Search results

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

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.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

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.

The use of linear regression analysis is common in the social sciences. The purpose of this paper is to show the advantage of a qualitative research method, namely, structured qualitative analysis (SQA), over the linear regression method by using different characteristics of data.

Data were gathered from a study of online consumer behavior in Taiwan. The authors changed the content of the data to have different sets of data. These data sets were used to demonstrate how SQA and linear regression works individually, and to contrast the empirical analyses and empirical results from linear regression and SQA.

The linear regression method uses one equation to model different characteristics of data. When facing a data set containing a big and a small size of different characteristics, linear regression tends to provide an equation by modeling the characteristics of the big size data and subsuming those of the small size. When facing a data set containing similar sizes of data with different characteristics, linear regression tends to provide an equation by averaging these data. The major concern is that the one equation may not be able to reflect the data of various characteristics (different values of independent variables) that result in the same outcome (the same value of dependent variable). In contrast, SQA can identify various variable combinations (multiple relationships) leading to the same outcome. SQA provided multiple relationships to represent different sizes of data with different characteristics so it created consistent empirical results.

Two research methods work differently. The popular linear regression tends to use one equation to model different sizes and characteristics of data. The single equation may not be able to cover different behaviors but may lead to the same outcome. Instead, SQA provides multiple relationships for different sizes of data with different characteristics. The analyses are more consistent and the results are more appropriate. The academics may re-think the existing literature using linear regression. It would be interesting to see if there are new findings for similar problems by using SQA. The practitioners have a new method to model real world problems and to understand different possible combinations of variables leading to the same outcome. Even the relationship obtained from a small data set may be very valuable to practitioners.

This paper compared online consumer behavior by using two research methods to analyze different data sets. The paper offered the manipulation of real data sets to create different data sizes of different characteristics. The variations in empirical results from both methods due to the various data sets facilitate the comparison of both methods. Hence, this paper can serve as a complement to the existing literature, focusing on the justification of research methods and on limitations of linear regression.

The analysis of certain structures must be performed with due consideration to non‐linear behavior, such as material and geometric non‐linearities. The existing methods for treating non‐linear structural behavior generally make use of repeated linearization, such as load increment methods. This paper demonstrates that there is an alternative type of linearization that appears to have significant advantages when applied to the analysis of non‐linear structural systems. Briefly stated, this alternative linearization can be thought of as a “monomialization”. This monomial (single‐termed power function) approximation more faithfully models the power function behavior inherent in typical structural systems. Conveniently, it becomes a linear form when transformed into log space. Thus, computational tools based on linear algebra remain useful and effective. Preliminary results indicate that the monomial approximation provides a higher quality approximation to non‐linear phenomena exhibited in structural applications. Consequently, incremental and iterative methods become more effective because larger steps can be taken. The net result is an increase in reliability of the solution process and a significant reduction in computational effort. Two examples are presented to demonstrate the method.

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.

The purpose of this paper is to review recent advances and current issues in the realm of sequentially linear analysis.

Sequentially linear analysis is an alternative to non‐linear finite element analysis of structures when bifurcation, snap‐back or divergence problems arise. The incremental‐iterative procedure, adopted in nonlinear finite element analysis, is replaced by a sequence of scaled linear finite element analyses with decreasing secant stiffness, corresponding to local damage increments. The focus is on reinforced concrete structures, where multiple cracks initiate and compete to survive.

Compared to nonlinear smeared crack models in incremental‐iterative settings, the sequentially linear model is shown to be robust and effective in predicting localizations, crack spacing and crack width as well as brittle shear behavior. To date, sequentially linear analysis has not been devised with a proper crack closing algorithm. Besides, of utmost importance for many practical applications, sequentially linear analysis requires an improvement of the algorithm to deal with non‐proportional loadings.

This article gives an up‐to‐date research overview on the applicability of sequentially linear analysis. For the issue of non‐proportional loading, it indicates solution directions.

A system for optimum reinforcement design and non‐linear analysis of reinforced concrete structures is presented. The specially‐tailored program ORCHID (Optimum Reinforced Concrete Highly Interactive Dimensioning) is utilized for the reinforcement design and optimization. The commercially available program DIANA (DIsplacement ANAlyzer) is adopted for the non‐linear analysis and evaluation of the different reinforcement designs provided by ORCHID. It is demonstrated how the two programs intended to complete two separate tasks can be integrated in an environment for performance‐based reinforcement design ensuring cost‐effectiveness through optimization and structural safety through satisfying serviceability conditions. Examples of a one‐way slab in bending and a deep beam in membrane action, highlighting the specific aspects of such an integrated analysis/design environment, are provided.

A method to solve shape and size optimisation problems with linear and non‐linear responses has been studied taking advantage of statistical methodologies. A nested optimisation procedure has been fixed. The global optimisation problem is decomposed in several subproblems where each non‐linear response is locally approximated with a first degree polynomial function identified by the definition and execution of an experimental plan. The approximating functions so obtained are used to evaluate the design sensitivity coefficients required by the optimisation procedure. The numerical results obtained during the optimisation process to verify exactly the value of the non‐linear responses are used to verify and to improve the approximating function accuracy. The non‐linear design sensitivity analysis method so defined has been used to solve a multidisciplinary shape optimisation problem involving a real 3D automotive structure.