Regional plantar foot pressure distributions on high-heeled shoes-shank curve effects

Forefoot pain is common in high-heeled shoe wearers due to the high pressure caused by the center of body mass moving forward and the increased arch height with heel elevation.Sufficient arch support could reduce the high pressure over forefoot.However,too much arch support could lead to abnormal foot alignment and pain over midfoot.Little information is reported on the relationship among plantar arch height,shank curve design and plantar pressure.This study aimed at quantifying the plantar arch height changes at different heel heights and investigating the effect of shank curve on plantar pressure distribution.The plantar arch height increased to(7.6±1.3) mm at heel height of 75 mm.The Chinese standard suggests the depth of last should be 8.5 mm for heel height of 75 mm.When a shank curve with higher depth of last(11 mm) was used,the peak pressure over forefoot further decreased in midstance phase,which might ease the forefoot problems,while the peak pressure over midfoot increased but not exceeded the discomfort pressure thresholds.To achieve a more ideal pressure distribution in high-heeled shoes,a higher than expected depth of last would be suggested that would not cause discomfort over midfoot.     

THREE-DIMENSIONAL FINITE ELEMENT SIMULATION OF TOTAL KNEE JOINT IN GAIT CYCLE

Based on CT scanning pictures from a volunteer＇s knee joint, a three-dimensional finite element model of the healthy human knee joint is constructed including complete femur, tibia, fibular, patellar and the main cartilage and ligaments. This model was validated using experimental and numerical results obtained from other authors. The pressure distribution of contact surfaces of knee joint are calculated and analyzed under the load action of ‘heel strike＇, ‘single limb stance＇ and ‘toe-off＇. The results of the gait cycle are that the contact areas of medial cartilage are larger than that of lateral cartilage; the contact force and contact areas would grow larger with the load increasing; the pressure of lateral meniscus is steady, relative to the significant variation of peak pressure in medial meniscus; and the peak value of contact pressure on all components are usually found at about 4570 of the gait cycle.     

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin (SUPG) method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid are performed by the Galerkin method. The second-order semiimplicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are linearized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effiectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.     

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.     

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.     

COMPUTATION OF FLEXURAL PROPERTIES OF HA/PLLA COMPOSITE USING A CELL MODEL APPROACH

A three-dimensional finite element analysis was conducted to evaluate the feasibility of predicting the flexural properties of hydroxyapatite-reinforced poly-L-lactide acid (HA/PLLA) biocomposite using three different schemes. The scheme 1, originated from a beam analysis, was used to determine the flexural modulus analytically while the scheme 2 and 3 were designed to have different loading and boundary conditions using a finite element cell modeling approach. An empirical approach using Chow's formula and experimental data were used for comparison with the predicted results. In order to reduce the computational time and save the storage space involved in determining the effect of varying particle volume fractions on the flexural properties of HA/PLLA, a superelement technique was applied. The results using the scheme 3 and the Chow's formula were found to be in reasonable agreement with experimental results over the range of particle volume fraction. In addition to the Chow's formula, local stress distribution and the failure processes in HA/PLLA were simulated using the finite element technique.     

A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered finite volume/finite element method for solution of the two dimensional (2D) incompressible Navier-Stokes equations on unstructured grids.An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling.The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by joining the centroid of cells sharing the common vertex.For the temporal integration of the momentum equations,an implicit second-order scheme is utilized to enhance the computational stability and eliminate the time step limit due to the diffusion term.The momentum equations are discretized by the vertex-centered finite volume method (FVM) and the pressure Poisson equation is solved by the Galerkin finite element method (FEM).The momentum interpolation is used to damp out the spurious pressure wiggles.The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both velocity and pressure.The classic test cases,the lid-driven cavity flow,the skew cavity flow and the backward-facing step flow,show that numerical results are in good agreement with the published benchmark solutions.     

Interfacial stress transfer behavior in a specially-shaped fiber/matrix pullout test

Specially designed fibers are widely used in engineering practice because the specially-designed shape can help to improve the bonding strength of the fiber and the interface. Studied in this paper is the interfacial shear stress transfer behavior on both sides of the specially designed fiber when it is being pulled out; in which automatic analysis of three-dimensional photoelasticity is employed and the finite element method is adopted. The results show that the stress transfer occurs mainly in the region near the fiber＇s embedded end where the stress reaches its critical point, leading to debonding of the interface. Before debonding, as the pullout loading increases, the peak value of shear stress transfers along the fiber from the embedded end to the interior of the matrix, and then stops at the hooked part of the fiber because of its impediment. When the interface begins to debond as the load increases, the shear stress can be transferred to the hooked part.     

