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.     

A multigrid accelerated hybrid unstructured mesh method for 3D compressible turbulent flow

 A cell vertex finite volume method for the solution of steady compressible turbulent flow problems on unstructured hybrid meshes of tetrahedra, prisms, pyramids and hexahedra is described. These hybrid meshes are constructed by firstly discretising the computational domain using tetrahedral elements and then by merging certain tetrahedra. A one equation turbulence model is employed and the solution of the steady flow equations is obtained by explicit relaxation. The solution process is accelerated by the addition of a multigrid method, in which the coarse meshes are generated by agglomeration, and by parallelisation. The approach is shown to be effective for the simulation of a number of 3D flows of current practical interest. Sponsored by The Research Council of Norway, project number 125676/410 Dedicated to the memory of Prof. Mike Crisfield, a respected colleague     

Prediction of brittle-to-ductile transitions in polystyrene

In this study it is attempted to predict brittle-to-ductile transitions (BDTs) in polystyrene blends, induced either by an increase in temperature or by a decrease in inter-particle distance. A representative, two-dimensional volume element (RVE) of a polystyrene matrix with 20% circular voids, is deformed in tension. During deformation a hydrostatic-stress based craze-nucleation criterion [1] is evaluated. The simulations demonstrate that crazes initiate at low temperatures while a transition from crazing to shear yielding (BDT) is found around 75 °C. The numerical results correlate well with tensile tests on similar heterogeneous polystyrene. The presence of an absolute length, as experimentally found, is more difficult to explain. Near a free surface a T_g-depression is measured for polystyrene and also the resistance to indentation in polystyrene is lower than expected from bulk properties. Both observations are rationalised by an enhanced segmental mobility of chains near a free surface. As a consequence of these findings, an absolute length-scale could be incorporated in the numerical simulations. For simplicity, the length-scale is modelled by taking a temperature gradient over a thin layer near the internal free surfaces of the RVE. Deformation of the RVE with different absolute length-scales shows that indeed also the experimentally found brittle-to-ductile transition can be predicted if the ligament thickness between the inclusions (‘voids’) in polystyrene is below a critical value of ca. 15 nm.     

Field Static Load Test on Kao-Ping-Hsi Cable-Stayed Bridge

Field load testing is an effective method for understanding the behavior and fundamental characteristics of a cable-stayed bridge. This paper presents the results of field static load tests on the Kao-Ping-Hsi cable-stayed bridge, the longest cable-stayed bridge in Taiwan, before it was open to traffic. A total of 40 loading cases, including the unit and distributed bending and torsion loading effects, were conducted to investigate the bridge behavior. The atmospheric temperature effect on the variations of the main girder deflections was also monitored. The results of static load testing include the main girder deflections, the flexural strains of the prestressed concrete girder, and the variations of the cable forces. A three-dimensional finite-element model was developed. The results show that the bridge under the planned load test conditions has linear superposition characteristics and the analytical model shows a very good agreement with the bridge responses. Further discussion of deflection and cable forces of the design specifications for a cable-stayed bridge is also presented.     

Finite element piezothermoelasticity analysis and the active control of FGM plates with integrated piezoelectric sensors and actuators

 An efficient finite element model is presented for the static and dynamic piezothermoelastic analysis and control of FGM plates under temperature gradient environments using integrated piezoelectric sensor/actuator layers. The properties of an FGM plate are functionally graded in the thickness direction according to a volume fraction power law distribution. A constant displacement-cum-velocity feedback control algorithm that couples the direct and inverse piezoelectric effects is applied to provide active feedback control of the integrated FGM plate in a closed loop system. Numerical results for the static and dynamic control are presented for the FGM plate, which consists of zirconia and aluminum. The effects of the constituent volume fractions and the influence of feedback control gain on the static and dynamic responses of the FGM plates are examined. Received: 13 March 2002 / Accepted: 5 March 2003 The work described in this paper was supported by a grant awarded by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1024/01E).     

