Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials

In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established.

EPSILON-ALGORITHM AND ETA-ALGORITHM OF GENERALIZED INVERSE FUNCTION-VALUED PAD APPROXIMANTS USING FOR SOLUTION OF INTEGRAL EQUATIONS

Two efficient recursive algorithms epsilon_algorithm and eta_algorithm are introduced to compute the generalized inverse function_valued Padé approximants. The approximants were used to accelerate the convergence of the power series with function_valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identities of the Pad approximants is also established by means of the connection of two algorithms.

Adomian decomposition method and Padé approximants for solving the Blaszak-Marciniak lattice

The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.

Approximation of thermoelasticity contact problem with nonmonotone friction

The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a nonmonotone and multivalued law. The coupling effect of the problem is neglected. Therefore, the thermic part of the problem is considered independently on the elasticity problem. For the displacement vector, we formulate one substationary problem for a non-convex, locally Lipschitz continuous functional representing the total potential energy of the body. All problems formulated in the paper are approximated with the finite element method.

Adomian Decomposition Method and Padé Approximants for Nonlinear Differential-Difference Equations

Combining Adomian decomposition method （ADM） with Pade approximants, we solve two differentiaidifference equations （DDEs）： the relativistic Toda lattice equation and the modified Volterra lattice equation. With the help of symbolic computation Maple, the results obtained by ADM-Pade technique are compared with those obtained by using ADM alone. The numerical results demonstrate that ADM-Pade technique give the approximate solution with faster convergence rate and higher accuracy and relative in larger domain of convergence than using ADM.

A Note on Pad Approximants Pairs as Limits of Algebraic Polynomials Pairs of Weighted Best Approximation in Orlicz Spaces

In this short note, we show the behavior in Orlicz spaces of best approximations by algebraic polynomials pairs on union of neighborhoods, when the measure of them tends to zero.

COMPUTATION FORMULAS OF GENERALIZED INVERSE PAD APPROXIMANTS USING FOR SOLUTION OF INTEGRAL EQUATIONS

For the generalized inverse function-valued Pade approximants, its intact computation formulas are given. The explicit determinantal formulas for the denominator scalar polynomials and the numerator function-valued polynomials are first established. A useful existence condition is given by means of determinant form.

Parabolic Approximation of the Weakly Nonlinear Mild Slope Equation with Bottom Friction

This paper presents a refined parabolic approximation model of the mild slope equation to simulate the combination of water wave refraction and diffraction in the large coastal region. The bottom friction and weakly nonlinear term are included in the model. The difference equation is established with the Crank-Nicolson scheme. The numerical test shows that some numerical prediction results will be inaccurate in complicated topography without considering weak nonlinearity; the bottom friction will make wave height damping and it can not be neglected for calculation of wave field in large areas.

Distribution of Points of Interpolation and of Zeros of Exactly Maximally Convergent Multipoint PadéApproximants

Given a regular compact set E in , a unit measure μ supported by , a triangular point set , and a function f , holomorphic on E , let πβ,fn,m be the associated multipoint β-Padé approximant of order (n,m) . We show that if the sequence πβ,fn,m , n∈Λ , ∧∈n,k are uniformly distributed on with respect to u as n∈Λ . Furthermore, a result about the behavior of the zeros of the exact maximally convergent sequence Λ is provided, under the condition that Λ is “dense enough”.

Anomalous{1012}tensile twinning and subsequent detwinning in a friction stir processed carbon fiber-reinforced Mg composite

1.Main text Owing to their low density and high specific strength,magnesium alloys and magnesium-based composites have great potential as structure metal materials in applications where lightweight matters[1–4].Deformation twins[5],especially the{1012}tension twins(also called tensile or extension twins)with a low critical resolved shear stress(CRSS)[6],are commonly observed in Mg alloys.They can provide the much-needed deformation along the c-axis in their hcp structure resulting from the very few easily activated slip systems in this crystal structure[7].The tensile twinning activation usually follows the macroscopic Schmid factor law[2],i.e.,the twin variant with the highest Schmid factor occurs,and it only appears when its Schmid factor is positive.

A review of linear friction welding of Ni -based superalloys

Ni-based superalloys are one of the most important materials employed in high-temperature applications within the aerospace and nuclear energy industries and in gas turbines due to their excellent corrosion,radiation,fatigue resistance,and high-temperature strength.Linear friction welding(LFW)is a new joining technology with near-net-forming characteristics that can be used for the manu-facture and repair of a wide range of aerospace components.This paper reviews published works on LFW of Ni-based superalloys with the aim of understanding the characteristics of frictional heat generation and extrusion deformation,microstructures,mechanical proper-ties,flash morphology,residual stresses,creep,and fatigue of Ni-based superalloy weldments produced with LFW to enable future optim-um utilization of the LFW process.

