Thermostructural analysis of rotationally symmetric multidirectional fibrous composite structures

The finite element method is used to analyze the thermostructural behavior of rotationally symmetric multidirectional fibrous composite structures. The analysis covers, in a single envelope, both heat transfer and the resulting elastic response associated with an anisotropic axisymmetric solid of revolution. The steady state heat transfer analysis includes all the normal modes, namely conduction, convection and radiation, and also the presence of external fluxes and internal heat generation sources. The multidirectional material model is based on a rotationally symmetric unit cell containing fibers oriented in three orthogonal planes such that they maintain material axisymmetry. Existing micromechanical theories and conventional transformation rules are employed to constitutive relations for proposed model. In the example analyses, an uncooled convergent-divergent nozzle is analyzed to project the advantages of a few advanced composites as thermostructural materials of practical importance.     

An interactive graphic software for the analysis of rotationally symmetric structures

Several efficient programs to analyse different kinds of structures have been developed at this centre. But the data preparation and comprehension of output have been time consuming. To facilitate data preparation some dedicated preprocessors were written but it has not been possible to make a visual check on structure modelling, deformations and stress patterns. With the availability of graphic facilities at this centre, the present project was taken up to develop graphic software for a program, ROTSYM, for the analysis of rotationally symmetric structures like cooling towers, chimneys, watertanks, etc. This software enables the designer to display the modelled structure, deformed geometry and stress patterns; thus cutting down the time required in data checking and output verification.     

Static analysis of circumferentially periodic structures with Potters' scheme

A rotationally or circumferentially periodic structure is one in which a series of identical sectors is repeated in the circumferential direction. Each sector is assumed to be loaded identically. Since the deflection shape of each sector is identical, only one sector has been taken for the analysis. The Potters' scheme of solving simultaneous equations is modified for the above analysis. This method is applied to different kinds of problems and results are compared.     

Explicit exact analysis of infinite periodic structures under general loading

This paper deals with the explicit analysis of infinite periodic structures under arbitrary loadings. In the context or structural stiffness optimization, with its inherent problem of multiple reanalysis, the purpose is to obtain expressions for the stress resultants anywhere in the infinite structure as an explicit function of the stiffnesses of the elements. Following the method of the representative cell the analysis of an infinite structures is reduced to the analysis of single module under transformed loading and boundary conditions by using the discrete Fourier transform. This produces the equilibrium, strain-displacements and constitutive equations in terms of complex-valued displacements, generalized strains and generalized stresses transforms. Next an existing formula is used to write the stress resultants transforms explicitly in terms of the stiffnesses. Finally one computes the stress resultants wherever needed in the real structure by means of the inverse Fourier transform. The exact formula for the stress resultants is usually impractical due to the large number of terms involved in the analytical expressions. What makes the approach practical herein is the very reduced size of the repeating module that is to be analysed, which renders the analytical formula more tractable in many cases. The technique is illustrated with the explicit analysis of an infinite truss with 1D translational symmetry and of an infinite grid of orthogonal beams on elastic supports with 2D translational symmetry. Received December 4, 2000     

Parallel processing techniques for finite element analysis of nonlinear large truss structures

Methods were developed for parallel processing of finite element solutions of large truss structures. The parallel processing techniques were implemented in two stages, i.e., the repeated forming of the nonlinear global stiffness matrix and the solving of the global system of equations. The Sequent Balance 21000 parallel computer was employed to demonstrate the procedures and the speed-up.     

Parallel multilevel solution of nonlinear shell structures

The analysis of large-scale nonlinear shell problems asks for parallel simulation approaches. One crucial part of efficient and well scalable parallel FE-simulations is the solver for the system of equations. Due to the inherent suitability for parallelization one is very much directed towards preconditioned iterative solvers. However thin-walled-structures discretized by finite elements lead to ill-conditioned system matrices and therefore performance of iterative solvers is generally poor. This situation further deteriorates when the thickness change of the shell is taken into account. A preconditioner for this challenging class of problems is presented combining two approaches in a parallel framework. The first approach is a mechanically motivated improvement called ‘scaled director conditioning’ (SDC) and is able to remove the extra-ill conditioning that appears with three-dimensional shell formulations as compared to formulations that neglect thickness change of the shell. It is introduced at the element level and harmonizes well with the second approach utilizing a multilevel algorithm. Here a hierarchy of coarse grids is generated in a semi-algebraic sense using an aggregation concept. Thereby the complicated and expensive explicit generation of course triangulations can be avoided. The formulation of this combined preconditioning approach is given and the effects on the performance of iterative solvers is demonstrated via numerical examples.     

周期B样条基函数系数的并行算法

在现有周期B样条插值方法中,需要用迭代算法确定B样条基函数系数。针对现有方法的不足,建立B样条基函数系数的并行算法。首先构造周期区域的正交B样条基,得出正交B样条基函数系数的并行算法;进一步利用正交B样条基函数系数与B样条基函数系数的关系,得出B样条基函数系数的并行算法;最后推导二阶、三阶、四阶周期插值B样条基函数系数及插值点函数值的显式算式。实验证明了该方法在实现B样条基函数系数快速并行算法的同时保持了B样条基函数简单的函数关系。     

Free vibration analysis of a rotationally restrained (FG) nanotube

Microsystem Technologies - In this study, free lateral vibration behavior of a functionally graded nanobeam in an elastic matrix with rotationally restrained ends is studied based on the...     

