An element-based displacement preconditioner for linear elasticity problems

Finite element analysis of problems in structural and geotechnical engineering results in linear systems where the unknowns are displacements and rotations at nodes. Although the solution of these systems can be carried out using either direct or iterative methods, in practice the matrices involved are usually very large and sparse (particularly for 3D problems) so an iterative approach is often advantageous in terms of both computational time and memory requirements. This memory saving can be further enhanced if the method used does not require assembly of the full coefficient matrix during the solution procedure. One disadvantage of iterative methods is the need to apply preconditioning to improve convergence. In this paper, we review a range of established element-based preconditioning methods for linear elastic problems and compare their performance with a new method based on preconditioning with element displacement components. This new method appears to offer a significant improvement in performance.     

Extracting Modes of Constrained Structure with Elastic Supports from Free Test Data

The dynamic flexibility (DF) and improved dynamic flexibility (IDF) methods can be applied to extract constrained structural modes from free-free modal test data. The residual flexibility method is also good for boundaries of constrained structure with rigid supports. Under elastic support boundary conditions both the DF and residual flexibility methods cannot produce accurate results. This paper expands the previously published IDF method to become a more general approach for structural design engineers. A new method called the general dynamic flexibility (GDF) method has been developed in this paper to extract constrained structural modes from free test data. The GDF method can always be applied as follows: (1) when the boundary support stiffness is very stiff, the GDF method can accurately obtain results from rigid support as by Liu et al. in 2001 and Zhang and Wei in 2003; (2) when the support stiffness is soft, the present method can produce results similar to those free-free modal parameters measured by hanging structures using rubber band; (3) when the support stiffness is zero, the method can reproduce true free-free modal parameters; and (4) when the support stiffness has any finite values, the GDF method can also achieve satisfactory results for engineering use. The algorithm included in the GDF method converges rapidly and is numerically stable in the analysis. This feature is very practical for many engineering applications for using the GDF method.     

Viscoelastic State for the Solutions of Spherically Symmetric Viscoelasticity Problems

The solutions of the spherically symmetric, linear, isothermal, and transient viscoelasticity problems via reciprocity theorem have been investigated for a specific material. The integral form of stress–strain relations has been used. The Laplace transform of a viscoelastic state, which is necessary for the integral equation arising as a result of reciprocity theorem, has been derived. This integral equation has been solved by Laplace transform. A sample problem has been solved to test the presented formulation. A numerical application of the analytic solution of this problem has been given.     

Defining Yield from Bender Element Measurements in Triaxial Stress Probe Experiments

This paper describes the elastic response of a block sample of compressible Chicago glacial clay under a variety of stresses and its relationship with the deformation characteristics at relatively large strains. The elastic shear stiffness was obtained from bender element tests during consolidation and shearing in drained triaxial stress probe tests. An empirical correlation was established based on the elastic shear stiffness in a preyield condition. By comparing the empirical correlation with the measured elastic shear stiffness in the stress region during probing, the changes of elastic shear stiffness were investigated. The departure of elastic shear stiffness from values computed by the empirical relation based on K0 loading directly relates to the yielding characteristics of the clay. The large-scale change of soil structure at yielding alters the well-established relationship between the elastic shear stiffness and stresses in the preyield condition. The mechanical yielding response of clays can be detected based on the systematic analysis of the elastic shear wave velocities.     

Boundary-integral equation analysis of twisted internally cracked axisymmetric bimaterial elastic solids

 Green's function is obtained for the infinite bimaterial elastic solid, containing an internal circular interface crack, loaded by a unit tangential co-axial circular source. An axisymmetric direct boundary integral equation (BIE) is used for the analysis of a finite bimaterial axisymmetric body containing an internal circular interface crack and a finite homogeneous cracked cylinder, both under torsional loading. Using the proposed technique, no discretization of the crack surface is necessary. Numerical results for both examples as obtained by the proposed method are presented and discussed. Received: 29 October 2001 / Accepted: 29 May 2002     

