Fuzzy-Model-Based Finite Frequency Fault Detection Filtering Design for Two-Dimensional Nonlinear Systems

This article studies the fault detection filtering design problem for Roesser type two-dimensional(2-D)nonlinear systems described by uncertain 2-D Takagi-Sugeno(T-S)fuzzy models.Firstly,fuzzy Lyapunov functions are constructed and the 2-D Fourier transform is exploited,based on which a finite frequency fault detection filtering design method is proposed such that a residual signal is generated with robustness to external disturbances and sensitivity to faults.It has been shown that the utilization of available frequency spectrum information of faults and disturbances makes the proposed filtering design method more general and less conservative compared with a conventional nonfrequency based filtering design approach.Then,with the proposed evaluation function and its threshold,a novel mixed finite frequency H_(∞)/H_(-)fault detection algorithm is developed,based on which the fault can be immediately detected once the evaluation function exceeds the threshold.Finally,it is verified with simulation studies that the proposed method is effective and less conservative than conventional non-frequency and/or common Lyapunov function based filtering design methods.

A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model

In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+
t2)is obtained,which is verified by the numerical results.

A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered fi- nite volume/finite element method for solution of the two di- mensional （2D） incompressible Navier-Stokes equations on unstructured grids. An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling. The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by join- ing the centroid of cells sharing the common vertex. For the temporal integration of the momentum equations, an im- plicit second-order scheme is utilized to enhance the com- putational stability and eliminate the time step limit due to the diffusion term. The momentum equations are discretized by the vertex-centered finite volume method （FVM） and the pressure Poisson equation is solved by the Galerkin finite el- ement method （FEM）. The momentum interpolation is used to damp out the spurious pressure wiggles. The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both veloc- ity and pressure. The classic test cases, the lid-driven cavity flow, the skew cavity flow and the backward-facing step flow, show that numerical results are in good agreement with the published benchmark solutions.

A new integration algorithm for finite deformation of thermo-elasto-viscoplastic single crystals

An algorithm for integrating the constitutive equations in thermal framework is presented, in which the plastic deformation gradient is chosen as the integration variable. Compared with the classic algorithm, a key feature of this new approach is that it can describe the finite deformation of crystals under thermal conditions. The obtained plastic deformation gradient contains not only plastic defor- mation but also thermal effects. The governing equation for the plastic deformation gradient is obtained based on ther- mal multiplicative decomposition of the total deformation gradient. An implicit method is used to integrate this evo- lution equation to ensure stability. Single crystal 1 100 aluminum is investigated to demonstrate practical applications of the model. The effects of anisotropic properties, time step, strain rate and temperature are calculated using this integration model.

Finite Element Simulation of the Polymeric Liquid Flow in Coat-hanger Die

A three - dimenslonal finite element model is developed to deal with the polymeric liquid flow in coat - hanger die. This model is used to predict the flow behavior of the 2％ CMC/watsr solution in the coat - hanger die with linearly taper manifolds and its validity is experimentally verified quantitatively and qualitatively by using Laser Doppler Velocimetry and Particle Image Velocimetry respectively.

An explicit finite volume element method for solving characteristic level set equation on triangular grids

Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.

Parametric study on single shot peening by dimensional analysis method incorporated with finite element method

Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and re- sistance to corrosion fatigue, cracking, etc. Compressive re- sidual stress and dent profile are important factors to eval- uate the effectiveness of shot peening process. In this pa- per, the influence of dimensionless parameters on maximum compressive residual stress and maximum depth of the dent were investigated. Firstly, dimensionless relations of pro- cessing parameters that affect the maximum compressive residual stress and the maximum depth of the dent were de- duced by dimensional analysis method. Secondly, the in- fluence of each dimensionless parameter on dimensionless variables was investigated by the finite element method. Fur- thermore, related empirical formulas were given for each di- mensionless parameter based on the simulation results. Fi- nally, comparison was made and good agreement was found between the simulation results and the empirical formula, which shows that a useful approach is provided in this pa- per for analyzing the influence of each individual parameter.

Deformation behaviors of 21-6-9 stainless steel tube numerical control bending under different friction conditions

For contact dominated numerical control(NC) bending process of tube, the effect of friction on bending deformation behaviors should be focused on to achieve precision bending forming. A three dimensional(3D) elastic-plastic finite element(FE) model of NC bending process was established under ABAQUS/Explicit platform, and its reliability was validated by the experiment. Then, numerical study on bending deformation behaviors under different frictions between tube and various dies was explored from multiple aspects such as wrinkling, wall thickness change and cross section deformation. The results show that the large friction of wiper die-tube reduces the wrinkling wave ratio η and cross section deformation degree ΔD and increases the wall thinning degree Δt. The large friction of mandrel-tube causes large η, Δt and ΔD, and the onset of wrinkling near clamp die. The large friction of pressure die-tube reduces Δt and ΔD, and the friction on this interface has little effect on η. The large friction of bending die-tube reduces η and ΔD, and the friction on this interface has little effect on Δt. The reasonable friction coefficients on wiper die-tube, mandrel-tube, pressure die-tube and bending die-tube of 21-6-9(0Cr21Ni6Mn9N) stainless steel tube in NC bending are 0.05-0.15, 0.05-0.15, 0.25-0.35 and 0.25-0.35, respectively. The results can provide a guideline for applying the friction conditions to establish the robust bending environment for stable and precise bending deformation of tube bending.

