the unknown coupling force and moments at the beam/plate interface and the unknown modal constants from the integral transform are determined by the continuity and compatibility conditions at the interface as well as the boundary conditions.It provides an easily implemented tool for exploring complex edge value problems for a class of higher-order partial differential equations represented by fully free‐stiffened Mindlin thick plates.The validity of the model is evaluated by comparing the calculated free and forced vibration responses of the beam‐stiffened plate with those calculated using a beamstiffened thin plate and those from finite element analysis.

The fundamental solution of the Keldysh typeoperator

In this paper we discuss the fundamental solution of the Keldysh type operator $ L_\alpha u \triangleq \frac{{\partial ^2 u}} {{\partial x^2 }} + y\frac{{\partial ^2 u}} {{\partial y^2 }} + \alpha \frac{{\partial u}} {{\partial y}} $ , which is a basic mixed type operator different from the Tricomi operator. The fundamental solution of the Keldysh type operator with $ \alpha > - \frac{1} {2} $ is obtained. It is shown that the fundamental solution for such an operator generally has stronger singularity than that for the Tricomi operator. Particularly, the fundamental solution of the Keldysh type operator with $ \alpha < \frac{1} {2} $ has to be defined by using the finite part of divergent integrals in the theory of distributions.

A Generalized Numerical Approach for Modeling Multiphase Flow and Transport in Fractured Porous Media

A physically based numerical approach is presented for modeling multiphase flow and transport processes in fractured rock.In particular,a general framework model is discussed for dealing with fracture-matrix interactions,which is applicable to both continuum and discrete fracture conceptualization.The numerical modeling approach is based on a general multiple-continuum concept,suitable for modeling any types of fractured reservoirs,including double-,triple-,and other multiplecontinuum conceptual models.In addition,a new,physically correct numerical scheme is discussed to calculate multiphase flow between fractures and the matrix,using continuity of capillary pressure at the fracture-matrix interface.The proposed general modeling methodology is verified in special cases using analytical solutions and laboratory experimental data,and demonstrated for its application in modeling flow through fractured vuggy reservoirs.

Plate Shape Control Theory and Experiment for 20-high Mill

Roll flattening theory is an important part of plate shape control theories for 20-high mill. In order to improve the accuracy of roll flattening calculation for 20-high mill, a new and more accurate roll flattening model was proposed. In this model, the roll barrel was considered as a finite length semi-infinite body. Based on the boundary integral equation method, the numerical solution of the finite length semi-infinite body under the distributed force was obtained and an accurate roll flattening model was established. Coupled with roll bending model and strip plastic deformation, a new and more accurate plate control model for 20-high mill was established. Moreover, the effects of the first intermediate roll taper angle and taper length were analyzed. The tension distribution calculated by analytical model was consistent with the experimental results.

NUMERICAL PREDICTION OF PROPELLER EXCITED ACOUSTIC RESPONSE OF SUBMARINE STRUCTURE BASED ON CFD,FEM AND BEM

A mesh-less Refined Integral Algorithm （RIA） of Boundary Element Method （BEM） is proposed to accurately solve the Helmholtz Integral Equation （HIE）.The convergence behavior and the practicability of the method are validated.Computational Fluid Dynamics （CFD）,Finite Element Method （FEM） and RIA are used to predict the propeller excited underwater noise of the submarine hull structure.Firstly the propeller and submarine＇s flows are independently validated,then the self propulsion of the ＂submarine＋propeller＂ system is simulated via CFD and the balanced point of the system is determined as well as the self propulsion factors.Secondly,the transient response of the ＂submarine＋ propeller＂ system is analyzed at the balanced point,and the propeller thrust and torque excitations are calculated.Thirdly the thrust and the torque excitations of the propeller are loaded on the submarine,respectively,to calculate the acoustic response,and the sound power and the main peak frequencies are obtained.Results show that：（1） the thrust mainly excites the submarine axial mode and the high frequency area appears at the two conical-type ends,while the torque mainly excites the circumferential mode and the high frequency area appears at the broadside of the cylindrical section,but with rather smaller sound power and radiation efficiency than the former,（2） the main sound source appears at BPF and 2BPF and comes from the harmonic propeller excitations.So,the main attention should be paid on the thrust excitation control for the sound reduction of the propeller excited submarine structure.

A tight sandstone multi-physical hydraulic fractures simulator study and its field application

During the past years,the recovery of unconventional gas formation has attracted lots of attention and achieved huge success.To produce gas from the low-permeability unconventional formations,hydraulic fracturing technology is essential and critical.In this paper,we present the development of a three-dimensional thermalhydraulic-mechanical numerical simulator for the simulation of hydraulic fracturing operations in tight sandstone reservoirs.Our simulator is based on integrated finite difference(IFD)method.In this method,the simulation domain is subdivided into sub domains and the governing equations are integrated over a sub domain with flux terms expressed as an integral over the sub domain boundary using the divergence theorem.Our simulator conducts coupled thermal-hydraulic-mechanical simulation of the initiation and extension of hydraulic fractures.It also calculates the mass/heat transport of injected hydraulic fluids as well as proppants.Our simulator is able to handle anisotropic formations with multiple layers.Our simulator has been validated by comparing with an analytical solution as well as Ribeiro and Sharma model.Our model can simulate fracture spacing effect on fracture profile when combining IFD with Discontinuous Displacement Method(DDM).