Flexibility is a particularly important biomechanical property for intracranial vascular stents. To study the flexibility of stent, the following work was carried out by using the finite element method: Four mechanical models were adopted to simulate the bending deformation of stents, and comparative studies were conducted about the distinction between cantilever beam and simply supported beam, as well as the distinction between moment-loading method and displacement-loading method. A complete process as implanting a stent including compressing, expanding and bending was also simulated, for analyzing the effects of compressing and expanding deformation on stent flexibility. At the same time, the effects of the arrangement and the number of bridges on stent flexibility were researched. The results show that: 1. A same flexibility index was obtained from cantilever beam model and simply supported beam model; displacement-loading method is better than moment-loading for simulating the bending deformation of stents. 2. The flexibility of stent with compressing and expanding deformation is lower than that in the initial form. 3. Crossly arranging the neighboring bridges in axial direction, can effectively improve the stent flexibility and reduce the flexibility difference in various bending directions; the bridge number, has proportional non-linear correlation with the stent rigidity as well as the maximum moment required for bending the stent.

This paper is concerned with the construction of high order mass-lumping finite elements on simplexes and a program for computing mass-lumping finite elements on triangles and tetrahedra. The polynomial spaces for mass-lumping finite elements, as proposed in the literature, are presented and discussed. In particular, the unisolvence problem of symmetric point-sets for the polynomial spaces used in mass-lumping elements is addressed, and an interesting property of the unisolvent symmetric point-sets is observed and discussed. Though its theoretical proof is still lacking, this property seems to be true in general, and it can greatly reduce the number of cases to consider in the computations of mass-lumping elements. A program for computing mass-lumping finite elements on triangles and tetrahedra, derived from the code for computing numerical quadrature rules presented in [7], is introduced. New mass-lumping finite elements on triangles found using this program with higher orders, namely 7, 8 and 9, than those available in the literature are reported.

An optimal control problem is considered to find a stable surface traction, which minimizes the discrepancy between a given displacement field and its estimation. Firstly, the inverse elastic problem is constructed by variational inequalities, and a stable approximation of surface traction is obtained with Tikhonov regularization. Then a finite element discretization of the inverse elastic problem is analyzed. Moreover, the error estimation of the numerical solutions is deduced. Finally, a numerical algorithm is detailed and three examples in two-dimensional case illustrate the efficiency of the algorithm.

A counterexample is constructed. It confirms that the error of conforming finite element solution is proportional to the coefficient jump, when solving interface elliptic equations. The Scott-Zhang operator is applied to a nonconforming finite element. It is shown that the nonconforming finite element provides the optimal order approximation in interpolation, in L2-projection, and in solving elliptic differential equation, independent of the coefficient jump in the elliptic differential equation. Numerical tests confirm the theoretical finding.

The paper makes a comparative study of the finite element method (FEM) and the finite difference method (FDM) for two-dimensional fractional advection-dispersion equation (FADE) which has recently been considered a promising tool in modeling non-Fickian solute transport in groundwater. Due to the non-local property of integro-differential operator of the space-fractional derivative, numerical solution of FADE is very challenging and little has been reported in literature, especially for high-dimensional case. In order to effectively apply the FEM and the FDM to the FADE on a rectangular domain, a backward-distance algorithm is presented to extend the triangular elements to generic polygon elements in the finite element analysis, and a variable-step vector Grünwald formula is proposed to improve the solution accuracy of the conventional finite difference scheme. Numerical investigation shows that the FEM compares favorably with the FDM in terms of accuracy and convergence rate whereas the latter enjoys less computational effort.

We analyze here, a two-grid finite element method for the two dimensional time-dependent incompressible Navier-Stokes equations with non-smooth initial data. It involves solving the non-linear Navier-Stokes problem on a coarse grid of size H and solving a Stokes problem on a fine grid of size h, h « H. This method gives optimal convergence for velocity in H1-norm and for pressure in L2-norm. The analysis mainly focuses on the loss of regularity of the solution at t = 0 of the Navier-Stokes equations.