EXPERIMENTAL ANALYSIS ON SOFT MATERIAL CONTACT PROBLEMS BY DIGITAL MOIR AND EMBEDDED-GRATING METHODS

Soft material is becoming increasingly important to many industries, which leads to the demand for a better understanding of its mechanical properties under large deformation. In this paper, a technique of integrating the digital moiré method and embedded-grating approach is presented for investigating mechanical behaviors of a vulcanized silicone rubber in contact with a wedge-shaped indenter. Two distinct deformation sectors are observed from the experimental result. A simple way of computing strain is also presented by analysing grid deformation within the framework of geometrical nonlinearity. Three regions were observed from strain distribution along the horizontal direction: the contact region, the sink-in region and the far-field region.Moreover, the extent of the sticky region and that of the slippy region within the contact interface are distinguished, which can provide realistic data for theoretical modelling. Based on the finite deformation elasticity theory, the distribution of contact pressure and shear stress over the contact interface are derived for prediction of possible cracks.     

Multiaxial fatigue life prediction of kiln roller under axis line deflection

This paper investigates the multiaxial fatigue life of the roller in rolling contact with wheels with respect to axis line deflection. The multiaxial fatigue criteria proposed by Wang and Brown, together with the ralnflow counting method and Miner- Palmgren＇s rule, are applied to the cumulative damage estimation and life prediction. As the axis line deflection of overlong kilns generally results in asymmetric load distribution on each roller, the load ratio is introduced to describe the deflection for quantitative stress analyses. The stress analyses are performed within the finite element code ANSYS. The tangential friction stress is calculated in terms ：of the condition of the rolling contact area. By taking one roller as an example, the plotted fatigue life versus load ratio curve discovers how the axis line deflection affects the fatigue life. This study is significant to prevent the fatigue failure of the roller and can provide basis to adjust and optimize the axis line of the rotary kiln.     

Crack buckling in soft gels under compression

Recent interest in designing soft gels with high fracture toughness has called for simple and robust methods to test fracture behavior. The conventional method of applying tension to a gel sample suffers from a difficulty of sample gripping. In this paper, we study a possible fracture mechanism of soft gels under uni-axial compression. We show that the surfaces of a pre-existing crack, oriented parallel to the loading axis, can buckle at a critical compressive stress. This buckling instability can open the crack surfaces and create highly concentrated stress fields near the crack tip, which can lead to crack growth. We show that the onset of crack buckling can be deduced by a dimensional argument com- bined with an analysis to determine the critical compression needed to induce surface instabilities of an elastic half space. The critical compression for buckling was verified for a neo-Hookean material model using finite element simulations.     

THREE DIMENSIONAL DYNAMIC ELASTICPLASTIC ANALYSIS OF THE INTERACTION OF A SET OF PERCUSSION BITS WITH ROCK MASSES

A three dimensional dynamic elastic-plastic finite element analysis of the interaction ofpercussion bits with rock roasses is presented.The dynamic contact problem was investigated with thenumerical method developed for high velocity impact calculations.The numerical analysis was carried out for three simultaneously loaded percussion bits arrangedon a straight line on the rock surface,the loading time was kept constant throughout this work.Thenumerical calculation for various strengths of the dynamic load on the percussion bits shows that a crit-ical minimum dynamic load exists for the generation of plastic deformations in the rock.For this criti-cal value of the load the maximum normal stress of the longitudinal wave in the percussion bit exceedsthe yield stress of the rock mass.     

New discrete element models for elastoplastic problems

The discrete element method （DEM） has attractive features for problems with severe damages, but lack of theoretical basis for continua behavior especially for nonlinear behavior has seriously restricted its application. The present study proposes a new approach to developing the DEM as a general and robust technique for modeling the elastoplastic behavior of solid materials. New types of connective links between elements are proposed, the interelement parameters are theoretically determined based on the principle of energy equivalence and a yield criterion and a flow rule for DEM are given for describing nonlinear behavior of materials. Moreover, a numerical scheme, which can be applied to modeling the behavior of a continuum as well as the transformation from a continuum to a discontinuum, is obtained by introducing a fracture criterion and a contact model into the DEM. The elastoplastic stress wave propagations and the tensile failure process of a steel plate are simulated, and the numerical results agree well with those obtained from the finite element method （FEM） and corresponding experiment, and thus the accuracy and efficiency of the DEM scheme are demonstrated.     

