Transient response of enstrophy transport to opposition control in turbulent channel flow

The transient response of the turbulent enstrophy transport to opposition control in the turbulent channel flow is studied with the aid of direct numerical simulation. It is found that the streamwise enstrophy and the spanwise enstrophy are suppressed by the attenuation of the stretching terms at first, while the vertical enstrophy is reduced by inhibiting the tilt of the mean shear. In the initial period of the control, the streamwise enstrophy evolves much slower than the other two components. The vertical vorticity component exhibits a rapid monotonic decrease and also plays an important role in the attenuation of the other two components.

Exact solutions for axisymmetric flexural free vibrations of inhomogeneous circular Mindlin plates with variable thickness

Circular plates with radially varying thickness, stiffness, and density are widely used for the structural optimization in engineering. The axisymmetric flexural free vibration of such plates, governed by coupled differential equations with variable coefficients by use of the Mindlin plate theory, is very difficult to be studied analytically. In this paper, a novel analytical method is proposed to reduce such governing equations for circular plates to a pair of uncoupled and easily solvable differential equations of the Sturm-Liouville type. There are two important parameters in the reduced equations. One describes the radial variations of the translational inertia and fiexural rigidity with the consideration of the effect of Poisson＇s ratio. The other reflects the comprehensive effect of the rotatory inertia and shear deformation. The Heun-type equations, recently well-known in physics, are introduced here to solve the flexural free vibration of circular plates analytically, and two basic differential formulae for the local Heun-type functions are discovered for the first time, which will be of great value in enriching the theory of Heun-type differential equations.

Fractal growth kinematics abstracted from snowflakes:topological evolution

Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the proportional movement transformation groups, necessary and sufficient conditions for self-similarity of multilevel structures are presented. The characteristic topology of snowflake-like fractal patterns, identical to the topology of ternary-segment fractal line, is proved. Moreover, the topological evolution of N-segment line is explored. The concepts of limit growth and infinite growth are clarified,and the corresponding growth conditions are derived. The topological invariant properties of N-segment line are exposed. In addition, the proposition that the topological evolution of the N-segment line is mainly controlled by the topological invariant N is verified.

Optimal transient growth in turbulent pipe flow

The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the governing equations onto the sub- space spanned by the radial vorticity and radial velocity. The method is validated by comparing with the previous studies. Two peaks of the maximum transient growth am- plification curve are found at different Reynolds numbers ranging from 20 000 to 250 000. The optimal flow structures are obtained and compared with the experiments and DNS results. The location of the outer peak is at the azimuthal wave number n = 1, while the location of the inner peak is varying with the Reynolds number. It is observed that the velocity streaks in the buffer layer with a spacing of 100δv are the most amplified flow structures. Finally, we consider the optimal transient growth time and its dependence on the azimuthal wave length. It shows a self-similar behavior for perturbations of different scales in the optimal transient growth process.

An improved time integration scheme based on uniform cubic B-splines and its application in structural dynamics

A time integration algorithm for structural dynamic analysis is proposed by uniform cubic B-spline functions. The proposed algorithm is successfully used to solve the dynamic response of a single degree of freedom （SDOF） system, and then is generalized for a multiple-degree of freedom （MDOF） system. Stability analysis shows that, with an adjustable algorithmic parameter, the proposed method can achieve both conditional and unconditional stabilities. Validity of the method is shown with four numerical simulations. Comparison between the proposed method and other methods shows that the proposed method possesses high computation accuracy and desirable computation efficiency.