Effects of friction stir processing and nano-hydroxyapatite on the microstructure,hardness,degradation rate and in-vitro bioactivity of WE43 alloy for biomedical applications

Nowadays,magnesium alloys are emerging in biomedical implants for their similar properties to natural bones.However,the rapid degradation of magnesium alloys in biological media hinders successful implantation.Refinement of microstructure,as well as reinforcement particles can significantly improve the degradation rate.In this work,multi-pass friction stir processing(FSP)was proposed to synthesize WE43/nano-hydroxyapatite(n HA)surface composite,the microstructure,reinforced particle distribution,micro-hardness,corrosion behavior and in-vitro bioactivity were studied.The subsequent FSP passes of WE43 alloy and WE43/n HA composite refined the grain size which was reduced by 94.29%and 95.92%(2.63 and 1.88μm,respectively)compared to base metal after three passes.This resulted in increasing the microhardness by 120%(90.86 HV0.1)and 135%(105.59 HV0.1)for the WE43 and WE43-n HA,respectively.It is found that increasing FSP passes improved the uniform distribution of n HA particles within the composite matrix which led to improved corrosion resistance and less degradation rate.The corrosion rate of the FSPed WE43/n HA composite after three passes was reduced by 38.2%(4.13 mm/year)and the degradation rate was reduced by 69.7%(2.87 mm/y).This is attributed to secondary phase(Mg24Y5and Mg41Nd5)particle fragmentation and redistribution,as well as a homogeneous distribution of n HA.Additionally,the growing Ca-P and Mg(OH)2layer formed on the surface represented a protective layer that reduced the degradation rate.The wettability test revealed a relatively hydrophilic surface with water contact angle of 49.1±2.2°compared to 71.2±2.1°for base metal.Also,biomineralization test showed that apatite layer grew after immersion 7d in simulated body fluid with atomic ratio of Ca/P 1.60 approaching the stoichiometric ratio(1.67)indicating superior bioactivity of FSPed WE43/n HA composite after three passes.These results raise that the grain refinement by FSP and introduction of n HA particles significantly improved the degradation rate and in-vitro bioactivity of WE43 alloy for biomedical applications.

A new insight into LPSO phase transformation and mechanical properties uniformity of large-scale Mg-Gd-Y-Zn-Zr alloy prepared by multi-pass friction stir processing

A large-scale fine-grained Mg-Gd-Y-Zn-Zr alloy plate with high strength and ductility was successfully prepared by multi-pass friction stir processing(MFSP)technology in this work.The structure of grains and long period stacking ordered(LPSO)phase were characterized,and the mechanical properties uniformity was investigated.Moreover,a quantitative relationship between the microstructure and tensile yield strength was established.The results showed that the grains in the processed zone(PZ)and interfacial zone(IZ)were refined from 50μm to 3μm and 4μm,respectively,and numerous original LPSO phases were broken.In IZ,some block-shaped 18R LPSO phases were transformed into needle-like 14H LPSO phases due to stacking faults and the short-range diffusion of solute atoms.The severe shear deformation in the form of kinetic energy caused profuse stacking fault to be generated and move rapidly,greatly increasing the transformation rate of LPSO phase.After MFSP,the ultimate tensile strength,yield strength and elongation to failure of the large-scale plate were 367 MPa,305 MPa and 18.0% respectively.Grain refinement and LPSO phase strengthening were the major strengthening mechanisms for the MFSP sample.In particularly,the strength of IZ was comparable to that of PZ because the strength contribution of the 14H LPSO phase offsets the lack of grain refinement strengthening in IZ.This result opposes the widely accepted notion that IZ is a weak region in MFSP-prepared large-scale fine-grained plate.

APPROXIMATE ANALYTICAL SOLUTION OF THE SELF-EXCITED VIBRATION OF PIECEWISE-SMOOTH SYSTEMS INDUCED BY DRY FRICTION——The Vibration Mechanism of the Chinese Cultural Relic Dragon Washbasin

Based on our previous work, a mathematical model of piecewise-smooth systems is established by means of phase-plane orbit analysis, and it is then used to study the intersting phenomena of Chinese cultural relic Dragon Washbasin. The mechanism of nonlinear damping is analyzed; the approximate analytical solution of self-excited vibration of piecewise-smooth nonlinear systems induced by dry friction is derived by means of KB Method, the results of which agree well with that of the numerical solution. Therefore, the method presented in this paper is proved to be very efficient in analyzing the self-excited vibration of piecewise-smooth systems induced by dry friction.

Low-Rank Positive Approximants of Symmetric Matrices

Given a symmetric matrix X, we consider the problem of finding a low-rank positive approximant of X. That is, a symmetric positive semidefinite matrix, S, whose rank is smaller than a given positive integer, , which is nearest to X in a certain matrix norm. The problem is first solved with regard to four common norms: The Frobenius norm, the Schatten p-norm, the trace norm, and the spectral norm. Then the solution is extended to any unitarily invariant matrix norm. The proof is based on a subtle combination of Ky Fan dominance theorem, a modified pinching principle, and Mirsky minimum-norm theorem.