A one‐step leapfrog HIE‐FDTD method for rotationally symmetric structures

In this work, they propose a one‐step leapfrog hybrid implicit‐explicit finite‐difference time‐domain (HIE‐FDTD) method for body‐of‐revolution (BOR). Meanwhile, its Convolutional Perfect Matched Layer (CPML) absorbing boundary condition is implemented. In this method, the implicit difference is applied in the angular direction. All the resultant updating equations are still explicit. However, the stability condition of the proposed method is relaxed. The analytical analysis shows that its time step is only determined by the smaller one of spatial increments Δρ and Δz. A scattering example is provided to demonstrate the new algorithm. At the same time, the relative of reflection error of the CPML is given with comparisons of Mur.     

Optimal design of periodic structures using evolutionary topology optimization

This paper presents a method for topology optimization of periodic structures using the bi-directional evolutionary structural optimization (BESO) technique. To satisfy the periodic constraint, the designable domain is divided into a certain number of identical unit cells. The optimal topology of the unit cell is determined by gradually removing and adding material based on a sensitivity analysis. Sensitivity numbers that consider the periodic constraint for the repetitive elements are developed. To demonstrate the capability and effectiveness of the proposed approach, topology design problems of 2D and 3D periodic structures are investigated. The results indicate that the optimal topology depends, to a great extent, on the defined unit cells and on the relative strength of other non-designable part, such as the skins of sandwich structures.     

Parallel generation of adaptive multiresolution structures for image processing

In the paper we present an algorithm for creating region-adjacency-graph (RAG) pyramids on TurboNet, an experimental parallel computer system. Each level of these hierarchies of irregular tessellations is generated by independent stochastic processes that adapt the structure of the pyramid to the content of the image. RAGs can be used in multiresolution image analysis to extract connected components from labeled images. The implementation of the algorithm is discussed and performance results are presented for three different communication techniques which are supported by the TurboNet's hybrid architecture. The results indicate that efficient communications are vital to good performance of the algorithm. © 1997 by John Wiley & Sons, Ltd.     

Long-time behavior of PML absorbing boundaries for layered periodic structures

In this work we consider a special case of the Perfectly Matched Layer (PML) divergence which is observed by the simulation of the planar periodic structures such as photonic crystal slabs or antenna arrays. This divergence is caused by an excitation of long-living artefact evanescent waves in these structures by an incident external pulse. We study the application of the known remedies to this problem: increasing the distance between the structure and PML, employing the κ parameter, employing non-PML absorbers. We also suggest a new simple and effective solution, where the usual PML is backed by an additional absorbing layer.     

Parallel automatic adaptive analysis

Consideration is given to the techniques required to support adaptive analysis of automatically generated unstructured meshes on distributed memory MIMD parallel computers. Emphasis is placed on the structures needed to support effective parallel computations when the numerical discretization, the mesh, is defined and evolves during the computation. The key base structures are a distributed mesh based on a topological hierarchy, and a parallel distributed octree. Parallel control of the mesh and octree structures is done through a set of partition communication operations and entity migration routines. Load balance is maintained through iterative load balance, or distributed repartitioning. Building on these structures, procedures to automatically generate and adaptively refine meshes in parallel, starting from CAD geometric models, are given. Finally, the combination of these techniques to produce a parallel automated analysis procedure is demonstrated.     

Convergence of topological patterns of optimal periodic structures under multiple scales

The current techniques for topology optimization of material microstructure are typically based on infinitely small and periodically repeating base cells. These base cells have no actual size. It is uncertain whether the topology of the microstructure obtained from such a material design approach could be translated into real structures of macroscale. In this work we have carried out a first systematic study on the convergence of topological patterns of optimal periodic structures, the extreme case of which is a material microstructure with infinitesimal base cells. In a series of numerical experiments, periodic structures under various loading and boundary conditions are optimized for stiffness and frequency. By increasing the number of unit cells, we have found that the topologies of the unit cells converge rapidly to certain patterns. It is envisaged that if we continue to increase the number of unit cells and thus reduce the size of each unit cell until it becomes the infinitesimal material base cell, the optimal topology of the unit cell would remain the same. The finding from this work is of significant practical importance and theoretical implication because the same topological pattern designed for given loading and boundary conditions could be used as the optimal solution for the periodic structure of vastly different scales, from a structure with a few (e.g. 20) repetitive modules to a material microstructure with an infinite number of base cells.     

On analysis of periodic polling systems

New alternative approach to the analysis of polling systems is developed. It is based on the theory of decomposable semi-regenerative processes.     

Precision rotationally invariant curve parameterization

The problem of rotationally invariant approximation of the curve given by points is considered. The arc length is chosen for the curve parameter. The algorithm of calculating it up to the fourth order of accuracy is developed. In addition, other characteristics of the curve are constructed, viz., the slope, the curvature, and its derivative. General requirements to parametric approximation of the curve are considered that provide for rotationally invariant approximation.     

Stability analysis of continuous-time periodic systems via theharmonic analysis

Asymptotic stability of finite-dimensional linear continuous-time periodic (FDLCP) systems is studied by harmonic analysis. It is first shown that stability can be examined with what we call the harmonic Lyapunov equation. Another necessary and sufficient stability criterion is developed via this generalized Lyapunov equation, which reduces the stability test into that of an approximate FDLCP model whose transition matrix can be determined explicitly. By extending the Gerschgorin theorem to linear operators on the linear space l₂, yet another disc-group criterion is derived, which is only sufficient. Stability of the lossy Mathieu equation is analyzed as a numerical example to illustrate the results     

Topology optimization for periodic multi-component structures with stiffness and frequency criteria

Structural and Multidisciplinary Optimization - Design of engineering structures may benefit from reduction in assembly complexity through use of periodic components, in which uniform...