The recurrent approach constructed via the stochastic central difference (SCD) is a very fast method for analyzing non-stationary random responses. However, the computational results depend to a great extent upon the discrete time-step size. A new recurrent approach is proposed in this report. It is based on the theory of linear differential equations. Theoretical analysis shows that this algorithm is unconditionally stable for all damped systems. Two examples show that the proposed approach is not sensitive to the
time-step.

*Keywords:* non-stationary response, linear differential equations, variance, finite difference, stochastic central difference.

C. Tran. Fuzzy control based on "true and false" philosophy for mechatronics systems. (Received in the final form July 21, 2008). CAMES 2009 (16)

For man, possessing the ability to recognize the specific situation that has arisen at any instant of time and taking the appropriate decision without using a mathematical model is what ?adaptation? means. Adaptive principles are being extended to more complex systems in widely different areas, in which we need to replace the traditional metaphor of a fixed environment with a dynamic and constantly changing one. Each mechatronic system, for example, is usually, faced with a multiplicity of choices and objectives of the system change with it. Its modeling requires more than a mathematical model that is based on clear definitions and axioms using the rules of logic deduction theory. To solve this problem, the new concept of system integration by software control, such as real-time multi-tasking operating system using fuzzy logic, is emphasized in the education of modem mechatronics engineering. In this paper, I would like to return, firstly, to the fundamental element of truth measure, which we can use as basis for constructing a way to spread the binary philosophy rather than its rejecting and to increase our ability to describe the real world. Next, in order to explanation into details one aspect of real-time software using fuzzy logic, applied in control of mechatronic systems, we present a fuzzy control technology that combines artificial intelligence and control methodologies. It achieves control purposes based on expert knowledge and experience expressed in the form of IF-THEN rules (Sugeno-type) or neural networks using neuro-
fuzzy based intelligent control scheme in order to create a real-time-adaptive control process. Application of this technology is presented in numerical example of trajectory control of PUMA 560 robot manipulators using Fuzzy Artificial Neural Network, FANN, rather than using Artificial Neural Network, ANN, only.

*Keywords:* fuzzy control, neural network, fuzzy-neural network, mechatronics, real-time software.

C.S. Chen, S.Y. Reutskiy, V.Y. Rozov. The method of the fundamental solutions and its modifications for electromagnetic field problems. (Received in the final form January 14, 2009) CAMES 2009 (16)

The paper presents the method of fundamental solutions (MFS) for solving electromagnetic problems. We compare the MFS with the method of boundary integral equations in solution of potential problems. We demonstrate the MFS technique together with the Laplace transform in application to the problem of scattering of electromagnetic pulses. A modification of the MFS - the method of approximate fundamental solutions (MAFS) is also considered in the paper. The method is applied to axisymmetric field problems.
Numerical examples justifying the methods are presented.

*Keywords:* fundamental solution, potential field, measurement data, electromagnetic scattering, axisymmetric problems.

R. Stocki, K. Kolanek, J. Knabel, P. Tauzowski. FE based structural reliability analysis using STAND environment. (Received in the final form December 19, 2008). CAMES 2009 (16)

An assessment of structural reliability requires multiple evaluations of the limit state function for various realizations of random parameters of the structural system. In the majority of industrial applications the limit state functions cannot be expressed explicitly in terms of the random parameters but they are specified using selected outcomes of the FE analysis. In consequence, in order to be useful in practice, a structural reliability analysis program should be closely integrated with a FE module or it should be interfaced with an advanced external FE program. When the FE source code is not available, which is usually the case, the only option is to establish a communication between the reliability analysis program and an external FE software through the batch mechanism of data modification, job submission and results extraction. The main subject of this article is to present the reliability analysis capabilities of STAND software, which is being developed in the Institute of Fundamental Technological Research of Polish Academy of Sciences. A special emphasis is put on the issues related to its interfacing with external general purpose FE codes. It is shown that when shape type random variables are used, leading to modifications of the FE mesh, or when the limit state function contains numerical noise, standard algorithms for localizing the design point often fail to converge and a special method based on some response surface approximation is needed. A proposition of such a strategy that employs an adaptive response surface approximation of the limit state function is presented in this article. Development of a reliability analysis program is a challenging project and calls for such a code organization, which would facilitate a simultaneous work of many programmers and allow for easy maintenance and modifications. The so-called object-oriented programming seems to provide a convenient framework to realize these objectives. The object-oriented approach is used in STAND development. The advantages
of this programming paradigm and a short description of the STAND's class hierarchy are presented in the text. The study is concluded with two numerical examples of interfacing STAND with state of the art commercial FE programs.

P. Gruber, J. Zeman, J. Kruis, M. Šejnoha. Homogenization of composites with interfacial debonding using duality-based solver and micromechanics. (Received in the final form February 13, 2009). CAMES 2009 (16)

One of the key aspects governing the mechanical performance of composite materials is debonding: the local separation of reinforcing constituents from matrix when the interfacial strength is exceeded. In this contribution, two strategies to estimate the overall response of particulate composites with rigid- brittle interfaces are investigated. The first approach is based on a detailed numerical representation of a composite microstructure. The resulting problem is discretized using the Finite Element Tearing and
Interconnecting method, which, apart from computational efficiency, allows for an accurate representation of interfacial tractions as well as mutual inter-phase contact conditions. The candidate solver employs the assumption of uniform fields within the composite estimated using the Mori-Tanaka method. A set of representative numerical examples is presented to assess the added value of the detailed numerical model over the simplified micromechanics approach.

*Keywords:* first-order homogenization, particulate composites, debonding, FETI method, micromechanics.

CAMES News: Calendar of events. CAMES 2009 (16)

CAMES News: International Centre for Mechanical Sciences (CISM) Preliminary Programme 2009. CAMES 2009 (16)