Flow interference between a stationary cylinder and an elastically mounted cylinder arranged in proximity

The flow interference between two circular cylinders, one stationary and the other free to oscillate in the transverse direction, are studied numerically at Re=150. The incompressible Navier–Stokes equation in two space dimensions, an assumption that is expected to be valid at the considered Re, is solved by the characteristic-based-split (CBS) finite element method using the T4/C3 MINI triangular element. The center-to-center spacing between the two cylinders is fixed at 4D, where D is the cylinder diameter. The angle of incident flow, α, with respect to the line through the two cylinder centers, varies within the range from α=0° to 90°. For the elastically mounted cylinder, the reduced mass considered is M_r=2.0; the structural damping coefficient is assigned to be zero, which encourages high amplitude oscillations. For each α, the computations are conducted for a wide range of reduced velocities, U_r. The flow interference is examined by scrutinizing (i) the frequency characteristics of the vortex shedding and oscillation; (ii) the dynamic response of the oscillating cylinder, including the amplitude of displacement, the drag and lift force characteristics and the phase relationship between the lift and the displacement series; and (iii) the flow response in terms of the instantaneous vorticity field. It was found that the flow interference type is significantly affected by the angle of the incident flow. As the cylinder is oscillated outside of the region of the wake behind the stationary cylinder (α≥30°), it behaves similarly to its isolated counterpart. In contrast, if the cylinder is partially or entirely submerged within the upstream wake (α<30°), then both the flow and body responses are substantially modified due to the vigorous interaction between the upstream wake and the oscillating cylinder; the response therefore belongs to the wake-induced regime. The U_r range associated with the higher amplitude response is significantly shifted toward a higher U_r. The maximum vibration amplitude builds up to a significantly higher level, even increasing the U_r far beyond the resonance regime. In general, the wake flow associated with the wake-induced vibration (WIV) regime appears to be more unperiodic than does that corresponding to the vortex-induced oscillation regime. It is also revealed that both the vortex-cylinder and the shear layer-cylinder interaction mechanisms are responsible for the characteristics of the responses of oscillating cylinder. The larger momentum required for the higher oscillation amplitude is obtained from the duration of the energy transfer from the fluid to the cylinder, which is ascribed to the phase lag between the lift force and the cylinder displacement.     

Surface wrinkling of mucosa induced by volumetric growth: Theory, simulation and experiment

Mechanics of living tissues focusing on the relationships between growth, morphology and function is not only of theoretical interest but can also be useful for diagnosis of certain diseases. In this paper, we model the surface wrinkling morphology of mucosa, the moist tissue that commonly lines organs and cavities throughout the body, induced by either physiological or pathological volumetric growth. A theoretical framework of finite deformation is adopted to analyze the deformation of a cylindrical cavity covered by mucosal and submucosal layers. It is shown that compressive residual stresses induced by the confined growth of mucosa can destabilize the tissue into various surface wrinkling patterns. A linear stability analysis of the critical condition and characteristic buckling patterns indicates that the wrinkling mode is sensitive to the thicknesses of the mucosal and submucosal layers, as well as the properties of the tissues. The thinner the mucosal layer and the lower its elastic modulus, the shorter the buckling wavelength. A series of finite element simulations are performed to validate the theoretical predictions and to study local wrinkling or non-uniform patterns associated with inhomogeneous growth. Our postbuckling analysis shows that the surface pattern may evolve towards a period-doubling morphology due to continuous growth of mucosa or submucosa beyond the critical state. Finally, the theoretical predictions and numerical simulations are compared to experimental observations.     

Numerical approximation for a non-linear membrane problem

We present a numerical study of large deformations of non-linearly elastic membranes. We consider the non-linear membrane model obtained by Le Dret and Raoult using Γ-convergence, in the case of a Saint Venant-Kirchhoff bulk material. We consider conforming P₁ and Q₁ finite element approximations of the membrane problem and use a non-linear conjugate gradient algorithm to minimize the discrete energy. We present numerical tests including membranes subjected to live pressure loads.     

A Hybrid Boundary/Finite Element Method for Simulating Viscous Flows and Shapes of Droplets in Electric Fields

A mixed boundary element and finite element numerical algorithm for the simultaneous prediction of the electric fields, viscous flow fields, thermal fields and surface deformation of electrically conducting droplets in an electrostatic field is described in this paper. The boundary element method is used for the computation of the electric potential distribution. This allows the boundary conditions at infinity to be directly incorporated into the boundary integral formulation, thereby obviating the need for discretization at infinity. The surface deformation is determined by solving the normal stress balance equation using the weighted residuals method. The fluid flow and thermal fields are calculated using the mixed finite element method. The computational algorithm for the simultaneous prediction of surface deformation and fluid flow involves two iterative loops, one for the electric field and surface deformation and the other for the surface tension driven viscous flows. The two loops are coupled through the droplet surface shapes for viscous fluid flow calculations and viscous stresses for updating the droplet shapes. Computing the surface deformation in a separate loop permits the freedom of applying different types of elements without complicating procedures for the internal flow and thermal calculations. Tests indicate that the quadratic, cubic spline and spectral boundary elements all give approximately the same accuracy for free surface calculations; however, the quadratic elements are preferred as they are easier to implement and also require less computing time. Linear elements, however, are less accurate. Numerical simulations are carried out for the simultaneous solution of free surface shapes and internal fluid flow and temperature distributions in droplets in electric fields under both microgravity and earthbound conditions. Results show that laser heating may induce a non-uniform temperature distribution in the droplets. This non-uniform thermal field results in a variation of surface tension along the surface of the droplet, which in turn produces a recirculating fluid flow in the droplet. The viscous stresses cause additional surface deformation by squeezing the surface areas above and below the equator plane.     

