Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.

Methodology for local correction of the heights of global geoid models to improve the accuracy of GNSS leveling

At present,one of the methods used to determine the height of points on the Earth’s surface is Global Navigation Satellite System(GNSS)leveling.It is possible to determine the orthometric or normal height by this method only if there is a geoid or quasi-geoid height model available.This paper proposes the methodology for local correction of the heights of high-order global geoid models such as EGM08,EIGEN-6C4,GECO,and XGM2019e_2159.This methodology was tested in different areas of the research field,covering various relief forms.The dependence of the change in corrected height accuracy on the input data was analyzed,and the correction was also conducted for model heights in three tidal systems:"tide free","mean tide",and"zero tide".The results show that the heights of EIGEN-6C4 model can be corrected with an accuracy of up to 1 cm for flat and foothill terrains with the dimensionality of 1°×1°,2°×2°,and 3°×3°.The EGM08 model presents an almost identical result.The EIGEN-6C4 model is best suited for mountainous relief and provides an accuracy of 1.5 cm on the 1°×1°area.The height correction accuracy of GECO and XGM2019e_2159 models is slightly poor,which has fuzziness in terms of numerical fluctuation.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Domain-based noise removal method using fourth-order partial differential equation

Due to the fact that the fourth-order partial differential equation （PDE） for noise removal can provide a good trade-off between noise removal and edge preservation and avoid blocky effects often caused by the second-order PDE, a domain-based fourth-order PDE method for noise removal is proposed. First, the proposed method segments the image domain into two domains, a speckle domain and a non-speckle domain, based on the statistical properties of isolated speckles in the Laplacian domain. Then, depending on the domain type, different conductance coefficients in the proposed fourth-order PDE are adopted. Moreover, the frequency approach is used to determine the optimum iteration stopping time. Compared with the existing fourth-order PDEs, the proposed fourth-order PDE can remove isolated speckles and keeps the edges from being blurred. Experimental results show the effectiveness of the proposed method.

Coseismic vertical deformation of the M_S8.0 Wenchuan earthquake from repeated levelings and its constraint on listric fault geometry

The devastating Ms8.0 Wenchuan earthquake ruptured two large parallel thrust faults along the middle segment of the Longmenshan thrust belt. Preseismic and postseismic leveling data indicated the hanging wall of the Yingxiu-Beichuan-Nanba thrust fault mainly presented coseismic uplift with respect to the reference point at Pingwu county town, and the observed maximum uplift of 4.7 m is located at Beichuan county （Qushan town） which is about 100 m west of the fault scarp. The foot wall of the Yingxiu-Beichuan-Nanba thrust fault mainly showed subsidence with maximum subsidence of 0.6 m near the rupture. By employing a listric dislocation model, we found that the fault geometry model of exponential dip angle δ=88°×[1-exp（-9/h）] with depth of 18 km and uniform thrust-slip of 5.6 m could fit the observed coseismic vertical deformation very well, which verifies the listric thrust model of the Longmenshan orogenic zone.

结合GPS/Leveling和正高改正确定GPS常年观测站正高

利用精密几何水准测量结合GPS/Leveling方法计算韩国行政自治部管辖内30所GPS常年观测站天线基准点的正高。并联合进行对水准点和GPS常年观测站偏心点的重力测量,使用正高改正方法计算出其改正量,提高正高的精确度。

Numerical Simulation of Continuous Tension Leveling Process of Thin Strip Steel and Its Application

Cold-rolled thin strip steel of high flatness quality undergoes multistage deformation during tension leveling. Thus, the parameters of set-up and manipulating are more difficult. With the aid of FE code MSC. MARC, the tension leveling process of thin strip steel was numerically simulated. Concentrating on the influence of the roll intermeshes in 2# anti-cambering on the distribution and magnitude of residual stresses in leveled strip steel, several experiments were clone with the tension leveler based on the results from the simulation. It was found from the simulation that the magnitude of longitudinal residual stresses in the cross-section of the leveled strip steel regularly presents obvious interdependence with the roll intermeshes in 2# anti-cambering. In addition, there is a steady zone as the longitudinal residual stresses of the surface layers in leveled strip steel vary with the roll intermeshes of 2# anticambering, which is of importance in the manipulation of tension levelers. It was also found that the distribution of strains and stresses across the width of strip steel is uneven during leveling or after removing the tension loaded upon the strip, from which it was found that 3D simulation could not be replaced by 2D analysis because 2D analysis in this case cannot represent the physical behavior of strip steel deformation during tension leveling.