Suppressive Influence of Time- Space White Noise on the Explosion of Solutions of Stochastic Fokker- Planck Delay Differential Equations

It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion.

Friction coefficient in rubber forming process of Ti-15-3 alloy

The forming limit diagram of Ti-15-3 alloy sheet was constituted at room temperature. The effects of different punch and rubber hardness on the limit principal strain distributions were investigated experimentally. Finite element analysis models of the samples with dimensions of 180 mm×180 mm were established to analyze the friction coefficients of different interfaces. Effects of various friction coefficients on the strain distributions were studied in detail. Finally, the friction coefficients in the cold forming were determined by contrasting the strain results between the experimental data and the simulated ones.

Fracture prediction in the tight-oil reservoirs of the Triassic Yanchang Formation in the Ordos Basin,northern China

It is important to predict the fracture distribution in the tight reservoirs of the Ordos Basin because fracturing is very crucial for the reconstruction of the low-permeability reservoirs. Three-dimensional finite element models are used to predict the fracture orientation and distribution of the Triassic Yanchang Formation in the Longdong area, southern Ordos Basin. The numerical modeling is based on the distribution of sand bodies in the Chang 7a and 72 members, and the different forces that have been exerted along each boundary of the basin in the Late Mesozoic and the Cenozoic. The calculated results demonstrate that the fracture orientations in the Late Mesozoic and the Ceno- zoic are NW-EW and NNE-ENE, respectively. In this paper, the two-factor method is applied to analyze the distribution of fracture density. The distribution maps of predicted fracture density in the Chang 71 and 72 members are obtained, indicating that the tectonic movement in the Late Mesozoic has a greater influence on the fracture development than that in the Cenozoic. The average fracture densities in the Chang 71 and 72 members are similar, but there are differences in their distributions. Compared with other geological elements, the lithology and the layer thickness are the primary factors that control the stress distribution in the study area, which further determine the fracture distribution in the stable Ordos Basin. The predicted fracture density and the two-factor method can be utilized to guide future exploration in the tight-sand reservoirs.

Three-dimensional hydrodynamic model of Xiamen waters

A semi-implicit and Eulerian - Lagrangian finite difference method for three-dimensionalshallow flow has been extended to a more complete system of equations incorporating second-moment turbulence closure model and transport equations of salinity and temperature. The simulation for flooding and drying of mudflats has been improved. The model is applied to Xiamen waters. Based on extensive survey data, water level elevation, temperature and salinity field along the eastern open boundary and at the Jiulong River inlets and runoffs are analyzed, specified and calibrated. The computed results show good agreement with the measured data, reproduce flooding, emergence of large and complex mudflat region.

Construction of n-sided polygonal spline element using area coordinates and B-net method

In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.

Theoretical analysis of the sound absorption characteristics of periodically stiffened micro-perforated plates

The vibro-acoustic responses and sound absorption characteristics of two kinds of periodically stiffened micro-perforated plates are analyzed theoretically. The connected periodical structures of the stiffened plates can be ribs or block-like structures. Based on fundamental acoustic formulas of the micro-perforated plate of Maa and Takahashi, semi-analytical models of the vibrating stiffened plates are developed in this paper. Approaches like the space harmonic method, Fourier transforms and finite element method （FEM） are adopted to investigate both kinds of the stiffened plates. In the present work, the vibro-acoustic responses of micro-perforated stiffened plates in the wavenumber space are expressed as functions of plate displacement amplitudes. After approximate numerical solutions of the amplitudes, the vibration equations and sound absorption coefficients of the two kinds of stiffened plates in the physical space are then derived by employing the Fourier inverse transform. In numerical examples, the effects of some physical parameters, such as the perforation ratio, incident angles and periodical distances etc., on the sound absorption performance are examined. The proposed approaches are also validated by comparing the present results with solutions of Takahashi and previous studies of stiffened plates. Numerical results indicate that the flexural vibration of the plate has a signif- icant effect on the sound absorption coefficient in the water but has little influence in the air.