弹性力学平面问题的等价边界积分方程的边界轮廓法

基于边界积分方程中被积函数散度为零的特性,提出了弹性力学平面问题的等价边界积分方程的边界轮廓法,该方法无需进行数值积分,只需要计算单元两结点势函数值之差。实例计算说明,基于传统的边界积分方程的边界轮廓法所得到的面力结果是错误,而本文建立的边界轮廓法则可给出精确的结果。     

The Method of Integrodifferential Relations for Linear Elasticity Problems

Some possible modifications of the governing equations of the linear theory of elasticity are considered. The stress–strain relation is specified by an integral equality instead of the local Hooke’s law. The modified integrodifferential boundary value problem is reduced to the minimization of a nonnegative functional under differential constraints. A numerical algorithm based on polynomial approximations of unknown functions (stresses and displacements) is developed and applied to linear elasticity problems. The bilateral estimation criteria of solution errors are proposed in order to analyze the algorithm convergence rate. The numerical results obtained by applying the integrodifferential relation method and the conventional variational method are compared and discussed.     

Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods

Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions(symmetric and non-symmetric)are studied in this work.Reliability of the obtained results is verified by the finite difference method(FDM)and the finite element method(FEM)with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes(regular and non-regular).The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.     

Numerical study around the corotational Maxwell model for the viscoelastic fluid flows

We present numerical results for the FEM (finite element method) presented in [Comput. Methods Appl. Mech. Engrg. 191 (2002) 5045–5065]. This method is devoted to the approximation of fluid flows obeying the Oldroyd model. A particularity of this method, is to take into account the purely viscoelastic case, the so-called Maxwell model, important in practice. Numerical results are given for a fluid flowing in an abrupt plane 4 to 1 contraction. We use the corotational Maxwell model as benchmark in the choice of our computations. Results are also given for the upper convected Maxwell model. Interesting effects appear on the velocity profile: a phenomenon of quasi slip at the downstream wall.     

Large free vibrations of a beam carrying a moving mass

The focus of this work is to develop a technique to obtain numerical solution over a long range of time for non-linear multi-body dynamic systems undergoing large amplitude motion. The system considered is an idealization of an important class of problems characterized by non-linear interaction between continuously distributed mass and stiffness and lumped mass and stiffness. This characteristic results in some distinctive features in the system response and also poses significant challenges in obtaining a solution.

In this paper, equations of motion are developed for large amplitude motion of a beam carrying a moving spring–mass. The equations of motion are solved using a new approach that uses average acceleration method to reduce non-linear ordinary differential equations to non-linear algebraic equations. The resulting non-linear algebraic equations are solved using an iterative method developed in this paper. Dynamics of the system is investigated using a time-frequency analysis technique.     

A new Finite Element Method for magneto-dynamical problems: two-dimensional results

A mixed Lagrange finite element technique is used to solve the Maxwell equations in the magneto-hydrodynamic (MHD) limit in an hybrid domain composed of vacuum and conducting regions. The originality of the approach is that no artificial boundary condition is enforced at the interface between the conducting and the insulating regions and the non-conducting medium is not approximated by a weakly conducting medium as is frequently done in the literature. As a first evaluation of the performance of the method, we study two-dimensional (2D) configurations, where the flow streamlines of the conducting fluid are planar, i.e., invariant in one direction, and either the magnetic field (“magnetic scalar” case) or the electric field (“electric scalar” case) is parallel to the invariant direction. Induction heating, eddy current generation, and magnetic field stretching are investigated showing the usefulness of finite element methods to solve magneto-dynamical problems with complex insulating boundaries.     

Finite element analysis of lift build-up due to aerofoil indicial motion

In this paper the problem of impulsively started aerofoil or suden change of incidence of an aerofoil in incompressible potential flow is investigated. The essence of solution lies in the representation of a timely and spatially varying wake in a largely irrotational potential flow field. This is achieved by representing the wake through velocity potential difference, which seems to be the only way of imposing a velocity difference condition in the finite element context with velocity potentials as the basic unknowns. Superposition is employed to meet various boundary conditions, which is justified by the linearity of the problem. The finite element solutions are compared with those from singularity method.     

固体力学应力分析中的有限域法

本文给出了用有限域法进行了和学应力分析的一般原理，并与目前广泛采用的有限元不做了比较。文中的研究表明：有限域法与有限元法极为相似，前者使用单位位移加权，后者从虚位移原理出发；两种方法的实施过程也有共同点，它们都进行网络部分及逼近。     

弹性力学的杂交自然单元法

为了解决自然单元法无法直接求解节点应力以及应力解精度不高的问题, 将应力杂交的思想引入自然单元法中, 与弹性问题的Hellinger-Reissner变分原理结合, 提出了弹性问题的杂交自然单元法. 算例表明: 杂交自然单元法的计算结果与解析解吻合, 证明该方法是可行的; 在求解应力方面, 杂交自然单元法比自然单元法有着更高的计算精度, 而且可以直接求解出节点的应力.