In this paper, we construct a nonlinear Extended State Observer (ESO) to estimate the dynamics of linear or nonlinear systems with parameter uncertainties and unknown external disturbances. We then apply ESO to the high-precision attitude control of a flexible satellite whose dynamics are unknown. Simulation results demonstrate the usefulness of the proposed control method.
*Keywords:* attitude control, extended state observer, flexible satellites.

M. Paszynski and A. Pelc. Numerical analysis of peristaltic blood flow in arteries. CAMES 2001 (8)

The problem of blood flow in arteries induced by peristaltic waves has been investigated. The methodology of modelling global circulation system has been outlined. Medical measurements required for problem formulation have been presented. Numerical solutions of blood flow in artery based on finite element method have been worked out. The paper presents local model of pulsatile blood flow in the human artery. Modelling of pulsatile flow in cardiovascular system could improve understanding and interpretation of flow measurements in arteries locally as well as ventricular-vascular interaction in healthy patients at rest and while exercising. Results achieved on local models could be generalized to formulate a global model of haemodynamics of cardiovascular system in man. This approach could help identifying physiology of optimal heart work at rest, physical activity and also in pathological conditions as hypertension, cardiac insufficiency, heart defects, coronary heart disease and origin and progression of artherosclerosis as well.

S.P. Anjali Devi, A. Alwyn Asir and M. Thiyagarajan Unsteady flow and heat transfer due to a suddenly stopped continuous moving surface. CAMES 2001 (8)

An approximate solution for the problem of unsteady flow and heat transfer caused by a suddenly stopped continuous moving surface and its gradual cooling has been obtained by solving the non-linear governing equations with the implicit finite difference scheme. Stability and convergence of the scheme are first verified. Then, the influence of the plate velocity, Prandtl number, time of stopping of the plate *t*_1 and the cooling constant on the flow pattern, temperature, wall shear stress and heat flux is analyzed. It is found that velocity, temperature, wall shear stress and heat flux decrease in time. When the plate moves faster, fluid velocity, wall shear stress and heat transfer intensity are augmented whereas temperature goes down. The Prandtl number increases and the cooling constant reduces temperature and heat flux.

W. Karmowski. A concept of overlapping meshless FEM and its application in experimental mechanics. CAMES 2001 (8)

In the paper a new meshless FEM method is proposed. The method is physically based and the defined element ensures agreement with equilibrium equations. A special functional is defined which consist of a smoothing term, a boundary term and eventually an experimental one. In one calculation both theoretical and experimental data are used to establish proper solution. The method may be used even in the case when constitutive equation is unknown, what is especially important for residual stress problems.

C. Cichon and J. Jaskowiec. Coupling generalized FC model to meshless EFG method for crack growth analysis in quasi-brittle materials. CAMES 2001 (8)

In the paper a crack growth analysis in quasi brittle materials in plane stress state coupling the Fictitious Crack model to meshless Element-Free Galerkin method is presented. The FC model has been generalized and as a result a uniform algorithm of the analysis of crack propagation, which is a combination of elementary states mode I and mode II has been prepared. The problem is nonlinear because the traction forces contain, besides external loads, cohesive forces on the boundaries of the crack which depend on the actual state of the displacement field. The efficiency of the method has been tested on two standard examples.

H.A. Attia. A recursive method for the dynamic analysis of a system of rigid bodies in plane motion. CAMES 2001 (8)

In this study, a recursive method for generating the equations of motion of a system of rigid bodies with all common types of kinematic joints in plane motion is presented. The method rests upon the idea of replacing the rigid body by a dynamically equivalent system of particles with added geometric constraints that fix the distance between the particles. Some kinematic constraints due to common types of kinematic joints are automatically eliminated. The concepts of linear and angular momentums are used to generate the rigid body equations of motion without either introducing any rotational coordinates or distributing the external forces and moments over the particles. For the open loop case, the equations of motion are generated recursively along the open chains. For the closed loop case, the system is transformed to open loops by cutting suitable kinematic joints with the addition of cut-joints kinematic constraints. An example of a multi-branch closed-loop system is chosen to demonstrate the generality and simplicity of the proposed method.