A New Class of Vector PadéApproximants in the Asymptotic Numerical Method: Application in Nonlinear 2D Elasticity

The Asymptotic Numerical Method (ANM) is a family of algorithms for path following problems, where each step is based on the computation of truncated vector series [1]. The Vector Padé approximants were introduced in the ANM to improve the domain of validity of vector series and to reduce the number of steps needed to obtain the entire solution path [1,2]. In this paper and in the framework of the ANM, we define and build a new type of Vector Padé approximant from a truncated vector series by extending the definition of the Padé approximant of a scalar series without any orthonormalization procedure. By this way, we define a new class of Vector Padé approximants which can be used to extend the domain of validity in the ANM algorithms. There is a connection between this type of Vector Padé approximant and Vector Padé type approximant introduced in [3, 4]. We show also that the Vector Padé approximants introduced in the previous works [1,2], are special cases of this class. Applications in 2D nonlinear elasticity are presented.

Predicting the friction angle of clays using a multi-layer perceptron neural network enhanced by yeo-johnson transformation and coral reefs optimization

The accurate prediction of the friction angle of clays is crucial for assessing slope stability in engineering applications.This study addresses the importance of estimating the friction angle and presents the development of four soft computing models:YJ-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and YJCSA-MLPnet.First of all,the Yeo-Johnson(YJ)transformation technique was used to stabilize the variance of data and make it more suitable for parametric statistical models that assume normality and equal variances.This technique is expected to improve the accuracy of friction angle prediction models.The friction angle prediction models then utilized multi-layer perceptron neural networks(MLPnet)and metaheuristic optimization algorithms to further enhance performance,including flower pollination algorithm(FPA),coral reefs optimization(CRO),ant colony optimization continuous(ACOC),and cuckoo search algorithm(CSA).The prediction models without the YJ technique,i.e.FPA-MLPnet,CRO-MLPnet,ACOC-MLPnet,and CSA-MLPnet,were then compared to those with the YJ technique,i.e.YJ-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and YJ-CSA-MLPnet.Among these,the YJ-CRO-MLPnet model demonstrated superior reliability,achieving an accuracy of up to 83%in predicting the friction angle of clay in practical engineering scenarios.This improvement is significant,as it represents an increase from 1.3%to approximately 20%compared to the models that did not utilize the YJ transformation technique.

PADE APPROXIMANTS AS LIMITS OF RATIONAL FUNCTIONS OF BEST APPROXIMATION IN ORLICZ SPACE

In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.

A novel method for simulating nuclear explosion with chemical explosion to form an approximate plane wave: Field test and numerical simulation

A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in nuclear explosion power,underground protection engineering enabled by explosion-proof impact theory and technology ushered in a new challenge.This paper proposes to simulate nuclear explosion tests with on-site chemical explosion tests in the form of multi-hole explosions.First,the mechanism of using multi-hole simultaneous blasting to simulate a nuclear explosion to generate approximate plane waves was analyzed.The plane pressure curve at the vault of the underground protective tunnel under the action of the multi-hole simultaneous blasting was then obtained using the impact test in the rock mass at the site.According to the peak pressure at the vault plane,it was divided into three regions:the stress superposition region,the superposition region after surface reflection,and the approximate plane stress wave zone.A numerical simulation approach was developed using PFC and FLAC to study the peak particle velocity in the surrounding rock of the underground protective cave under the action of multi-hole blasting.The time-history curves of pressure and peak pressure partition obtained by the on-site multi-hole simultaneous blasting test and numerical simulation were compared and analyzed,to verify the correctness and rationality of the formation of an approximate plane wave in the simulated nuclear explosion.This comparison and analysis also provided a theoretical foundation and some research ideas for the ensuing study on the impact of a nuclear explosion.

Prediction of corrosion rate for friction stir processed WE43 alloy by combining PSO-based virtual sample generation and machine learning

The corrosion rate is a crucial factor that impacts the longevity of materials in different applications.After undergoing friction stir processing(FSP),the refined grain structure leads to a notable decrease in corrosion rate.However,a better understanding of the correlation between the FSP process parameters and the corrosion rate is still lacking.The current study used machine learning to establish the relationship between the corrosion rate and FSP process parameters(rotational speed,traverse speed,and shoulder diameter)for WE43 alloy.The Taguchi L27 design of experiments was used for the experimental analysis.In addition,synthetic data was generated using particle swarm optimization for virtual sample generation(VSG).The application of VSG has led to an increase in the prediction accuracy of machine learning models.A sensitivity analysis was performed using Shapley Additive Explanations to determine the key factors affecting the corrosion rate.The shoulder diameter had a significant impact in comparison to the traverse speed.A graphical user interface(GUI)has been created to predict the corrosion rate using the identified factors.This study focuses on the WE43 alloy,but its findings can also be used to predict the corrosion rate of other magnesium alloys.