Model for the Whole Roller Leveling Process of Plates with Random Curvature Distribution Based on the Curvature Integration Method

A model based on the curvature integration method has been applied in an online plate leveling system. However, there are some shortcomings in the current leveling models. On the one hand, the models cannot deal with the leveling process of plates with a random curvature distribution. On the other hand, the current models are suitable only for stable leveling processes and ignore the biting in and tailing out stages. This study presents a new plate-leveling model based on the curvature integration method, which can describe the leveling process of plates with random curvature distribution. Further, the model is solved in two cases in order to take the biting in and tailing out stages into consideration. The proposed model is evaluated by comparing with a plate leveling experiment. Finally, the leveling process of a plate with a wave bent is studied using the proposed model. It is found that the contact angles vary greatly during the biting in and tailing out stages. However, they are relatively steady during the 5 roller leveling stage. In addition, the contact angle of roller No. 2 is the smallest, which is close to 0. Roller leveling can effectively eliminate bending in the plate, but there are regions in the head and tail of the plate, where roller leveling is not effective. The non-leveling region length is about 2 times that of the roller space. This study proposes a quasi-static plate-leveling model, which makes it possible to analyze the dynamic straightening process using a curvature integration method. It also makes it possible to analyze the straightening process of a plate with random curvature distribution.

Fuzzy Sliding Mode Control for the Vehicle Height and Leveling Adjustment System of an Electronic Air Suspension

The accurate control for the vehicle height and leveling adjustment system of an electronic air suspension(EAS) still is a challenging problem that has not been effectively solved in prior researches. This paper proposes a new adaptive controller to control the vehicle height and to adjust the roll and pitch angles of the vehicle body(leveling control) during the vehicle height adjustment procedures by an EAS system. A nonlinear mechanism model of the full?car vehicle height adjustment system is established to reflect the system dynamic behaviors and to derive the system optimal control law. To deal with the nonlinear characters in the vehicle height and leveling adjustment processes, the nonlinear system model is globally linearized through the state feedback method. On this basis, a fuzzy sliding mode controller(FSMC) is designed to improve the control accuracy of the vehicle height adjustment and to reduce the peak values of the roll and pitch angles of the vehicle body. To verify the effectiveness of the proposed control method more accurately, the full?car EAS system model programmed using AMESim is also given. Then, the co?simulation study of the FSMC performance can be conducted. Finally, actual vehicle tests are performed with a city bus, and the test results illustrate that the vehicle height adjustment performance is effectively guaranteed by the FSMC, and the peak values of the roll and pitch angles of the vehicle body during the vehicle height adjustment procedures are also reduced significantly. This research proposes an effective control methodology for the vehicle height and leveling adjustment system of an EAS, which provides a favorable control performance for the system.

Present-day 3D deformation field of Northeast China,observed by GPS and leveling

A broad view of present-day 3D deformation field around the Northeast China region was derived from GPS and leveling observations. We draw the following conclusions： First, the Northeast China region moved towards northwest with an average velocity of 5 ram/a, with respect to South China. The entire Northeast China region was in a low strain state from the strain rate field. Second, we processed two periods of first- order leveling data in 1970s and 1990s, showing the vertical deformation of the Northeast China region is ＂uplift in western part and subsidence in eastern part＇

Research on Precise Trigonometric Leveling in Place of First Order Leveling

Through the analysis of the principle, error sources and precision of trigonometric leveling, this paper points out the key problems about first order leveling replaced by trigonometric leveling; and for the first time puts forward that, in some given conditions, it is not only feasible but also valuable to replace first order leveling by precise trigonometric leveling, and proves it by experimentation as well. The content and conclusion of this paper have consulting significance and practicable value for our setting down relational criterion and production practice.

Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative

Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.

