Computer Assisted Mechanics and Engineering Sciences 

About: Computer Assisted Mechanics and Engineering Sciences is an academic journal. The journal publishes majorly in the area(s): Finite element method & Artificial neural network. It has an ISSN identifier of 1232-308X. Over the lifetime, 566 publications have been published receiving 2870 citations.

A method to improve design reliability using optimal Latin hypercube sampling

Abstract: In the paper an algorithm for design reliability improvement is proposed. Its key part consists in the computation of the correlations between constraint functions and design variables which are subsequently used to find the new design iteration. It is shown that the optimal Latin hypercube (OLH) sampling provides an extremely efficient technique for assessing the values of correlation coefficients. Since finding the large OLH designs is not a trivial task, a study on the OLH generation algorithms was performed. Two algorithms were found to be particularly effective, namely, the columnwise-pairwise algorithm and the genetic algorithm. The presented strategy proves to be especially useful when alternative gradient-based methods cannot be used, which is often the case for computationally expensive problems involving noisy and highly nonlinear responses. The method is best suited for problems where the probability of failure for the initial design is large and the main interest is to find a more reliable design rather than the optimal one in the sense of reliability-based optimization. The method is illustrated with two numerical examples. One model example and one concerning the problem of thin-walled beam crash.

Approximation with harmonic and generalized harmonic polynomials in the partition of unity method

Abstract: The aim of the paper is twofold. In the flrst part, we present an analysis of the approximation properties of \complete systems", that is, systems of functions which satisfy a given difierential equation and are dense in the set of all solutions. We quantify the approximation properties of these complete systems in terms of Sobolev norms. As a flrst step of the analysis, we consider the approximation of harmonic functions by harmonic polynomials. By means of the theory of Bergman and Vekua, the approximation results for harmonic polynomials are then extended to the case of general elliptic equations with analytic coe‐cients if the harmonic polynomials are replaced with their analogs, \generalized harmonic polynomials". In the second part of the paper, we present the Partition of Unity Method (PUM). This method has the feature that it allows for the inclusion of a priori knowledge about the local behavior of the solution in the ansatz space. Therefore, the PUM can lead to very efiective and robust methods. We illustrate the PUM with an application to Laplace’s equation and the Helmholtz equation.

Neural network for constitutive modelling in finite element analysis

Abstract: Finite element method has, in recent years, been widely used as a powerful tool in analysis of engineering problems. In this numerical analysis, the behavior of the actual material is approximated with that of an idealized material that deforms in accordance with some constitutive relationships. Therefore, the choice of an appropriate constitutive model, which adequately describes the behavior of the material, plays a significant role in the accuracy and reliability of the numerical predictions. Several constitutive models have been developed for various materials. Most of these models involve determination of material parameters, many of which have no physical meaning [1, 2]. In this paper a neural network-based finite element analysis will be presented for modeling engineering problems. The methodology involves incorporation of neural network in a finite element program as a substitute to conventional constitutive material model. Capabilities of the presented methodology will be illustrated by application to practical engineering problems. The results of the analyses will be compared to those obtained from conventional constitutive models.

Analysis of linear mechanical structures with uncertainties by means of interval methods

Abstract: One of the simplest ways of representation of uncertain or inexact data, as well as inexact computations with them, is based on interval arithmetic. In this approach, an uncertain (real) number is represented by an interval (a continuous bounded subset) of real numbers which presumably contains the unknown exact value of the number in question. Despite its simplicity, it conforms very well to many practical situations, like tolerance handling or managing rounding errors in numerical computations. Also, the so-called α -cut method of handling fuzzy sets membership functions is based on replacing a fuzzy set problem with a set of interval problems. The purpose of this paper is to investigate possibilities of and problems with application of interval methods in (qualitative) analysis of linear mechanical systems with parameter uncertainties, in particular truss structures and frames. The paper starts with an introduction to interval arithmetic and systems of linear interval equations, including an overview of basic methods for finding interval estimates for the set of solutions of such systems. The methods are further illustrated by several examples of practical problems, solved by our hybrid system of analysis of mechanical structures. Finally, several general problems with using interval methods for analysis of such linear systems are identified, with promising avenues for further research indicated as a result. The problems discussed include estimation inaccuracy of the algorithms (especially the fundamental problem of matrix coefficient dependence), their computational complexity, as well as inadequate development of methods for analysis of interval systems with singular matrices.