Based on two-grid discretization, a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed. The method is based on a fixed point iteration for the equations on a coarse grid, where a Stokes problem is solved at each iteration. Then, on overlapped local fine grids, corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution. Error bounds of the approximate solution are derived. Numerical results on examples of known analytical solutions, lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.

In this paper, we present a superconvergence result for the bi-k degree time-space fully discontinuous finite element of first-order hyperbolic problems. Based on the element orthogonality analysis (EOA), we first obtain the optimal convergence order of discontinuous Galerkin finite element solution. Then we use orthogonality correction technique to prove a superconvergence result at right Radau points, which is higher one order than the optimal convergence rate. Finally, numerical results are presented to illustrate the theoretical analysis.

This study presents a finite element (FE) model of the human hand-arm system to derivenatural frequencies and mode shapes. The FE model is calibrated by considering modalparameters obtained from experimental vibration analyzed by using operational modalanalysis (OMA) and transmissibility. Modal and harmonic analyses of the FE model areperformed for two boundary conditions. The first one considers fixed shoulder conditionwhile the second one introduces the trunk in order to permit motion of the shoulder. Theresults show that the natural frequencies of the second model that permits shoulder motionare comparable with those determined from measurements. Especially, the natural frequencyabout 12 Hz, which is corresponding to the frequency of maximum weight in ISO-5349-1(2001), is not present in the model with fixed shoulder condition, while it appears in thesecond model. The results of the present study suggest that improved finite element modelsof the human hand-arm system may reveal hand-arm injury mechanism, the understanding ofwhich may assist in deriving appropriate frequency weightings for the assessment ofdifferent components of the hand-arm vibration syndrome.

A new class of nonparametric nonconforming quadrilateral finite elements is introducedwhich has the midpoint continuity and the mean value continuity at the interfaces ofelements simultaneously as the rectangular DSSY element [J. Douglas, Jr., J.E. Santos, D.Sheen and X. Ye, ESAIM: M2AN 33 (1999) 747–770.] Theparametric DSSY element for general quadrilaterals requires five degrees of freedom tohave an optimal order of convergence [Z. Cai, J. Douglas, Jr., J.E. Santos, D. Sheen andX. Ye, Calcolo 37 (2000) 253–254.], while the newnonparametric DSSY elements require only four degrees of freedom. The design of newelements is based on the decomposition of a bilinear transform into a simple bilinear mapfollowed by a suitable affine map. Numerical results are presented to compare the newelements with the parametric DSSY element.

In this article a two dimensional incompressible viscous flow past a square cylinder oscillating in cross flow with zero and 45 degree angles of attack is numerically studied by a Characteristics Based Splitter (CBS) finite element method. The solver is coupled to a mesh movement scheme using the Arbitrary Lagrangian-Eulerian (ALE) formulation to account for the body motion in the flow field. First, the accuracy of the numerical code is tested by comparing the numerical results obtained for the flow over the stationary square cylinder at the three different Reynolds numbers (Re = 100, 200, and 300) with the experimental data available. Then, the numerical results for the square cylinder undergoing transverse oscillations in the two angles of attack at different values of frequency and amplitude are investigated to determine the lock-on region. The results indicate physical similarity between circular and square cylinders concerning lock-on regions. Also the effect of lock-on phenomenon on the flow field pattern and time-averaged drag coefficient is investigated.

A theoretical investigation of the unsteady flow of a Newtonian fluid through a channel is presented using an alternative boundary condition to the standard no-slip condition, namely the Navier boundary condition, independently proposed over a hundred years ago by both Navier and Maxwell. This boundary condition contains an extra parameter called the slip length, and the most general case of a constant but different slip length on each channel wall is studied. An analytical solution for the velocity distribution through the channel is obtained via a Fourier series, and is used as a benchmark for numerical simulations performed utilizing a finite element analysis modified with a penalty method to implement the slip boundary condition. Comparison between the analytical and numerical solution shows excellent agreement for all combinations of slip lengths considered.