Numerical Study of Finite Element Method Based Solutions for Propagation of Wetting Fronts in Unsaturated Soil

The accurate prediction of the propagation of a wetting front in an unsaturated soil subjected to surficial infiltration is of practical importance to many geotechnical and geoenvironmental problems. The finite element method is the most common solution technique as the hydraulic soil properties are highly nonlinear. Two important issues are often found to create difficulties in such analyses. First, numerical oscillations are usually observed in the calculated pore pressures at the wetting front. Second, when a reasonable mesh size and time step are used, the elevation of the wetting front may be seriously overpredicted. This paper is focused on the second issue. The under-relaxation (UR) technique used in the iterative process within each time step is found to have a serious impact on rate of convergence with refinement in mesh size and time step. Two different techniques are typically used; the first evaluates the hydraulic conductivity using an average of heads calculated from the preceding time node and the most recent iteration of the current time node (UR1), and the second evaluates the hydraulic conductivity using the average of heads calculated from the two most recent iterations of the current time nodes (UR2). The study shows that UR1, which is adopted in programs such as SEEP/W, ensures that the solution converges rapidly to a stable solution within a time step, but may converge to the wrong wetting front at a given elapsed time unless a sufficiently refined mesh is used. UR2 converges much more slowly within a time step, but the error in the wetting front is smaller than that generated by UR1.     

A continuum-based modeling of MEMS devices for estimating their resonant frequencies

A continuum-based modeling of coupled electrostatics-structure interactions is presented for the frequency computations of MEMS devices. The present general formulation of electrostatics accounting for free space is validated first by specializing it to one-dimensional uniform motion of conducting surfaces and comparing the resulting electrostatics to conventional lumped models. The general coupled electrostatics-structure interactions are then applied for the prediction of resonant frequencies of MEMS devices due to bias-voltage changes and temperature variations. Comparisons of predicted resonant frequencies obtained by the present coupled electrostatics-structure interaction models with experimental results available in the literature demonstrate that the proposed continuum-based interaction modeling yields high-confidence predictions of resonant frequencies of MEMS devices.     

Model Validation for Bridge-Road-Vehicle Dynamic Interaction System

The dynamic response of highway bridges subjected to moving truckloads has been observed to be dependent on (1) dynamic characteristics of the bridge; (2) truck configuration, speed, and lane position on the bridge; and (3) road surface roughness profile of the bridge and its approach. Historically, truckloads were measured to determine the load spectra for girder bridges. However, truckload measurements are either made for a short period of time [for example, weigh-in-motion (WIM) data] or are statistically biased (for example, weigh stations) and cost prohibitive. The objective of this paper is to present results of a 3D computer-based model for the simulation of multiple trucks on girder bridges. The model is based on the grillage approach and is applied to four steel girder bridges tested under normal truck traffic. Actual truckload data collected using a discrete bridge WIM system are used in the model. The data include axle loads, truck gross weight, axle configuration, and statistical data on multiple presence (side by side or following). The results are presented as a function of the static and dynamic stresses in each girder and compared with code provisions for dynamic load factor. The study provides an alternate method for the development of live-load models for bridge design and evaluation.     

A comparative study of numerical solutions to non-linear discrete crack modelling of concrete beams involving sharp snap-back

Numerical problems are often encountered in modelling crack propagation in concrete beams using non-linear finite element (FE) analysis, especially when sharp snap-back behaviour in load-displacement relations occurs. This paper firstly identifies 16 arc-length control based numerical strategies based on extensive literature review. They are then used to carefully model the structural behaviour of a four-point single notched shear beam using discrete crack modelling approach in which cracks are represented by interface elements with bilinear softening constitutive laws. Based on extensive FE analyses, detailed comparisons of the merits and demerits of these numerical algorithms are then made. The results indicate that the effectiveness and efficiency of different algorithms may vary considerably from one to another, with the local arc-length based procedures in conjunction with tangential stiffness strategy and reversible unloading model being the most robust.