Investigation of high-quality-factor aluminum nitride MEMS cantilever resonators

This paper presents the design,fabrication,and characterization of cantilever-type resonators with a novel stacked structure.Aluminum nitride is adopted as the material for both the structural layer and the piezoelectric layer;this simplifies the fabrication process and improves the quality factor of the resonator.Both in-plane and out-of-planeflexural modes were investigated.The effect of the structural dimensions and electrode patterns on the resonator’s performance were also studied.Finite-element simulations and experiments examining anchor loss and thermoelastic damping,which are the main loss mechanisms affecting the quality factor of these resonators,were carried out.The optimal structural dimensions and electrode patterns of the cantilever-type resonators are presented.A quality factor of 7922 with a motional impedance of 88.52 kΩand a quality factor of 8851 with a motional impedance of 67.03 kΩwere achieved for the in-plane and out-of-planeflexural-mode resonators,respectively.The proposed resonator design will contribute to the development of high-performance devices such as accelerometers,gyroscopes,and pressure sensors.

Limit state analysis of rigid retaining structures against seismically induced passive failure in heterogeneous soils

Soils are not necessarily uniform and may present linearly varied or layered characteristics,for example the backfilled soils behind rigid retaining walls.In the presence of large lateral thrust imposed by arch bridge,passive soil failure is possible.A reliable prediction of passive earth pressure for the design of such wall is challenging in complicated soil strata,when adopting the conventional limit analysis method.In order to overcome the challenge for generating a kinematically admissible velocity field and a statically allowable stress field,finite element method is incorporated into limit analysis,forming finiteelement upper-bound(FEUB)and finite-element lower-bound(FELB)methods.Pseudo-static,original and modified pseudo-dynamic approaches are adopted to represent seismic acceleration inputs.After generating feasible velocity and stress fields within discretized elements based on specific criteria,FEUB and FELB formulations of seismic passive earth pressure(coefficient K_(P))can be derived from work rate balance equation and stress equilibrium.Resorting to an interior point algorithm,optimal upper and lower bound solutions are obtained.The proposed FEUB and FELB procedures are well validated by limit equilibrium as well as lower-bound and kinematic analyses.Parametric studies are carried out to investigate the effects of influential factors on seismic K_(P).Notably,true solution of K_(P) is well estimated based on less than 5%difference between FEUB and FELB solutions under such complex scenarios.

Solution of shallow-water equations using least-squares finite-element method

A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.

Least-squares finite-element method for shallow-water equations with source terms

Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.

Finite-element 3D modeling of stress patterns around a dipping fault

Stresses in a block around a dipping fracture simulating a damage zone of a fault are reconstructed by finite-element modeling. A fracture corresponding to a fault of different lengths, with its plane dipping at different angles, is assumed to follow a lithological interface and to experience either compression or shear. The stress associated with the destruction shows an asymmetrical pattern with different distances from the highest stress sites to the fault plane in the hanging and foot walls. As the dip angle decreases,the high-stress zone becomes wider in the hanging wall but its width changes negligibly in the foot wall.The length of the simulated fault and the deformation type affect only the magnitude of maximum stress,which remains asymmetrical relative to the fault plane. The Lh/Lfratio, where Lhand Lfare the widths of high-stress zones in the hanging and foot walls of the fault, respectively, is inversely proportional to the fault plane dip. The arithmetic mean of this ratio over different fault lengths in fractures subject to compression changes from 0.29 at a dip of 80°to 1.67 at 30°. In the case of shift displacement, ratios are increasing to 1.2 and 2.94, respectively.Usually they consider vertical fault planes and symmetry in a damage zone of faults. Following that assumption may cause errors in reconstructions of stress and fault patterns in areas of complex structural setting. According geological data, we know the structures are different and asymmetric in hanging and foot walls of fault. Thus, it is important to quantify zones of that asymmetry. The modeling results have to be taken into account in studies of natural faults, especially for practical applications in seismic risk mapping, engineering geology, hydrogeology, and tectonics.

Mesomechanics Finite-element Method for Determining the Shear Strength of Mudded Intercalation Materials

A new method regarding mesomechanics finite-element research is proposed to predict the peak shear strength of mudded intercalation materials on a mesoscopic scale. Based on geometric and mechanical parameters, along with the strain failure criteria obtained by sample＇s deformation characteristics, uniaxial compression tests on the sample were simulated through a finite-element model, which yielded values consistent with the data from the laboratory uniaxial compression tests, implying that the method is reasonable. Based on this model, a shear test was performed to calculate the peak shear strength of the mudded intercalation, consistent with values reported in the literature, thereby providing a new approach for investigating the mechanical properties of mudded intercalation materials.