Simulation of residual stresses and their effects on thermal barrier coating systems using finite element method

Thermal barrier coating(TBC)systems are widely used in industrial gas-turbine engines.However,premature failures have impaired the use of TBCs and cut down their lifetime,which requires a better understanding of their failure mechanisms.In the present study,experimental studies of isothermal cycling are firstly carried out with the observation and estimation of microstructures.According to the experimental results,a finite element model is established for the analysis of stress perpendicular to the TBC/BC interface.Detailed residual stress distributions in TBC are obtained to reflect the influence of mechanical properties,oxidation,and interfacial roughness.The calculated results show that the maximum tensile stress concentration appears at the peak of TBC and continues to increase with thermal cycles.Because of the microstructural characteristics of plasma-sprayed TBCs,cracks initialize in tensile stress concentration(TSC)regions at the peaks of TBC and propagate along the TBC/BC interface resulting in the spallation of TBC.Also,the inclusion of creep is crucial to failure prediction and is more important than the inclusion of sintering in the simulation.

Design theory and dynamic mechanical characterization of the deployable composite tube hinge

This paper presents a design theory and dynamic mechanical characterizations of the composite tape-spring hinge made by two parallel single tape springs.First,the theoretical models of moment-rotation angle on anisotropy tape springs with antisymmetric laminates are proposed.Second,the relationships of moment-rotation angle for tape-spring hinges with different sizes are simulated and analyzed by means of the finite element method (FEM),which is in good agreement with the results from theoretical predictions.Finally,the dynamic vibration analysis for deployable composite tube hinges with different dampings is done during the process of deployment.

Comparison of the very high cycle fatigue behaviors of INCONEL 718 with different loading frequencies

In order to clarify the differences of very high cycle fatigue(VHCF) behavior of nickel based superalloy IN718 with different loading frequencies,stress-controlled fatigue tests were carried out by using ultrasonic testing method(20 KHz) and rotary bending testing method(52.5 Hz),both at room temperatures,to establish stress versus cycles to failure(S-N) relationships.Results disclosed that cycles to failure at a given stress level increased with an increase of the applied frequency,i.e.,the higher frequency produced an upper shift of the S-N curves.Fractographic analysis suggested that crack initiation and propagation behaviors had large differences:cracks in low-frequency tests preferentially initiated from multiple sources on the specimen surface,while in high-frequency tests,cracks mostly originated from a unique source of subsurface inclusions.Subsequently,frequency-involved modeling was proposed,based on the damage accumulation theory,which could well illustrate qualitatively those comparisons due to different loading frequencies.

A continuum theory of surface piezoelectricity for nanodielectrics

In this paper,a phenomenological continuum theory of surface piezoelectricity accounting for the linear superficial interplay between electricity and elasticity is formulated primarily for elastic dielectric materials.This theory is inspired by the physical idea that once completely relaxed,an insulating free dielectric surface will sustain a nontrivial spontaneous surface polarization in the normal direction together with a tangential self-equilibrated residual surface stress field.Under external loadings,the surface Helmholtz free energy density is identified as the characteristic function of such surfaces,with the in-plane strain tensor of surface and the surface free charge density as the independent state variables.New boundary conditions governing the surface piezoelectricity are derived through the variational method.The resulting concepts of charge-dependent surface stress and deformationdependent surface electric field reflect the linear electromechanical coupling behavior of nanodielectric surfaces.As an illustrative example,an infinite radially polarizable piezoelectric nanotube with both inner and outer surfaces grounded is investigated.The novel phenomenon of possible surface-induced polarity inversion is predicted for thin enough nanotubes.

Experimental investigation of the thermally induced vibration of a space boom section

Thermally induced vibration(TIV)is a typical failure of large-scale space structures.This paper reports a laboratory experiment that aims to investigate this unusual structural behavior of complex engineering structures.With the help of a Fourier finite element program,the fixing of a space boom section is well designed so that the TIV can be successfully observed.Although the observed torsional vibration mode is different from the bending vibration mode predicted by the classic theory based on a simple beam model,it can be successfully explained by the general thermal structural interaction theory.This demonstrates the validity of the theoretical model and the necessity of using finite element program to analyze complex engineering structures.

