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Isogeometric finite element analysis has become a powerful alternative to standard finite elements due to their flexibility in handling complex geometries. One major drawback of NURBS based isogeometric finite elements is their less effectiveness of local refinement. In this study, we present an alternative to NURBS based isogeometric finite elements that allow for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. We will demonstrate the efficiency of the proposed method by two numerical examples.

In the context of finite element model updating using output-only vibration test data, natural frequencies and mode shapes are used as validation criteria. Consequently, the correct pairing of experimentally obtained and numerically derived natural frequencies and mode shapes is important. In many cases, only limited spatial information is available and noise is present in the measurements. Therefore, the automatic selection of the most likely numerical mode shape corresponding to a particular experimentally identified mode shape can be a difficult task. The most common criterion for indicating corresponding mode shapes is the modal assurance criterion. Unfortunately, this criterion fails in certain cases and is not reliable for automatic approaches. In this paper, the purely mathematical modal assurance criterion will be enhanced by additional physical information from the numerical model in terms of modal strain energies. A numerical example and a benchmark study with experimental data are presented to show the advantages of the proposed energy-based criterion in comparison to the traditional modal assurance criterion.

We present recent developments of adaptive wavelet solvers for elliptic eigenvalue problems. We describe the underlying abstract iteration scheme of the preconditioned perturbed iteration. We apply the iteration to a simple model problem in order to identify the main ideas which a numerical realization of the abstract scheme is based upon. This indicates how these concepts carry over to wavelet discretizations. Finally we present numerical results for the Poisson eigenvalue problem on an L-shaped domain.

The application of partly decoupled approach by means of continuum mechanics facilitates the calculation of structural responses due to welding. The numerical results demonstrate the ability of a qualitative prediction of welded connections. As it is intended to integrate the local effects of a joint in structural analysis of steel constructions, it is necessary to meet higher approaches towards quality. The wide array of material parameters are presented, which are affecting the thermal, metallurgical and mechanical behavior, and which have to be identified. For that purpose further investigations are necessary to analyze the sensitivity of the models towards different material properties. The experimental determination of every material parameter is not possible due to the extraordinary laborious efforts needed. Besides that, experimentally identified parameters can be applied only for the tested steel quality for measured temperature-time regimes. For that reason alternative approaches for identification of material parameters, such as optimization strategies, have to be applied. After a definition of material parameters a quantitative prediction of welded connections will also be possible. Numerical results show the effect of phase transformation, activated by welding process, on residual stress state. As these phenomena occur in local areas in the range of crystal and grain sizes, the description of microscopic phenomena and their propagation on a macroscopic level due to approaches of homogenization might be expedient. Nevertheless, one should bear in mind, the increasing number of material parameters as well as the complexity of their experimental determination. Thus the microscopic approach should always be investigated under the scope of ability and efficiency of a required prediction. Under certain circumstances a step backwards, adopting a phenomenological approach, also can be beneficial.

Nodal integration of finite elements has been investigated recently. Compared with full integration it shows better convergence when applied to incompressible media, allows easier remeshing and highly reduces the number of material evaluation points thus improving efficiency. Furthermore, understanding it may help to create new integration schemes in meshless methods as well. The new integration technique requires a nodally averaged deformation gradient. For the tetrahedral element it is possible to formulate a nodal strain which passes the patch test. On the downside, it introduces non-physical low energy modes. Most of these "spurious modes" are local deformation maps of neighbouring elements. Present stabilization schemes rely on adding a stabilizing potential to the strain energy. The stabilization is discussed within this article. Its drawbacks are easily identified within numerical experiments: Nonlinear material laws are not well represented. Plastic strains may often be underestimated. Geometrically nonlinear stabilization greatly reduces computational efficiency. The article reinterpretes nodal integration in terms of imposing a nonconforming C0-continuous strain field on the structure. By doing so, the origins of the spurious modes are discussed and two methods are presented that solve this problem. First, a geometric constraint is formulated and solved using a mixed formulation of Hu-Washizu type. This assumption leads to a consistent representation of the strain energy while eliminating spurious modes. The solution is exact, but only of theoretical interest since it produces global support. Second, an integration scheme is presented that approximates the stabilization criterion. The latter leads to a highly efficient scheme. It can even be extended to other finite element types such as hexahedrals. Numerical efficiency, convergence behaviour and stability of the new method is validated using linear tetrahedral and hexahedral elements.