Stiffness Degradation Characteristics Destructive Testing and Finite-Element Analysis of Prestressed Concrete T-Beam

The failure behavior of the precast prestressed concrete T girder was investigated by destructive test and finite-element analysis,and the mid-span deflection,girder stiffness and the variation of the cross section strain in the loading process were obtained,and the mechanical properties,mechanical behavior,elastic and plastic behavior and ultimate bearing capacity of T girder with large span were revealed.Furthermore,the relationship between the beam stiffness degradation,the neutral axis in cross-section,steel yielding and concrete cracking are investigated and analyzed.A method was proposed to predict the residual bearing capacity of a bridge based on the variation of the position of the cross section strain distribution and the section neutral axis,which provided a theoretical basis for predicting the stiffness detection and carrying capacity assessment of prestressed concrete beam.

A Finite-Element Analysis on the Rheorolling Process of Semi-Solid Spring Steel

With a geometrical model of porous material, a 3D finite-element analysis on the rolling process of spring steel60Si2Mn in the semi-solid state is carried out using software MARC. In terms of flat and groove rolling conditions,stress field and strain field are studied. The simulation results show that the rigid-viscoplastic model can accuratelydescribe the semi-solid metal rolling process. Semi-solid slurry has the characteristics of low flow stress and goodfluidity. During groove rolling, distribution of stress and strain on the cross-section of deformation zone is moreuniform than that during flat rolling. The results of simulation are in good agreement with the experiment data, andshow that semi-solid material fits for groove rolling.

TWO-GRID METHOD FOR CHARACTERISTICS FINITE-ELEMENT SOLUTION OF 2D NONLINEAR CONVECTION-DOMINATED DIFFUSION PROBLEM

For two-dimension nonlinear convection diffusion equation, a two-grid method of characteristics finite-element solution was constructed. In this method the nonlinear iterations is only to execute on the coarse grid and the fine-grid solution can be obtained in a single linear step. For the nonlinear convection-dominated diffusion equation, this method can not only stabilize the numerical oscillation but also accelerate the convergence and improve the computational efficiency. The error analysis demonstrates if the mesh sizes between coarse-grid and fine-grid satisfy the certain relationship, the two-grid solution and the characteristics finite-element solution have the same order of accuracy. The numerical is more efficient than that of characteristics example confirms that the two-grid method finite-element method.

Finite-element modeling and simulations of the intra-body communication used for biomedical monitoring

The finite-element modeling and simulations of the intra-body communication （IBC） were investigated to provide a theoretical basis for biomedical monitoring. A finite-element model for the whole human body was developed to simulate the IBC. The simulation of galvanic coupling IBC and electrostatic coupling IBC were implemented along with different signal transmission paths, and their attenuations were calculated. Our study showed that the position near the signal electrode had higher potential than other positions in the two types of IBC, while the potential generally decreased along the axis of the body parts. Both signal attenuations of the two types IBC increased with increasing signal transmission distance, and the electrostatic coupling IBC had comparatively higher receiving potential than the galvanic coupling IBC. The results indicated that the proposed modeling method could be used for the research of biomedical monitoring based on IBC technology.

Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.

Pilot biomechanical design of biomaterials for artificial nucleus prosthesis using 3D finite-element modeling

Pilot biomechanical design of biomaterials for artificial nucleus prosthesiswas carried out based on the 3D finite-element method. Two 3D models of lumbar intervertebral discrespectively with a real human nucleus and with the nucleus removed were developed and validatedusing published experimental and clinical data. Then the models with a stainless steel nucleusprosthesis implanted and with polymer nucleus prostheses of various properties implanted were usedfor the 3D finite-element biomechanical analysis. All the above simulation and analysis were carriedout for the L4/L5 disc under a human worst--daily compression load of 2000 N. The results show thatthe polymer materials with Young's modulus of elasticity E = 0.1-100 MPa and Poisson's ratio v=0.35-0.5 are suitable to produce artificial nucleus prosthesis in view of biomechanicalconsideration.

3-D Finite-Element Numerical Simulation of Centrifugal Induction Electrosalg Casting Solidification Process

A 3-D finite-element numerical simulation model of temperature field for CIESC casting solidification process was developed with the aid of ANSYS software and a series of corresponding experiments were made. The results showed that the good agreement was obtained between the numerical simulation and the experiments. Based on the numerical simulation results, the characteristics of temperature distribution in the castings during CIESC solidification process were analyzed and summarized. According to the G/R-1/2 method and numerical simulation results, there is no any shrinkage defect in the CIESC casting and structure or casting is fine and compact.

A Mixed Finite-Element Method on Polytopal Mesh

In this paper,we introduce new stable mixed finite elements of any order on polytopal mesh for solving second-order elliptic problem.We establish optimal order error estimates for velocity and super convergence for pressure.Numerical experiments are conducted for our mixed elements of different orders on 2D and 3D spaces that confirm the theory.

