Optimal design of Schwedler and ribbed domes via hybrid Big Bang-Big Crunch algorithm

An optimum topology design algorithm based on the hybrid Big Bang-Big Crunch optimization (HBB-BC) method is developed for the Schwedler and ribbed domes. A simple procedure is defined to determine the Schwedler and ribbed dome configuration. This procedure includes calculating the joint coordinates and element constructions. The nonlinear response of the dome is considered during the optimization process. The effect of diagonal members on the results is investigated and the optimum results of Schwedler domes obtained by the HBB-BC method demonstrate the efficiency of these domes to cover large areas without intermediate supports.     

Improved group theoretic method using graph products for the analysis of symmetric-regular structures

In this paper, a new combined graph-group method is proposed for eigensolution of special graphs. Symmetric regular graphs are the subject of this study. Many structural models can be viewed as the product of two or three simple graphs. Such models are called regular, and usually have symmetric configurations. The proposed method of this paper performs the symmetry analysis of the entire structure via symmetric properties of its simple generators. Here, a graph is considered as the general model of an arbitrary structure. The Laplacian matrix, as one of the most important matrices associated with a graph, is studied in this paper. The characteristic problem of this matrix is investigated using symmetry analysis via group theory enriched by graph theory. The method is developed and decomposition of the Laplacian matrix of such graphs is studied in a step-by-step manner, based on the proposed method. This method focuses on simple paths which generate large networks, and finds the eigenvalues of the network via analysis of the simple generators. Group theory is the main tool, which is improved using the concept of graph products. As a mechanical application of the method, a benchmark problem of group theory in structural mechanics is studied in this paper. Vibration of cable nets is analyzed and the frequencies of the networks are calculated using the combined graph-group method.     

Graph products for configuration processing of space structures

In this paper four undirected graph products and four directed graph products are presented for the formation of structural models. The undirected products are extensively used in graph theory and combinatorial optimization, however, the directed products defined in this paper are more suitable for the formation of practical structural models. Here, the directed and undirected products are employed for the configuration processing of space structures. This application can easily be extended to the formation of finite element models.     

Localized identification of shear building with embedded foundation in frequency domain

For studying the behavior of structure in an earthquake, it is advisable to model the structure as a multi‐degrees of freedom system, consisting of numerous single‐degree of freedom substructures and pay attention to soil–structure interaction. System identification is divided into two categories: namely time domain method and frequency domain approach. In this paper, a localized substructure identification of shear building considering the soil–structure interaction is presented using a frequency domain approach. In order to deal with noise‐corrupted data, a spectral smoothing technique with Parzen's window reduction method is adapted. It is shown that better convergence and accuracy can be achieved by the present technique. As a result, it is shown that by taking into account the soil–structure interaction more realistic results can be obtained. Copyright © 2007 John Wiley & Sons, Ltd.     

Stability analysis of hyper symmetric skeletal structures using group theory

The main objective of this article is to develop a methodology for the efficient calculation of buckling loads for frame structures having high-order symmetry properties in order to reduce the size of their associated eigenvalue problems. This is achieved by decomposing the second-order stiffness matrix of a symmetric model into submatrices using a representation of its symmetry group, via a step-by-step approach. The physical interpretation of the resulting submatrices is shown as substructures (factors), and the possibility of further decomposition is then investigated for each of the constructed submodels. Due to the similarity in transformation, the constructed submatrices contain the eigenvalues of the main structural matrix. The buckling load of the entire structure is obtained by calculating the buckling loads of its factors. The methods of the present paper provide a mathematical foundation and a logical means to deal with symmetry instead of looking for various boundary conditions to be imposed for symmetric structures, as in the traditional methods. Examples are provided to illustrate the simplicity and efficiency of the present method.     

Performance-based seismic design of steel frames using ant colony optimization

In this paper, a performance-based optimal seismic design of frame structures is presented using the ant colony optimization (ACO) method. This discrete metaheuristic algorithm leads to a significant improvement in consistency and computational efficiency compared to other evolutionary methods. A nonlinear analysis is utilized to arrive at the structural response at various seismic performance levels, employing a simple computer-based method for push-over analysis which accounts for first-order elastic and second-order geometric stiffness properties. Two examples are presented to illustrate the capabilities of ACO in designing lightweight frames, satisfying multiple performance levels of seismic design constraints for steel moment frame buildings, and a comparison is made with a standard genetic algorithm (GA) implementation to show the superiority of ACO for the discussed optimization problem.     

Parameter estimation and prediction uncertainties for multi-response kinetic models with uncertain inputs

Error-in-variables model (EVM) methods are used for parameter estimation when independent variables are uncertain. During EVM parameter estimation, output measurement variances are required as weighting factors in the objective function. These variances can be estimated based on data from replicate experiments. However, conducting replicates is complicated when independent variables are uncertain. Instead, pseudo-replicate runs may be performed where the target values of inputs for repeated runs are the same, but the true input values may be different. Here, we propose a method to estimate output-measurement variances for use in multivariate EVM estimation problems, based on pseudo-replicate data. We also propose a bootstrap technique for quantifying uncertainties in resulting parameter estimates and model predictions. The methods are illustrated using a case study involving n-hexane hydroisomerization in a well-mixed reactor. Case-study results reveal that assumptions about input uncertainties can have important influences on parameter estimates, model predictions and their confidence intervals.