We consider a structural truss problem where all of the physical model parameters are uncertain: not just the material values and applied loads, but also the positions of the nodes are assumed to be inexact but bounded and are represented by intervals. Such uncertainty may typically arise from imprecision during the process of manufacturing or construction, or round-off errors. In this case the application of the finite element method results in a system of linear equations with numerous interval parameters which cannot be solved conventionally. Applying a suitable variable substitution, an iteration method for the solution of a parametric system of linear equations is firstly employed to obtain initial bounds on the node displacements. Thereafter, an interval tightening (pruning) technique is applied, firstly on the element forces and secondly on the node displacements, in order to obtain tight guaranteed enclosures for the interval solutions for the forces and displacements.

Steel structural design is an integral part of the building construction process. So far, various methods of design have been applied in practice to satisfy the design requirements. This paper attempts to acquire the Differential Evolution Algorithms in automatization of specific synthesis and rationalization of design process. The capacity of the Differential Evolution Algorithms to deal with continuous and/or discrete optimization of steel structures is also demonstrated. The goal of this study is to propose an optimal design of steel frame structures using built-up I-sections and/or a combination of standard hot-rolled profiles. All optimized steel frame structures in this paper generated optimization solutions better than the original solution designed by the manufacturer. Taking the criteria regarding the quality and efficiency of the practical design into consideration, the produced optimal design with the Differential Evolution Algorithms can completely replace conventional design because of its excellent performance.

A practical framework for generating cross correlated fields with a specified marginal distribution function, an autocorrelation function and cross correlation coefficients is presented in the paper. The contribution promotes a recent journal paper [1]. The approach relies on well known series expansion methods for simulation of a Gaussian random field. The proposed method requires all cross correlated fields over the domain to share an identical autocorrelation function and the cross correlation structure between each pair of simulated fields to be simply defined by a cross correlation coefficient. Such relations result in specific properties of eigenvectors of covariance matrices of discretized field over the domain. These properties are used to decompose the eigenproblem which must normally be solved in computing the series expansion into two smaller eigenproblems. Such decomposition represents a significant reduction of computational effort. Non-Gaussian components of a multivariate random field are proposed to be simulated via memoryless transformation of underlying Gaussian random fields for which the Nataf model is employed to modify the correlation structure. In this method, the autocorrelation structure of each field is fulfilled exactly while the cross correlation is only approximated. The associated errors can be computed before performing simulations and it is shown that the errors happen especially in the cross correlation between distant points and that they are negligibly small in practical situations.

PARAMETER IDENTIFICATION OF MESOSCALE MODELS FROM MACROSCOPIC TESTS USING BAYESIAN NEURAL NETWORKS
(2010)

In this paper, a parameter identification procedure using Bayesian neural networks is proposed. Based on a training set of numerical simulations, where the material parameters are simulated in a predefined range using Latin Hypercube sampling, a Bayesian neural network, which has been extended to describe the noise of multiple outputs using a full covariance matrix, is trained to approximate the inverse relation from the experiment (displacements, forces etc.) to the material parameters. The method offers not only the possibility to determine the parameters itself, but also the accuracy of the estimate and the correlation between these parameters. As a result, a set of experiments can be designed to calibrate a numerical model.

Since the 90-ties the Pascal matrix, its generalizations and applications have been in the focus of a great amount of publications. As it is well known, the Pascal matrix, the symmetric Pascal matrix and other special matrices of Pascal type play an important role in many scientific areas, among them Numerical Analysis, Combinatorics, Number Theory, Probability, Image processing, Sinal processing, Electrical engineering, etc. We present a unified approach to matrix representations of special polynomials in several hypercomplex variables (new Bernoulli, Euler etc. polynomials), extending results of H. Malonek, G.Tomaz: Bernoulli polynomials and Pascal matrices in the context of Clifford Analysis, Discrete Appl. Math. 157(4)(2009) 838-847. The hypercomplex version of a new Pascal matrix with block structure, which resembles the ordinary one for polynomials of one variable will be discussed in detail.