A New Volumetric Parameter for a Comparative Finite-Element Analysis of a Six- or Four-Implant Mandibular Total-Arch Rehabilitation

In a full-arch implant rehabilitation ad modum Branemark, the distribution of stress and strain in mandibular bone is influenced by the type, number and position of implants used. In particular, the biomechanical behaviour of the bone structure after complete osseointegration depends on the load transferred to the bone by each fixture. In this study, a finite-element analysis of two models was performed. Models of an all-on-four configuration and a six-implant configuration were compared in a worst-case scenario. A new V parameter is presented to aid the quantitative and comparative analysis of the all-on-four and six-implant configurations. The influence of orthotropy was also investigated, and a geometric change in the all-on-four configuration is presented.

The Calculation of Stress-Strain State of Anisotropic Composite Finite-Element Area with Different Boundary Conditions on the Surface

The numerical analytic research approach of stress-strain state of anisotropic composite finite element area with different boundary conditions on the surface, is represented below. The problem is solved by using a spatial model of the elasticity theory. Differential equation system in partial derivatives reduces to one-dimensional problem using spline collocation method in two coordinate directions. Boundary problem for the system of ordinary higher-order differential equation is solved by using the stable numerical technique of discrete orthogonalization.

FINITE-ELEMENT MODELLING OF SOIL-GEOGRID INTERACTION DEALING WITH THE PULLOUT BEHAVIOUR OF GEOGRIDS

To predict the behavior of geogrids embedded in sand under pullout loading conditions, the two dimensional plane-stress finite element model was presented. The interactions between soil and geogrid were simulated as non-linear springs, and the stiffness of the springs was determined from simple tests in the specially designed pullout box. The predicted behavior of the geogrid under pullout load agrees well with the observed data including the load-displacement properties, the displacement distribution along the longitudinal direction and the mobilization of the frictional and bearing resistance. (Edited author abstract) 8 Refs.

Deep Learning Applied to Computational Mechanics:A Comprehensive Review,State of the Art,and the Classics

Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.

Stress distribution variations during nanoindentation failure of hard coatings on silicon substrates

Regarding quality inspection of technologically important nanocomposite hard coatings based on Ti,B,Si,C,and N and bioceramics such as hydroxyapatite that are used in small-scale high-precision devices and bio-implants,it is essential to study the failure mechanisms associated with nanoindentation,such as fracture,delamination,and chipping.The stress imposed by the indenter can affect the fracture morphology and the interfacial fracture energy,depending on indenter shape,substrate type,crystallographic properties,pre-existing flaws,internal microcracks,and pre-strain.Reported here are finite-element-based fracture studies that provide insights into the different cracking mechanisms related to the aforementioned failure process,showing that the fracture morphology is affected by the interaction of different cracking events.The interfacial fracture energy,toughness,and residual stress are calculated using existing models with minor adjustments,and it is found that increasing the indenter sharpness improves the shear stress distribution,making the coating more prone to separation.Depending on the prevailing type of stress,the stress distribution beneath the depression results in either crack formation or a dislocation pile-up leading to strain hardening.Different forms of resistances resulting from the indentation process are found to affect the tip–sample conduction,and because of its stronger induced plasticity than that of a Berkovich indenter tip,a sharper cube-corner tip produces more resistance.

Analysis of an Axial-flux Slotted Limited-angle Torque Motor with Quasi-Halbach Array for Torque Performance Improvement

Better torque performance and higher reliability have long been the focus of research for slotted limited-angle torque motors(LATMs),which are primarily used to position first-stage valves in electrohydraulic servosystems.This paper presents a high reliability axial-flux slotted LATM with quasi-Halbach array for torque performance improvement including constant torque range(CTR)and output torque.Firstly,the structure with two sets of windings and the operation principle of the proposed slotted LATM is analyzed.Secondly,a brief design procedure is presented,the structure selections of open slot and double-stator single-rotor(DSSR)interior rotor with surface mounted quasi-Halbach permanent magnet(PM)array are illustrated,and the geometric parameters are optimized to obtain the optimal design of the proposed slotted LATM.Then,3-D finite-element method(FEM)is employed to compare the proposed slotted LATM with the conventional surface mounted PM slotted LATM in terms of cogging torque,no-load back EMF,and output torque,and the results show that the proposed LATM with quasi-Halbach array has a 10%improvement in output torque and a 25%improvement in CTR.Meanwhile,the flux linkages and torque performance of the two sets of windings under various conditions verify good magnetic isolation.Finally,prototypes of two different rotor types are manufactured and a series of experiments are performed to validate the analysis.