Study on the mechanical behavior of adhesive interface by digital image correlation

The shear modulus of the adhesive layer and the failure mode of adhesive structure on single lap joint specimens under tensile tests are investigated in this paper.The aluminum-aluminum adherends are bonded by two different adhesives:polydimethylsiloxane (PDMS) and epoxy.The full deformation fields are measured using the digital image correlation (DIC) method with the images on the middle part of the adhesive layer recorded by a high resolution microscope.Then,the shear modulus values of the two adhesives are calculated with a simple pure shear strain model.A numerical model is proposed to simulate the single lap joint structure under tensile load in comparison with the experimental results.The results show that this method can successfully estimate the shear modulus of the adhesive layer.The failure behavior of epoxy adhesive/adherend interface is also analyzed and discussed.

High-temperature fatigue crack propagation study of superalloy GH4169 by single-lens 3D digital image correlation

The characterization of fatigue crack propagation behavior is crucial for performance and reliability evaluation of aerospace materials.In this study,high-temperature(maximum:650℃)fatigue crack propagation experiments of Ni-based superalloy GH4169 were conducted.The bi-prism-based single-lens 3D digital image correlation(BSL 3D DIC)technique was used to insitu measure the displacement and strain fields near fatigue crack tip.Based on the deformation information,the modeΙstress intensity factor range△K and the crack opening displacement(COD)were determined for characterizing the crack closure effect.As the major fatigue crack growth model,the parameters of modified Paris’law were obtained based on the effective stress intensity factor range△Keff and the fatigue crack propagation rate(FCPR).Additionally,two kinds of J integrals,JP(path integral method)and JK(stress intensity factor K method),were used to evaluate the small-scale yielding approximation.

Study of the location of testing area in residual stress measurement by Moiré interferometry combined with hole-drilling method

This paper investigates the effect of the location of testing area in residual stress measurement by Moiréinterferometry combined with hole-drilling method.The selection of the location of the testing area is analyzed from theory and experiment.In the theoretical study,the factors which affect the surface released radial strainεr were analyzed on the basis of the formulae of the hole-drilling method,and the relations between those factors andεr were established.By combining Moiréinterferometry with the hole-drilling method,the residual stress of interference-fit specimen was measured to verify the theoretical analysis.According to the analysis results,the testing area for minimizing the error of strain measurement is determined.Moreover,if the orientation of the maximum principal stress is known,the value of strain will be measured with higher precision by the Moiréinterferometry method.

Determination of mixed-mode interfacial fracture toughness for thermal barrier coatings

In this work,a test method was developed to determine the interfacial fracture toughness of the air plasma sprayed (APS) thermal barrier coatings (TBCs) over a wide range of mode mixities.For this mixed-mode test method,the analytical expressions for the energy release rate and stress intensity factors were derived based on the energy theory and the concept of "equivalence".The fidelity of these expressions was affirmed by selected finite element analysis.The experimental results showed that the critical energy release rate increased with the increase of the positive mode mixity,which was mainly due to the increase in contact/friction effect and plastic work dissipation with increasing shear mode loading.Furthermore,an elliptical interfacial failure criterion in terms of the stress intensity factors was proposed.The agreement between the experimental results in the literature and those in our work indicated that our test method and the corresponding analytical solutions can well determine the interfacial fracture toughness of the TBCs over a wide range of mode mixities.

Determination of residual stress distribution combining slot milling method and finite element approach

Residual stress plays a vital role in the structural strength and stability. The determination of residual stress at single-point has become mature at present. However, the method to determine residual stress distribution is still in shortage. For this problem, a finite element approach combined with slot milling method was developed in this study. In the method, firstly a slot is milled on the specimen surface to release the residual stress and then the released displacement field is measured by optical method, such as digital image correlation(DIG), finally the finite element approach is used to determine the residual stress distribution along the slot. In order to verify the feasibility of the method, it was applied to study the residual stress introduced by shot peening,mainly about the stress distribution along the direction vertical to the shot peened surface. Since the influence depth of shot peening was too small, we utilized focused ion beam(FIB) to determine the microscale residual stress distribution. The result measured by X-ray diffraction(XRD) demonstrated that the method was feasible to determine the residual stress distribution.

