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The purpose of this paper is to report the implementation of an alternative time integration procedure for the dynamic non-linear analysis of structures.

The time integration algorithm discussed in this work corresponds to a spectral decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion. This is achieved by solving an eigenvalue problem in the time domain that only depends on the approximation basis being implemented. Complete sets of orthogonal Legendre polynomials are used to define the time approximation basis required by the model.

A classical example with known analytical solution is presented to validate the model, in linear and non-linear analysis. The efficiency of the numerical technique is assessed. Comparisons are made with the classical Newmark method applied to the solution of both linear and non-linear dynamics. The mixed time integration technique presents some interesting features making very attractive its application to the analysis of non-linear dynamic systems. It corresponds in essence to a modal decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion.

One of the main advantages of this technique is the possibility of considering relatively large time step increments which enhances the computational efficiency of the numerical procedure. Due to its characteristics, this method is well suited to parallel processing, one of the features that have to be conveniently explored in the near future.

This paper aims to reasonably quantify the radial deformation of turbine blade from a probabilistic design perspective. A probabilistic design for turbine blade radial deformation considering non-linear dynamic influences can quantify risk and thus control blade tip clearance to further develop the high performance and high reliability of aeroengine. Moreover, the need for a cost-effective design has resulted in the development of probabilistic design method with high computational efficiency and accuracy to quantify the effects of these uncertainties.

An extremum response surface method-based support vector machine (SVM-ERSM) was proposed based on SVM of regression to improve the computational efficiency and precision of blade radial deformation dynamic probabilistic design regarding non-linear material properties and dynamically thermal and mechanical loads.

Through the example calculation and comparison of methods, the results show that the blade radial deformation reaches at the maximum at t = 180 s; the probabilistic distribution and inverse probabilistic features of output parameters and the major factors (rotor speed and gas temperature) are gained; besides, the SVM-ERSM holds high computational efficiency and precision in the non-linear dynamic probabilistic design of aeroengine typical components.

The present efforts provide a method to design turbine besides other aeroengine components considering dynamic and non-linear factors base on probabilistic design for further research.

Moreover, the present study provides a way to design dynamic (motion) structures from a probabilistic perspective.

It is proved that the dynamic probabilistic design-based SVM-ERSM could produce a more reasonable blade radial deformation while maintaining low failure probability, as well as offer a useful reference for blade-tip clearance control and a promising insight to the optimal design of aeroengine typical components.

This paper presents several methods for enhancing computational efficiency in both static and dynamic analysis of structural systems with localized non‐linear behaviour. A significant reduction of computational effort with respect to brute‐force non‐linear analysis is achieved in all cases at the insignificant (or no) loss of accuracy. The presented methodologies are easily incorporated into a standard computer program for linear analysis.

Dynamic non‐linear circuits driven by DC voltage and current sources are considered in the paper. The problem of identification of asymptotically stable equilibrium states is analyzed. The circuits are studied where there is a one‐to‐one correspondence between each operating point of a DC model of a dynamic circuit and equilibrium state of the dynamic circuit. A method is developed, based on quantities concerning resistive circuits only, enabling us to select some of the operating points being asymptotically stable equilibrium states. It is shown that these operating points are asymptotically stable equilibrium states of some class of dynamic circuits which differ one from another in characteristics of the capacitors and inductors. The approach is illustrated by a numerical example.

A method for non‐linear static and dynamic analysis of flexible systems submerged in water is outlined. The systems considered here include cable and beam elements, as well as buoys and clump weights. Contact and lift‐off between members and the sea floor is also accounted for. The formulation used allows for very large deformations and material non‐linearities. Hydrostatic buoyancy and hydrodynamic drag forces are considered throughout the analyses. These capabilities have been implemented in the general purpose non‐linear finite element program FENRIS. Aspects concerning efficient solution of the non‐linear static and dynamic equations are discussed. In particular, an efficient start‐up procedure for analysis of highly flexible systems is described. The paper shows applications involving static and dynamic analysis of a floating structure kept in place by six mooring lines and a flexible riser system.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

The paper describes the application of the simple rotation‐free basic shell triangle (BST) to the non‐linear analysis of shell structures using an explicit dynamic formulation. The derivation of the BST element involving translational degrees of freedom only using a combined finite element–finite volume formulation is briefly presented. Details of the treatment of geometrical and material non linearities for the dynamic solution using an updated Lagrangian description and an hypoelastic constitutive law are given. The efficiency of the BST element for the non linear transient analysis of shells using an explicit dynamic integration scheme is shown in a number of examples of application including problems with frictional contact situations.

Complexity researchers have identified four basic assumptions underlying non‐linear dynamic systems (NDS): the assumption that change is a constant; the assumption that emergent systems are not reducible to their parts; the assumption of mutual dependence; and the assumption that complex systems behave in non‐proportional ways. In this paper I use these new assumptions as a basis for explaining why order emerges in organizations, and for uncovering a three‐stage process model of complex adaptive systems change (CASC). The insights from these NDS models are revealed through examples from two entrepreneurial firms undergoing transformative shifts in their development. These assumptions of NDS and the model of CASC may therefore be useful for understanding order creation and self‐organizing processes in work groups, project ventures, and organizations.

Educational change and improvement are constant processes. Practically every country in the world today is attempting to improve, reform, transform or change its educational system. The results of these development efforts have generally been disappointing. A general consensus seems to be that the gap between societal expectations and educational achievements is wide and becoming greater. The perceived failures of education are particularly difficult for political and educational leaders to understand given the massive influx of resources invested in educational systems in recent years. This is a result of a linear expectation wherein output is proportional to the input. Non‐linear theory, proposed in this paper as a more valid way of conceptualizing educational development efforts, does not assume this proportional relationship. This paper addresses non‐linear theory by using it to examine educational development efforts in Western and Eastern European nations.