Numerical simulation of capsule deformation in simple shear flow

The transient deformation of two-dimensional non-circular and three-dimensional non-spherical capsules in simple shear flow is studied numerically, using the hybrid immersed boundary and multi-block lattice Boltzmann method recently proposed by the present authors. The capsules are modeled as Newtonian liquid drops enclosed by elastic membranes; the liquids inside and outside the capsule have the same physical properties. The present results show important different behaviors between two-dimensional and three-dimensional capsules in shear flow. For two-dimensional non-circular capsules without considering the membrane bending rigidity, or considering the bending with the minimum bending-energy configurations (shapes at which the bending-energy has a global minimum) being uniform-curvature shapes, the capsules will always achieve the steady tank treading motion (a capsule deforms to a steady shape with a steady inclination and the membrane rotates around the liquid inside). However, for three-dimensional non-spherical capsules without membrane bending rigidity, such a steady mode does not exist; with the shear rate decreasing, the three-dimensional capsules’ motion changes from swinging mode (a capsule undergoes periodic shape deformation and inclination oscillation while its membrane is rotating around the liquid inside) to flipping mode. The deformation of two-dimensional capsules, with their initial non-circular shapes taken as the minimum bending-energy configurations, is also considered. It is quite interesting to find such two-dimensional capsules behave qualitatively similar to three-dimensional capsules: there is a swinging-to-flipping transition induced by lowering the shear rate.     

Inertia effect on the transient deformation of elastic capsules in simple shear flow

The transient deformation of cylindrical liquid-filled capsules with elastic membranes is studied in simple shear flow at small and moderate Reynolds numbers. The aim of the study is to investigate the inertia effect on the deformation of elastic capsules and the flow structure around them. The simulation is based on a hybrid method which introduces the immersed boundary concept in the framework of the multi-block lattice Boltzmann model. The deformation of capsules with circular and elliptical resting shapes is studied; the membrane constitutive model is Hooke’s law. However, the present model can be implemented to capsules with arbitrary resting configurations and constitutive laws. The simulation results show that inertia has important effect on the transient deformation process, steady configuration and tank treading frequency of a capsule in simple shear flow; Inertia also significantly affects the flow structure and vorticity field around and inside a capsule.     

Shape optimization of shear panel damper for improving the deformation ability under cyclic loading

This paper presents a shape optimization approach for a low-yield steel shear panel damper to improve the deformation ability. A minimization problem of maximum cumulative equivalent plastic strain, an index of the deformation ability of the shear panel damper is formulated subject to a constraint of total absorbing energy. The response surface methodology as well as the design of experiment technique are applied to the optimization process. In this study, finite element analysis with iso-tropic/kinematic hardening model is adopted to simulate the cyclic elasto-plastic behavior instead of experimental approach, and the numerical solutions are validated by comparing with previous experimental results. With the numerical analysis, the shape parameters effects are investigated and second order polynomials are fitted to obtain the regression equations for the maximum cumulative equivalent plastic strain and the total absorbing energy. The final optimal shape is determined by using the established regression equations. The shape optimization approach can substantially improve the deformation capacity of the shear panel damper.     

A simple selectively integrated torsion—Flexure coupled tapered beam element with transverse shear deformation

A tapered beam element with torsional flexibility and transverse shear deformation is developed for use in swept plate studies. Recently established guidelines for selective reduced integration allow the use of independent interpolation functions for the transverse deflection $\text{w}$, rotation ψ and torsional rotation θ to obtain an element that does not lock in extremely thin situations encountered in thin beam/plate analysis. The element is tested for free vibration and for the static case of a severely swept cantilever plate of high aspect-ratio subjected to uniform distributed load. The results indicate very good performance of the element.     

一种微变形的WGMRES算法

GMRES方法是解决大型稀疏非对称的线性方程组最有效的方法,在计算中存在着许多对标准GMRES进行改进的算法。Weighted GMRES算法使用加权方式来加快GMRES算法的收敛速度。主要研究WGMRES算法的计算过程,并对此做出简单的变形,从而提出一种新的计算方法。实验结果表明,该方法具有加快收敛的效果。     

大型索网天线结构在轨变形分析及软件研发

针对大型索网天线结构分析存在拉索单元抗拉不抗压引起的本构非线性和大变形引起的几何非线性等难点,基于参变量变分原理和非线性有限元法,开发大型索网天线结构在轨变形分析与预测软件LFAS,实现周边桁架式索网天线结构的参数化建模、静力分析、动力分析以及找形分析等功能;该软件按模块化设计,可以方便地扩展其他功能模块.数值算例表明：LFAS具有更高的收敛性和精度,特别适合大型索网天线结构的高精度分析和控制.     

Topological sensitivity analysis in large deformation problems

The aim of the present work is to apply the topological sensitivity analysis (TSA) to large-deformation elasticity based on the total Lagrangian formulation. The TSA results in a scalar function, denominated topological derivative, that gives for each point of the domain the sensitivity of a given cost function when a small hole is created. An approximated expression for the topological derivative is obtained by numerical asymptotic analysis. Numerical results of the presented approach are considered for elastic plane problems.     

On the evaluation of stress intensity factors for a simple crack under parametric loading

Two analytical approaches for the evaluation of stress intensity factors at the tips of a single straight crack in plane isotropic elasticity under symmetric tensile loading along the crack edges including a parameter are considered. The first method leads to an ordinary differential equation for the stress intensity factor (or to a system of such equations) with respect to the loading parameter, whereas the second method leads to closed-form results for the related integral by using Laplace transform techniques. Several elementary transcendental functions, such as the exponential function, were used in the loading distribution for an illustration of the present approaches and related results are presented. The computer algebra system Maple V was also used together with Gröbner bases (for the derivation of the differential equations) and with definite integration (for the derivation of the closed-form formulae).     