Analyses of mechanically-assembled 3D spiral mesostructures with applications as tunable inductors

Mechanically-guided assembly allows the formation of 3D spiral-shaped inductors through controlled buckling, which could provide an increased quality(Q) factor and broadened working angle in near field communication, as compared to the planar design. An understanding of the microstructure-property relationship is essential in the design optimization of the assembly process. This work presents a theoretical model to analyze the deformations during the assembly of the 3D spiral-shaped mesostructure from a bilayer precursor that consists of a supporting ribbon and a 2D coil on its top. As validated by both the experiments and finite element analyses(FEA), this mechanics model allows accurate predictions of the assembled 3D configurations. In combination of electromagnetic simulations, we investigated the effects of various key design parameters on the final 3D configuration and the Q factor when operated as an inductor. The results suggest a significant role of the gravity effect on the assembled spiral configuration, especially for flexible coil designs with relative small cross-sectional areas or long wires.This study can serve as a reference for the design of spiral-shaped 3D inductors in different device applications.

3D optical measurement of relative displacement for the tuberosities in the shoulder prosthesis

In this paper,a binocular 3-D computer vision measurement system is used to measure the relative displacement for the greater and lesser tuberosities in the shoulder prosthesis.The basic principles of binocular optical measurement are introduced in detail,and the loading apparatus is designed for external rotation and anteflexion of the shoulder prosthesis.Both the motion of external rotation and anteflexion of the shoulder are measured,and the corresponding displacement values for the greater and lesser tuberosities are extracted.These results will play an important role in evaluating the stability of humeral tuberosity in the shoulder prosthesis.

An inverse approach to identifying the in vivo material parameters of female pelvic floor muscles using MRI data

Dear Editor,Pelvic floor(PF)dysfunctions comprise of a wide spectrum of interrelated clinical conditions and represent an important health problem.The PF supporting system can be regarded as a loaded structure with a complex geometry that supports the increase of abdominal pressure and maintain normal position of pelvic organs(Figure 1A).The weakening of the PF supporting system is considered to be the cause of

A 2-D mesoscopic model for the evaluation of creep damage induced by void growth in polycrystalline metals

At elevated temperature, creep failures of polycrystalline metals after long-term constant loading are often caused by the nucleation, growth and coalescence of creep voids on the grain boundaries. Void h＇action is an important parameter for the evaluation of creep damage level of structural materials operating at high temperature. In this paper, a 2-D numerical simulation method was developed for analyzing the void fraction evolution during the process of creep, based on some hypothesis from experiments. The model was implemented and then was used to predict the evolution of void fraction in the 2.25Cr-1Mo steel of uniaxial creep experiment at 570 ℃, in which the simulation results showed good agreement with the experimental results.

The form-invariance of wave equations without requiring a priori relations between field variables

According to the principle of relativity,the equations describing the laws of physics should have the same forms in all admissible frames of reference,i.e.,form-invariance is an intrinsic property of correct wave equations.However,so far in the design of metamaterials by transformation methods,the form-invariance is always proved by using certain relations between field variables before and after coordinate transformation.The main contribution of this paper is to give general proofs of form-invariance of electromagnetic,sound and elastic wave equations in the global Cartesian coordinate system without using any assumption of the relation between field variables.The results show that electromagnetic wave equations and sound wave equations are intrinsically form-invariant,but traditional elastodynamic equations are not.As a by-product,one can naturally obtain new elastodynamic equations in the time domain that are locally accurate to describe the elastic wave propagation in inhomogeneous media.The validity of these new equations is demonstrated by some numerical simulations of a perfect elastic wave rotator and an approximate elastic wave cloak.These findings are important for solving inverse scattering problems in many fields such as seismology,nondestructive evaluation and metamaterials.