Multiresolution method for bending of plates with complex shapes

A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.

SOLUTION OF DIFFERENT HOLES SHAPE BORDERS OF FIBRE REINFORCED COMPOSITE PLATES BY INTEGRAL EQUATIONS

Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.

3D analysis of functionally graded material plates with complex shapes and various holes

In this paper, the basic formulae for the semi-analytical graded FEM on FGM members are derived. Since FGM parameters vary along three space coordinates, the parameters can be integrated in mechanical equations. Therefore with the parameters of a given FGM plate, problems of FGM plate under various conditions can be solved. The approach uses 1D discretization to obtain 3D solutions, which is proven to be an effective numerical method for the mechanical analyses of FGM structures. Examples of FGM plates with complex shapes and various holes are presented.

Spatio-Temporal Kinematic Decomposition of Movements

We propose the new experimental method for investigating and approximating the organization and structure of movements with given accuracy. The composition of approximating trajectories illuminating the movement traits discloses the level of movement expertise in dancers and golf players. The method allows estimating the level of movement expertise, drawing the detailed structure of movements, and classifying movements into a given repertoire automatically.

Structural Dimension Optimization of Robotic Belt Grinding System for Grinding Workpieces with Complex Shaped Surfaces Based on Dexterity Grinding Space

To improve the grinding quality of robotic belt grinding systems for the workpieces with complex shaped surfaces, new concepts of the dexterity grinding point and the dexterity grinding space are proposed and their mathematical descriptions are defined. Factors influencing the dexterity grinding space are analyzed. And a method to determine the necessary dexterity grinding space is suggested. Based on particle swarm optimization （PSO） method, a strategy to optimize the grinding robot structural dimensions and position with respect to the grinding wheel is put forward to obtain the necessary dexterity grinding space. Finally, to grind an aerial engine blade, a dedicated PPPRRR （P： prismatic R： rotary） grinding robot structural dimensions and position with respect to the grinding wheel are optimized using the above strategy. According to simulation results, if the blade is placed within the dexterity grinding space, only one gripper and one grinding machine are needed to grind its complex shaped surfaces.

AFM Measurements and Tip Characterization of Nanoparticles with Different Shapes

Unambiguous identification of the measurement methodologies is fundamental to reduce the uncertainty and support traceability of particle shape and size at the nanoscale. In this work, the critical aspects in atomic force microscopy measurements, that is, drawbacks on sample preparation, instrumental parameters, image pre-processing, size reconstruction, and tip enlargement, are discussed in reference to quantitative dimensional measurements on different kinds of nanoparticles (inorganic and biological) with different shapes (spherical, cylindrical, complex geometry). Once the cross-section profile is extracted, top-height measurements on isolated nanoparticles of any shape can be achieved with sub-nanometer accuracy. Lateral resolution is affected by the pixel size and shape of the probe, causing dilation in the atomic force microscopy image. For the reconstruction of critical sizes of inorganic non-spherical nanoparticles, a geometric approach that considers the nominal shape because of the synthesis conditions is presented and discussed.

3D shape measurement of larger complex objects based on fringe cycle correction

The grating fringe on the reference plane is broadened in the intersecting axis system because of oblique-angle projection. In order to solve this problem, we study the theoretical model of the temporal phase unwrapping method based on the fringe cycle correction. We also study the 3D shape measurement theoretical model of the larger complex objects after considering the coordinate deviation and lens distortion. Experimental results demonstrate that the fringe cycle on the reference plane can be corrected to a constant value, the lens distortion can be corrected, and 3D shape of larger complex objects can be accurately measured.

Enhanced ultrasonic total focusing imaging of CFRP corner with ray theory-based homogenization technique

Ultrasonic testing is effective in defect characterization and quality assurance of Carbon Fiber Reinforced Plastic(CFRP) components in the aerospace industry. Due to the coupling between complex shape and elastic anisotropy, the Phased Array Ultrasonic Testing(PAUT) and time-based Total Focusing Method(TFM) face significant challenges in the calculation of wave propagation. A wave velocity distribution model is established for a multidirectional convex corner of CFRP based on a homogenization theory and the above coupling effects are also incorporated. A ray-tracing method is proposed based on Dijkstra’s shortest path search algorithm. The predicted time of flight ensures that this technique, the homogenized TFM, could synthesize a high-quality focused image by post-processing on the full matrix capture data. Experiments on a laminate with three φ1.5 mm Side-Drilled Holes(SDHs) in different circumferential directions confirm a successful homogenized TFM imaging that all SDHs can be effectively detected. As compared to the isotropic scenario, the maximum positioning error is reduced to 0.12, 0.08, and 0.38 mm, and the Signal-to-Noise Ratios(SNRs) are increased by 2.1, 1.1, and 11.8 dB, respectively. It is suggested that the ray-tracing assisted TFM technique can effectively improve the imaging of corners in CFRP components.

Si-DLC films deposited by a novel method equipped with a co-potential auxiliary cathode for anti-corrosion and anti-wear application

A novel DLC film deposition method was proposed to realize the deposition of DLC film on the surface of complex shaped workpiece.Meanwhile,Si-DLC film was deposited on the surface of M2 high-speed steel(HSS M2)and 304 stainless steel(304SS),and the microstructure,surface roughness,mechanical properties,corrosion resistance and tribological properties of Si-DLC films were characterized in detail.Results show that Si-DLC film at different axial positions of the auxiliary cathode possesses similar microstructure,film thickness and surface roughness,and the as-deposited Si-DLC film shows the low intrinsic stress of<0.3 GPa.Compared with the 304SS substrate,the Si-DLC film presents more noble corrosion potential,lower corrosion current density and higher polarization resistance,exhibiting higher corrosion resistance.Moreover,the Si-DLC film exhibits higher hardness,elastic factor and plastic factor than HSS M2 substrate and the corresponding adhesive strength is more than 10 N.The Si-DLC film sliding against GCr15 steel ball shows a lower friction coefficient than that of HSS M2 substrate and the wear rate of GCr15 steel ball sliding against the Si-DLC is lower than that of HSS M2 substrate.In addition,this novel method was used to deposit Si-DLC film on gears,drills and bearings without rotating sample racks.As a consequence,this method possesses great potential and can be generalized for the deposition of DLC film on the surface of complex shape workpiece.