Divergence and flutter instabilities of nanobeams in moving state accounting for surface and shear effects

Transverse vibrations of elastically rested moving beam-like nanostructures accounting for surface effect are of high concern. The role of nonlocality on the free dynamic response of moving nanobeams has been revealed in recent years; nevertheless, the influence of the surface energy on the mechanical behavior of such elements has not been explained yet. In this paper, equations of motion of rested nanoscaled beams in the moving state are derived carefully via surface energetic-shear deformable beam models. Subsequently, the transverse vibrations of the nanostructure are evaluated using Galerkin-based assumed mode method. The explicit expressions of divergence velocities are obtained analytically, and these are successfully verified with the results of a numerical approach. The roles of crucial parameters on the first divergence velocity are addressed in some detail. Additionally, the stable and unstable regions are determined systematically and the influence of both surface energy and shear energy on the stability of moving nanostructure is discussed.     

Buckling of laminated anisotropic shells including transverse shear deformation

The subspace iteration method used in the buckling options of the shell code FASOR is discussed. Buckling modes of a laminated anisotropic cylindrical shell and a sandwich spherical cap are presented and compared with previously published results.     

Amplifying shear deformation of finger pad increases tracing distances

Human sensory inputs and motor outputs mutually affect one another. We pursue the idea that a tactile interface can influence human motor outputs by intervening in sensory–motor relationships. This study focuses on the shear deformation of a finger pad while a person traces a line or circle. During these tracing movements, the finger pads were deformed using a tactile interface. The tracing distances increased when the finger pad deformations were amplified by the tactile interface, which indicates that the intervention in the haptic sensorimotor loop affected the tracing movements. Elucidation of such interaction between the tracing movements and the shear deformations of finger pads enhances the understanding of human-assistive haptic techniques.     

传感器在大型锚杆剪切模型试验中的应用

在某大型水利水电工程建设的原位监测工作中,发生锚杆应力计应力超量程问题.是否由裂隙的滑移剪切造成的,在室内进行了大型锚杆剪切模型试验,模拟锚杆在滑移剪切荷载作用下的工作性状.在试验中采用了多种类型的应力和应变传感器,并进行了优化组合,为整个试验数据的成功获得奠定了基础.     

Analytical method of predicating the instabilities of a micro arch-shaped beam under electrostatic loading

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.     

Elastic-plastic large deformation analysis of soil slopes

A complete finite-element stress analysis regarding the static response of a homogeneous vertical slope throughout the entire range of loading up to ultimate load is presented. Soil is modelled as a linear elastic-perfectly plastic material with the Drucker-Prager yield condition and its associated flow rule. Emphasis has been put on the effect of large soil deformation on the solutions.

It was found that (1) large deformation analysis is required for any progressive failure solutions of slopes; (2) bulging or progressive loss of ground along the vertical cut is the actual mode of failure for a vertical slope; (3) the velocity field near the limit load shows both “discontinuity” and “slip” along a well defined surface which corresponds to a log-spiral shape; and (4) comparison of properly defined limit or collapse load between finite-element solutions and limit analysis solutions shows an excellent agreement.     

Dynamic stability of bars considering shear deformation and rotatory inertia

Dynamic stability of bars including shear deformation and rotatory inertia are investigated in this paper using finite element formulation for various slenderness ratios. Stability and frequency parameters and instability regions for these bars for various end conditions and slenderness ratios are presented. A master dynamic stability curve covering all the end conditions and slenderness ratios of the bar is presented in the non-dimensionalized form.     

Effect of shear deformation on the yielding of circular plates

Shear Deformation Plate Theory (SDPT) is used to analyse the first yield response of axisymmetric circular plates. Expressions for the first yield pressure and the associated plate centre deflection of uniformly loaded, simply supported and clamped plates are presented. Corresponding Classical Thin Plate Theory (CPT) expressions are also deduced. It is demonstrated that the SDPT and CPT expressions are related via correction factors which are functions of the plate thickness-ratio β, and Poisson's ratio. Graphs of the correction factors plotted against β are presented. They illustrate that inherent shear flexibility causes a slight reduction in the first yield pressure compared with the CPT value when the plate edges are simply supported and a slight increase when they are clamped. Plate centre deflections are, however, increased significantly for both support conditions.     

Axisymmetric pressure boundary loading for finite deformation analysis using p-FEM

Follower loads, i.e. loads which depend on the boundary displacements by definition, frequently occur in finite deformation boundary-value problems. Restricting to axisymmetrical applications, we provide analytical and numerical solutions for a set of problems in compressible Neo-Hookean materials so to serve as benchmark problems for verifying the accuracy and efficiency of various FE methods for follower load applications. Thereafter, the weak formulation for the follower-load in 3-D domain is reduced to an axisymmetrical setting, and, subsequently, consistently linearized in the framework of p-FEMs, exploiting the blending function mapping techniques. The set of axisymmetric benchmark solutions is compared to numerical experiments, in which the results obtained by a p-FEM code are compared to these obtained by a state-of-the-art commercial h-FEM code and to the “exact” results. These demonstrate the efficiency and accuracy of p-FEMs when applied to problems in finite deformations with follower loads.