CFD simulation of an industrial hydrocyclone with Eulerian-Eulerian approach: A case study

In the present study, a three-dimensional computational fluid dynamics simulation together with experimental field measurements was applied to optimize the performance of an industrial hydrocyclone at Sarcheshmeh copper complex. In the simulation, the Eulerian–Eulerian approach was used for solid and liquid phases, the latter being water. In this approach, nine continuous phases were considered for the solid particles with different sizes and one continuous phase for water. The continuity and momentum equations with inclusion of buoyancy and drag forces were solved by the finite volume method. The k–e RNG turbulence model was used for modeling of turbulency. There was a good agreement between the simulation results and the experimental data. After validation of the model accuracy, the effect of inlet solid percentage, pulp inlet velocity, rod inserting in the middle of the hydrocyclone and apex diameter on hydrocyclone performance was investigated. The results showed that by decreasing the inlet solid percentage and increasing the pulp inlet velocity, the efficiency of hydrocyclone increased. Decreasing the apex diameter caused an increase in the hydrocyclone efficiency.

NUMERICAL SIMULATION OF STRESS-STRAIN DISTRIBUTIONS FOR WELD METAL SOLIDIFICATION CRACKING IN STAINLESS STEEL

This paper analyzed the characteristics of welding solidification crack of stainless steels,and clearly re- vealed the the of the deformation in the molten - the pool and the solidification shrinkage on the stress - strain fields in the trail of molten - weld pool.Moreover, rheologic properties of the alloys in solid - liquid zone were also obtained by measuring the hading and unloading deform curves of the steels.As a result, a numerical model for simulation of stress - strain distributions of welding solidifi- cation crack was developed. On the basis of the model,the thesis simulated the driving force of solidifi- cation crack of stainless steels, that is, stress - strain fields in the trail of molten-weld pool with fi- nite element method.

Two 8-node quadrilateral spline elements by B-net method

Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.

Numerical Analysis of the Adhesive Forces in Nano-Scale Structure

Nanohairs, which can be found on the epidermis of Tokay gecko＇s toes, contribute to the adhesion by means of van der Waals force, capillary force, etc. This structure has inspired many researchers to fabricate the attachable nano-scale structures. However, the efficiency of artificial nano-scale structures is not reliable sufficiently. Moreover, the mechanical parameters related to the nano-hair attachment are not yet revealed qualitatively. The mechanical parameters which have influence on the ability of adhesive nano-hairs were investigated through numerical simulation in which only van der Waals force was considered. For the numerical analysis, finite element method was utilized and van der Waals force, assumed as 12-6 Lennard-Jones potential, was implemented as the body force term in the finite element formulation.

Pseudo-beam method for compressive buckling characteristics analysis of space inflatable load-carrying structures

This paper extends Le van＇s work to the case of nonlinear problem and the complicated configuration. The wrinkling stress distribution and the pressure effects are also included in our analysis. Pseudo-beam method is presented based on the inflatable beam theory to model the inflatable structures as a set of inflatable beam elements with a prestressed state. In this method, the discretized nonlinear equations are given based upon the virtual work principle with a 3-node Timoshenko＇s beam model. Finite element simulation is performed by using a 3-node BEAM189 element incorporating ANSYS nonlinear program. The pressure effect is equivalent included in our method by modifying beam element cross-section parameters related to pressure. A benchmark example, the bending case of an inflatable cantilever beam, is performed to verify the accuracy of our proposed method. The comparisons reveal that the numerical results obtained with our method are close to open published analytical and membrane finite element results. The method is then used to evaluate the whole buckling and the loadcarrying characteristics of an inflatable support frame subjected to a compression force. The wrinkling stress and region characteristics are also shown in the end. This method gives better convergence characteristics, and requires much less computation time. It is very effective to deal with the whole load-carrying ability analytical problems for large scale inflatable structures with complex configuration.

Finite element analysis of chip formation and residual stresses induced by sequential cutting in side milling with microns to sub- micron uncut chip thickness and finite cutting edge radius

In this paper, the effect of four sequential cuts in side milling of Ti6Al4V on chip formation and residual stresses （RS） are investigated using finite element method （FEM）. While the open literature is limited mainly to the studies of orthogonal sequential cutting with the constant uncut chip thickness greater than 0.01 mm, it is suggested herein to investigate not only the variable uncut chip thickness which characterises the down milling process, but also the uncut chip thickness in the sub-micron range using a finite cutting edge radius. For the resulting ductile machining regime, the characteristics of the chip mor- phology, the force profiles, the plastic deformation and temperature distributions have been analyzed. Furthermore, this study revealed that the RS should be extracted toward the area where the insert exits the workpiece in the FE simulation of the down-milling process. The simulation of a number of sequential cuts due to the consecutive engagements of the insert is required in order to capture the gradual accumulation of the RS before reaching an asymptotic convergence of the RS profile. The predicted RS are in reasonable agreement with the experimental results.