OPTIMUM DESIGN OF PROCESSING CONDITION AND EXPERIMENTAL INVESTIGATION OF GRATING FABRICATION WITH HOT EMBOSSING LITHOGRAPHY

The cross-section profiles of polymer deformation in the hot embossing lithography process were studied by finite element method for various temperature, time and pressure. In order to successfully fabricate high-frequency grating lines, an optimal imprint condition was selected and the related experiments were carried out. The fabricated gratings were illuminated by the SEM image and AFM analysis, which agree well with the simulated results. Therefore, the finite element methods are helpful for a better comprehension of the polymer flow phenomena governing the pattern definition and the design of optimum processing conditions for successful grating fabrication.     

Analytical solution for bending beam subject to lateral force with different modulus

A bending beam, subjected to state of plane stress, was chosen to investigate. The determination of the neutral surface of the structure was made, and the calculating formulas of neutral axis, normal stress, shear stress and displacement were derived. It is concluded that, for the elastic bending beam with different tension-compression modulus in the condition of complex stress, the position of the neutral axis is not related with the shear stress, and the analytical solution can be derived by normal stress used as a criterion,improving the multiple cyclic method which determines the position of neutral point by the principal stress. Meanwhile, a comparison is made between the results of the analytical solution and those calculated from the classic mechanics theory, assuming the tension modulus is equal to the compression modulus, and those from the finite element method (FEM) numerical solution. The comparison shows that the analytical solution considers well the effects caused by the condition of different tension and compression modulus. Finally, a calculation correction of the structure with different modulus is proposed to optimize the structure.     

ANALYSIS OF COMPOSITE LAMINATE BEAMS USING COUPLING CROSS-SECTION FINITE ELEMENT METHOD

Beams and plates manufactured from laminates of composite materials have distinct advantages in a significant number of applications. However, the anisotropy arising from these materials adds a significant degree of complexity, and thus time, to the stress and deformation analyses of such components, even using numerical approaches such as finite elements. The analysis of composite laminate beams subjected to uniform extension, bending, and/or twisting loads was performed by a novel implementation of the usual finite element method. Due to the symmetric features of the deformations, only a thin slice of the beam to be analysed needs to be modelled. Conventional three-dimensional solid finite elements were used for the structural discretization. The accurate deformation relationships were formulated and implemented through the coupling of nodal translational degrees of freedom in the numerical analysis. A sample solution for a rectangular composite laminate beam is presented to show the validity and accuracy of the proposed method.     

A streamline diffusion nonconforming finite element method for the time-dependent linearized Navier-Stokes equations

A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.     

An effective boundary element method for analysis of crack problems in a plane elastic plate

A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.     

THEORETICAL INVESTIGATION ON THE DYNAMIC PERFORMANCE OF CMUT FOR DESIGN OPTIMIZATION

Although many modeling approaches exist for analyzing the behavior of capacitive micro-machined ultrasonic transducers(CMUTs),the relation equation between the design parameters with input and output is still lacking.What there is can only be used to analyze the dynamic performance of CMUT indirectly and qualitatively,such as stiffness and sound pressure.A lumped-parameter theoretical model based on the dynamic theory is proposed in this paper.The relation equations between the design parameters with inputs and outputs are given.The results obtained by the proposed model agree well with those by finite element method(FEM)simulation.The dynamic and static behavior of CMUT can be clearly depicted,which is helpful for design and optimization iterations.This shows that the proposed model makes it easier to optimize the parameters of a CMUT with respect to output and bandwidth directly and to better understand the influence of each parameter.     

Analytical solution of bending-compression column using different tension-compression modulus

Based on elastic theory of different tension-compression modulus, the analyttcal solution was deduced for bending-compression column subject to combined loadings by the flowing coordinate systemaxis, stress, strain andand phased integration methoddisplacement were developed,The formulations for the neutralthe finite element program was compiled for calculation, and the comparison between the result of finite element and analytical solution were given too. Finally, compare and analyze the result of different modulus and the same modulus, obtain the difference of two theories in result, and propose the reasonable suggestion for the calculation of this structure.