M. Kurutz and Z. Gáspár. Imperfection-sensitivity analysis by using classical and catastrophe theory methods. CAMES 2001 (8)

Comparison of the classical methods and the tools of the catastrophe theory is presented through the imperfection-sensitivity analysis of the classical stable-symmetric bifurcation problem. Generally, classical *global* methods are related to a large interval, while catastrophe theory concerns the neighborhood of the critical point only, being a *local* method. Unfortunately, in most cases of practical problems, by using classical global methods, there can hardly be obtained analytical solutions for the multivalued imperfection-sensitivity functions and the associated highly folded imperfection-sensitivity surfaces. In this paper, an approximate solution based on the catastrophe theory is presented, in comparison with the exact solution obtained in graphical way. It will be shown that by considering the problem as an imperfect version (at a fixed imperfection) of a higher order catastrophe, a topologically good solution can be obtained in a considerably large, quasi in a *nonlocal* domain.

M. Klósak, T. Lodygowski and J.R. Klepaczko. Remarks on numerical estimation of the critical impact velocity in shear. CAMES 2001 (8)

A phenomenon called the Critical Impact Velocity (CIV), which is directly related to material behavior under dynamic loads, is of special interest in this paper. Deformation trapping due to thermoplastic instability caused by the propagation of plastic waves is the main physical reasons for the CIV. This critical value of shear velocity should be considered as a material constant, but it is difficult to estimate due to complicated material response. Analytical approaches may only provide some preliminary estimates, because they are based on simple constitutive relations. On the other hand, experimental techniques are more reliable, but then there exist problems in specimen design. Numerical techniques such as FE method offer a possibility to treat the problem in a more general aspect. Numerical results obtained in the environment of ABAQUS code demonstrate the role to be played by computer simulations as compared to the analytical and experimental findings. The CIV in shear is studied for the case of martensitic steel VAR4340, and the FE models are based on geometry of the Modified Double Shear specimen (MDS). Thus, the principal questions are formulated as follows: to which extent the analytical approach approximate the CIV, what is the role of experimental results and what information can be obtained after numerical simulations.

W. Sosnowski and I. Marczewska. Minimization of the energy in metal forming process of the cylindric shape tool through punch shape changes. CAMES 2001 (8)

In this paper the sensitivity based optimization problem is considered. The shape of the first of two contacting bodies is optimized on the basis of sensitivities calculated for the second body i.e. workpiece. The finite element simulation of sheet metal forming process and direct differentiation method of sensitivity analysis is used. Some energy measure of deforming sheet metal is chosen as a cost functional. Its gradients with respect to the tool (punch) shape parameters are evaluated. Tool shape optimization based on `exact' sensitivity results is performed. Calculated sensitivities with respect to the tool shape parameters are the input for the optimization algorithm. The cost functional is minimized, yielding the optimal shape of the tool.
The theory is illustrated by numerical example. Shape optimization of the compressor cover produced in one of sheet stamping factories is performed.
*Keywords:* sheet metal forming, sensitivity, optimization, tools design.

J. Ronda, K.W. Colville and O. Mahrenholtz. Non-constant coefficient friction models in 3d simulation of drawing processes. CAMES 2001 (8)

Different friction models: the classic one proposed by Amontons-Coulomb (AC) with a constant friction coefficient, a three-parameter model proposed by Wriggers et al. [1], and a model based on the concept of `work-hardening' proposed by de Souza Neto et al. [2], are applied to the 3-D square-cup drawing and S-rail stamping FE simulations. The benchmark problems used during NUMISHEET'93 for a cup drawing and NUMISHEET'96 for S-rail stamping were simulated here. The results obtained for these three models are presented to illustrate the influence of the friction model on the drawing process. [1] P. Wriggers, T. vu Van, E. Stein. Finite element formulation of large deformation impact-contact problems with friction. Computers and Structures, 37: 319-331, 1990. [2] E.A. de Souza Neto, K. Hashimoto, D. Peric, D.R.J. Owen. A phenomenological model for frictional contact accounting for wear effects. Phil. Trans. R. Soc. London, A354: 819-843, 1996.

S. Reutskiy and B. Tirozzi. Trefftz spectral method for elliptic equations of general type. CAMES 2001 (8)

A new numerical method for 2D linear elliptic partial differential equations in an arbitrary geometry is presented. The special feature of the method presented is that the trial functions, which are used to approximate a solution, satisfy the PDE only approximately. This reduction of the requirement to the trial functions extends the field of application of the Trefftz method. The method is tested on several one- and two-dimensional problems.