Shrink fits are low-price connections which are widely used in industry and industrialconnections. In designing shrink fits it is important to consider radial interface foroptimized performance and also to choose an accurate method of fabrication and assembling.Parts which have to be assembled are usually exposed to thermo-mechanical loads. Mode andtime duration of heat transfer have a significant effect on required hydraulic force,stress time rate of creation in parts and joint ability to withstand against externalloads. Therefore, planning a set of appropriate thermal and structural procedures hassignificant role in reducing energy consumption, optimized performance and promoting thespeed of parts assembly. Despite of the fact, few researches have been done on shrink fitoperation and design, rather than dimensional design. In this study, shrink fits arestudied in two main processes: first heating and mounting process and then backing to theambient condition. A 3D coupled thermal and structural simulation based on FEM is done oneach process through well-known Solidworks Premium. To evaluate the accuracy, exactanalytical solution of two steel rings shrink fit is compared with the approach outcomes.Results of validated method are used for choosing the most optimum sub processes of shrinkfit fabrication.

Early damage detection on structures plays a very important role for ensuring safety and reliability. This paper provides an efficient method based on wavelet transforms in order to detect and localize damage on structures subjected to moving loads such as beams and bridges. A numerical model based on the experimental test-rig utilized in this study is developed by using a finite element commercial software. Different types of damage on the bridge of the numerical model are simulated and transient analyses are performed by incorporating a load which moves constantly along the beam nodes. Continuous wavelet transform diagrams using the vertical acceleration responses show that damage can be identified and localized even with significant percentages of noise. Nevertheless, the method is improved by filtering the signals, removing the border effects, and calculating the total wavelet energy of the beam from the coefficients along the selected range of scales. Thus, the accumulation of wavelet energy could indicate the presence of damage. Finally, laboratory experiments are conducted to validate this work and a good agreement between numerical and experimental results is obtained.

In this study, a novel procedure has been developed for predicting the notched strengths of composite plates each with a center hole. In this approach, the stress distribution of a composite plate with a center hole is first obtained by a finite element analysis, in which the experimental notched strength is applied at the boundary of the finite element model. Secondly, the point stress criterion (PSC) is used to find the characteristic length for each plate with different size of hole by an interpolation of the finite element analysis results. The characteristic length is then expressed as an empirical function of the hole size as well as the width of the plate. Finally, the notched strengths of composite plates are predicted based on the empirical function and the finite element analysis results incorporated with the principle of superposition in elasticity. For validation, three different cases from the literatures are adopted for comparison. It is shown that the predicted notched strengths by this new methodology agree well with both the experimental results and the results from analytical solutions based PSC.

In this paper, we propose a new two-level preconditioned C-G method which uses the quadratic smoothing and the linear correction in distorted but topo-logically structured grid. The CPU time of this method is less than that of the multigrid preconditioned C-G method (MGCG) using the quadratic element, but their accuracy is almost the same. Numerical experiments and eigenvalue analysis are given and the results show that the proposed two-level preconditioned method is efficient.

Static bending of a twisted Timoshenko beam subjected to combined transverse and axial loadings is studied. The equilibrium equations are established in the twist coordinates by applying the principle of minimum potential energy. The governing equations are then reduced into solvable algebraic equations using a finite element approach. The effects of the twist angle, thickness-to-width ratio, length-to-thickness ratio, loading and boundary conditions on the static bending characteristics of the twisted beams are investigated. The present parametric analyses will provide engineers a good insight into the influence of various structural aspects of the twisted beam on its response to different static loads.

The study of nonlinear dynamic behavior of laminate composed of steel and rubber layersalso referred as “Shim”, used for vibro-acoustic insulation in brake system, isinvestigated. The simulation of the vibro-acoustic nonlinear behavior of Shim depending onfrequency, taking into account the large deformations and various nonlinearhyper-viscoelastic laws of rubber are considered. This paper presents a solution tocontribute in the identification of the best design of Shim in terms of damping vibrationof brake systems, using analytical and numerical method. The choice of the best structuredepends essentially on the nature of rubber, on the stacking sequence of materials, ontheir thickness, on the number of layers and on volume fraction of rubber. An analyticalstudy, with the use of the transfer matrix method is presented. A model on the finiteelement software ANSYS is constructed. The results lead to conclusions about the beststructure and design of Shim in term of vibro-acoustic insulation.