Elasticity of Space-Time: Basis of Newton’s 2nd Law of Motion

In this paper we derive Newton’s 2nd Law of Motion from the constitutive equation of elasticity of a space-time continuum in four dimensions. This we do by introducing a four-dimensional material continuum with a Minkowskian metric, in analogy with Einstein’s general theory of relativity. The four-continuum is deformable in both space and time. The physics of the deformation is embedded in a variational principle, which is a form-invariant extension of its classical mechanical counterpart in three dimensions, but with the acceleration term absent. General dynamic equations of elasticity in four dimensions are thereby derived. When the constraint of temporal inextensibility (universal time) is introduced, these equations yield readily the dynamic equations of elasticity in three dimensions. The presence of the inertia term in these equations, is a direct consequence of the temporal curvature induced by the deformation of the four-continuum. Newton’s law of motion for rigid bodies follows when the additional constraint of spatial inextensibility is introduced.     

Stress analysis with arbitrary body force by boundary element method

Linear stress analysis without body force can be easily carried out by means of the boundary element method. Some cases of linear stress analysis with body force can also be solved without the domain integral. However domain integrals are generally necessary to solve the linear stress problems with complicated body forces. This paper shows that the linear stress problems with complicated body forces can be solved approximately without the domain integral. In order to solve these problems, the domain is divided into small areas using contour lines of body force. In these areas, the distributions of body force are assumed approximately to satisfy the Laplace equation.     

用于数控设备的弹性环联轴器

介绍了一种适用于数控设备改造的无键联轴器，从其原理、设计、加工各方面作了阐述，并且总结了许 多实际应用经验和适用参数。     

Elastohydrodynamic theory for wet oblique collisions

This paper presents a model for oblique collisions of spherical particles with a plane surface covered with a thin liquid layer. Elastohydrodynamic theory developed previously for fully immersed collisions [Davis, Serayssol and Hinch 1986 JFM 63 479-497] is modified for the normal component of motion to account for the finite thickness of the liquid layer. The resulting time evolution of the film thickness profile is then used along with sliding lubrication to determine the tangential component of motion. The critical Stokes number (dimensionless ratio of particle inertia and viscous forces), below which no rebound is seen, is predicted in terms of the physical properties of the materials involved in the collision, as described by a compliance parameter representing a dimensionless measure of elastic deformation due to viscous forces. Beyond the critical Stokes number, the normal restitution coefficient is found to increase with the Stokes number and the compliance parameter, asymptoting to the dry restitution coefficient at high Stokes numbers. The lubrication suction resistance during rebound is limited by cavitation. The tangential restitution is independent of the impact angle and is linearly dependent on the ratio of the fluid layer thickness to the sphere radius, in addition to depending on the Stokes number and compliance parameter. The tangential restitution is found to be close to unity and is generally higher for a larger value of the compliance parameter. Moreover, the tangential restitution is seen to increase with the Stokes number at small compliance and decrease with the Stokes number at large compliance. The change in rotational velocity exhibits trends that are the reverse of the tangential restitution. Finally, closed-form expressions have been developed for describing the restitution coefficients and dimensionless change in rotational velocity.     

化学微交联聚氯乙烯的结构和性能

通过氯乙烯/邻苯二甲酸二烯丙酯(VC/DAP)悬浮共聚,合成了含部分凝胶结构的化学微交联PVC树脂,对微交联PVC的玻璃化转变行为、加工性能、消光性能、加热-形变行为和力学性能进行了研究。当DAP用量在0.25%mol以下时,PVC的玻璃化温度变动不大。凝胶含量的增加将导致交联PVC_d~T的光泽度下降,消光性能提高;塑化时间和加工扭矩均增加,加工性能急剧变差;加热变形值下降,最高使用温度提高。凝胶对PVC拉伸性能的影响较为复杂,但压缩永久变形则随凝胶含量的增加而下降,材料的弹性性能逐渐提高。