An algorithm for higher order Hopf normal forms

Normal form theory is important for studying the qualitative behavior of nonlinear oscillators. In some cases, higher order normal forms are required to understand the dynamic behavior near an equilibrium or a periodic orbit. However, the computation of high-order normal forms is usually quite complicated. This article provides an explicit formula for the normalization of nonlinear differential equations. The higher order normal form is given explicitly. Illustrative examples include a cubic system, a quadratic system and a Duffing–Van der Pol system. We use exact arithmetic and find that the undamped Duffing equation can be represented by an exact polynomial differential amplitude equation in a finite number of terms.published_or_final_versio

Mixed mode cracks in Reissner plates

Based on the sixth order Reissner plate theory, the generalized displacement functions for a cracked plate are derived by eigenfunction expansion method. The fractal two-level finite element method is employed to obtain the stress (moment and shear) intensity factors for the center cracked plate subjected to out-of-plane bending and twisting loads. The numerical results from the present method are checked with those available in literature. Highly accurate stress intensity factors are predicted for a wide range of thickness to crack length ratio and a full range of PoissonÆs ratio provided that the radius of fractal mesh to thickness ratio is not less than 1/10.postprin

Three-dimensional mixed mode analysis of a cracked body by fractal finite element method

A semi-analytical method namely fractal finite element method is presented for the determination of stress intensity factor for the straight three-dimenisonal plane crack. Using the concept of fractal geometry, infinite many of finite elements are generated virtually around the crack border. Based on the analytical global displacement function, numerous DOFs are transformed to a small set of generalised coordinates in an expeditious way. No post-processing and special finite elements are required to develop for extracting the stress intensity factors. Examples are given to illustrate the accuracy and efficiency of the present method. Very good accuracy (with less than 3% errors) is obtained for the maximum value of SIFs for different modes.postprin

Wind flow in the recessed cavities of a tall building

Fulltext in: http://www.iawe.org/Proceedings/7APCWE/M3D_3.pdfTechnical Session: M3-D Computational Wind Engineering (2), no.3In a congested city like Hong Kong, residential tall buildings are often built with an irregular plan form and with a number of apartments arranged as wing sections extending from a central core. To provide views and sufficient ventilation to the apartments, deeply recessed cavities are placed between adjacent building wings. This paper reports a CFD study of the wind-induced flow inside a recessed cavity of a tall building with an objective to assess the adequacy of ventilation inside the cavity. The dimensions of the cavity are varied systematically to investigate the flow exchange between the cavity and the outside at different heights. It is found that the flow inside the cavity is not a simple cross flow or a stagnation flow. Flow exchange takes place in different directions along the building heights.link_to_subscribed_fulltex

A new reduced control design based on the theory of wave domaincontrol

The work in this paper is based on the theory discussed previously by Wang et al. (1994). The main idea is to establish a transformation, which changes the original system into an image system, in which the control force is designed in the context of wave domain control and wave control, so that the number of degrees of freedom in the undisturbed state of the image system can be reduced. The design of control in the original system can be derived by inverse transformation. This method, compared with the previous one, is more general and is easy to apply.published_or_final_versio

Parametric quadratic programming method for elastic contact fracture analysis

A solution procedure for elastic contact fracture mechanics has been proposed in this paper. The procedure is based on the quadratic programming and finite element method (FEM). In this paper, parametric quadratic programming method for two-dimensional contact mechanics analysis is applied to the crack problems involving the crack surfaces in frictional contact. Based on a linear complementary contact condition, the parametric variational principle and FEM, a linear complementary method is extended to analyze contact fracture mechanics. The near-tip fields are properly modeled in the analysis using special crack tip elements with quarterpoint nodes. Stress intensity factor solutions are presented for some frictional contact fracture problems and are compared with known results where available.postprin

Robust stabilization of singular-impulsive-delayed systems with nonlinear perturbations

Many dynamic systems in physics, chemistry, biology, engineering, and information science have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical process, and these complex dynamic behaviors can be modeled by singular impulsive differential systems. This paper formulates and studies a model for singular impulsive delayed systems with uncertainty from nonlinear perturbations. Several fundamental issues such as global exponential robust stabilization of such systems are established. A simple approach to the design of a robust impulsive controller is then presented. A numerical example is given for illustration of the theoretical results. Meanwhile, some new results and refined properties associated with the M-matrices and time-delay dynamic systems are derived and discussed.published_or_final_versio

Estimating the value enhancement effects of refurbishment

There have been very few empirical studies investigating the value enhancement effects of refurbishment and most rely on cross-sectional data, which cannot show the before and after effects conclusively because of the heterogeneous nature of the properties. The problem of refurbishment is more complicated in buildings or housing estates with multiple-ownerships, since refurbishment is a collective decision, which can sometimes be difficult to achieve. This paper uses panel data in Hong Kong to estimate the impact of refurbishment on the market value of properties in a large housing estate. The results show that the refurbishment brought about approximately a 9% increase in the market value of the properties, which far exceeds the cost of refurbishment. It suggests that property owners of a housing estate will benefit if they can reach a collective decision on renovation.published_or_final_versio

Body-force linear elastic stress intensity factor calculation using fractal two level finite element method

Fractal two level finite element method (F2LFEM) for the analysis of linear fracture problems subjected to body force loading is presented. The main objective here is to show that by employing the F2LFEM a highly accurate and an efficient linear analysis of fracture bodies subjected to internal loading can be obtained as it is hard to find any analytical and exact values of stress intensity factor (SIF) for any kind of geometry subjected to internal loading. Also in this paper, a fast method to transform the body force to the reduced force vector is presented and has been effectively employed. The problems solved here include both the single mode or mixed mode cracks subjected to internal body-force or external loading. In comparison with other numerical algorithms, it seems that with a small amount of computational time and computer storage, highly accurate results can be obtained. © 1995.link_to_subscribed_fulltex

Fractal two-level finite element analysis of cracked Reissner's plate

A cracked thick plate subjected to edge moment and transverse loading was customarily analysed either by a fine finite element mesh or by singular elements. In this paper an alternative method is recommended in which conventional finite elements with infinitesimal mesh are used and the number of unknowns is reduced by interpolating the nodal displacements by means of the global interpolating function around the singular region. The global interpolating function is derived by using eigenfunction technique based on Reissner's transverse shear plate theory. The crack parameters such as stress intensity factor and moment intensity factor can be evaluated directly from the coefficients of the global interpolating function. New elements need not to be generated and integration is avoided completely. Accurate results with error less than 0-5% are achieved with little computational efforts. Examples on edge cracked plate and central cracked plate subjected to both edge moment and transverse loading are considered.link_to_subscribed_fulltex