An Efficient Technique for Finding the Eigenvalues of Fourth-Order Sturm-Liouville Problems

In this work, we present a computational method for solving eigenvalue problems of fourth-order ordinary differential equations which based on the use of Chebychev method. The efficiency of the method is demonstrated by three numerical examples. Comparison results with others will be presented.

Boundary determination of leveling capacity for plate roller leveler based on curvature integration method

Leveler is widely used to improve the quality of defective mild steel plates.Its typical ranges of the leveling capacity are constrained by three criteria,namely the maximum stroke of rollers,allowable total leveling force and motor power.In this work,an optimization model with equality and inequality constraints was built for the maximum yield stress search of each thickness of plates.The corresponding search procedure with three loops was given.The approximate range by the simplification model could be used as the initial value for the actual range search of the leveling capacity.Therefore,the search speed could be accelerated compared with a global search.The consistency of the analytical results and field data demonstrates the reliability of the proposed model and procedure.The typical ranges of the leveling capacity are expressed by several boundary curves which are helpful to judge whether the incoming plate can be leveled quickly or not.Also,these curves can be used to find the maximum yield stress for a specific thickness or the maximum thickness for a yield stress for plates.

A Fourth-order Covergence Newton-type Method

A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton＇s method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton and Newton-type methods. The results show that the proposed method has some more advantages than others. It enriches the methods to find the roots of non-linear equations and it is important in both theory and application.

POSITIVE SOLUTIONS OF FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Under suitable conditions on h(x) and f(u), the authors show that the following boundary value problem has at least one positive solution. Moreover, the authors also establish several existence theorems of multiple positive solutions.

Symmetry Reductions of Cauchy Problems for Fourth-Order Quasi-Linear Parabolic Equations

This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries （GCSs）. Complete group classification results are presented, and some examples are given to show the main reduction procedure.

Symmetry Reduction and Cauchy Problems for a Class of Fourth-Order Evolution Equations

We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations toCauchy problems for systems of ordinary differential equations (ODEs).We classify a class of fourth-order evolutionequations which admit certain higher-order generalized conditional symmetries (GCSs) and give some examples to showthe main reduction procedure.These reductions cannot be derived within the framework of the standard Lie approach,which hints that the technique presented here is something essential for the dimensional reduction of evolu tion equations.

Adiabatic Shear Localization for Steels Based on Johnson-Cook Model and Second-and Fourth-Order Gradient Plasticity Models

To consider the effects of the interactions and interplay among microstructures, gradient-dependent models of second- and fourth-order are included in the widely used phenomenological Johnson-Cook model where the effects of strain-hardening, strain rate sensitivity, and thermal-softening are successfully described. The various parameters for 1006 steel, 4340 steel and S-7 tool steel are assigned. The distributions and evolutions of the local plastic shear strain and deformation in adiabatic shear band （ASB） are predicted. The calculated results of the second- and fourth- order gradient plasticity models are compared. S-7 tool steel possesses the steepest profile of local plastic shear strain in ASB, whereas 1006 steel has the least profile. The peak local plastic shear strain in ASB for S-7 tool steel is slightly higher than that for 4340 steel and is higher than that for 1006 steel. The extent of the nonlinear distribution of the local plastic shear deformation in ASB is more apparent for the S-7 tool steel, whereas it is the least apparent for 1006 steel. In fourth-order gradient plasticity model, the profile of the local plastic shear strain in the middle of ASB has a pronounced plateau whose width decreases with increasing average plastic shear strain, leading to a shrink of the portion of linear distribution of the profile of the local plastic shear deformation. When compared with the sec- ond-order gradient plasticity model, the fourth-order gradient plasticity model shows a lower peak local plastic shear strain in ASB and a higher magnitude of plastic shear deformation at the top or base of ASB, which is due to wider ASB. The present numerical results of the second- and fourth-order gradient plasticity models are consistent with the previous numerical and experimental results at least qualitatively.

Superlinear Fourth-order Elliptic Problem without Ambrosetti and Rabinowitz Growth Condition

This paper deals with superlinear fourth-order elliptic problem under Navier boundary condition. By using the mountain pass theorem and suitable truncation, a multiplicity result is established for all λ〉 0 and some previous result is extended.