The finite element in time method (FET) is a fast and reliable implicit numerical method for obtaining steady state solutions of the periodically forced dynamical systems with clearances. Delineation of the stable and unstable solutions could help in predicting regular and chaotic motions of such dynamical systems and transitions to either type of response. Stability of the FET solutions can be investigated via the Floquet theory, without any special effort for calculating the monodromy matrix. The applicability of the stability analysis is demonstrated through the study of two-degree-of-freedom systems with clearances. Close agreement is found between obtained results and published findings of the harmonic balance method and the piecewise full decoupling method.

B. Kanber. An improved version of artificial boundary node approach. CAMES 2007 (14)

This paper proposes an improvement of the artificial boundary node approach using the least square method. The original artificial boundary node approach requires the selection of an offset by the user. The success of the original method depends on the correct choice of the offset. However, the improved version uses a least square line and the solution does not depend on a single offset. The solution is carried on using at least two different offsets and final solution is obtained by replacing the offset as zero in the least square equation. The improved version supplies good accuracy and stability in the boundary element solution. Three different case studies are solved to validate proposed method in 2-D elasticity. All results are compared with each others, conventional BEM, FEM, ANSYS and analytical results whenever possible.
*Keywords:* Artificial boundary node, boundary element method, least square method, singular integrals.

M.E. Sayed-Ahmed, H.A. Attia. MHD flow and heat transfer of a Bingham fluid in an eccentric annulus with the Hall effect. CAMES 2007 (14)

The steady laminar flow and heat transfer of an incompressible, electrically conducting, non-Newtonian Bingham fluid in an eccentric annulus are studied in the presence of an external uniform magnetic field. The inner cylinder is subject to a constant heat flux while the outer cylinder is adiabatic and, the viscous and Joule dissipations are taken into consideration. The governing momentum and energy equations are solved numerically using the finite difference approximations. The velocity, the temperature, the volumetric flow rate and the average Nusselt number are computed for various values of the physical parameters.

J.L. Marcelin. Genetic optimal shape design of thin axisymmetric shells and axisymmetric structures. CAMES 2007 (14)

This work gives some applications of genetic algorithms for shape optimization of thin axisymmetric shells and axisymmetric structures. Calculations are relatively fast for thin axisymmetric shells. For general axisymmetric structures, the concept of mobile or fixed substructures is used and associated to an automatic mesh generator, so calculations are also relatively fast for axisymmetric structures. The limitations or the optimization constraints are included in the chromosomes coding. Three applications are presented; the first one deals with the optimization of the shape of a drop of water, the second one deals with the optimization of the shape of a bottle, and the third one deals with the optimization of the shape of a hydraulic hammer's rear bearing.
*Keywords:* shape optimization, axisymmetric shells, axisymmetric structures, genetic algorithms.

J. Repalle, R.V. Grandhi. Forging preform shape optimization using surrogate models. CAMES 2007 (14)

Forging of practical products from simple billet shapes is a complex and nonlinear process due to the multi-disciplinary phenomenon of material flow and processing conditions. General forgings are usually produced in a number of stages in order to avoid defects such as underfill, extra flash, voids, and folds. In spite of advancements in analysis techniques, forging process simulations do not provide function sensitivity information. Hence, the research focuses on exploring efficient non-gradient based preform shape optimization methods. In this research, an attempt is made to develop a preform shape design technique based on interpolative surrogate models, namely Kriging. These surrogate models yield insight into the relationship between output responses and input variables and they facilitate the integration of discipline-dependent analysis codes. Furthermore, error analysis and a comparison between Kriging and other approximation models (response surface and multi-point approximations) are presented. A discussion about what the results mean to a designer is provided. A case study of an automotive component preform shape design is presented for demonstration.
*Keywords:* preform shape optimization, surrogate models, Kriging, response surface model, multi-point approximation model.

A. Siddiq, S. Schmauder. Modelling of crystal plasticity effects on the crack initiation energies of a bi-crystal interface (Nb/Al

The present paper examines the crystal orientation effects on the energy at the crack-tip of niobium/alumina joints. The analyses have been done using crystal plasticity theory. The single crystal parameters are identified for each family of slips system in [1]. These identified parameters are being used to examine the orientation effects of the niobium single crystal on the energy at the crack-tip. Differences in the fracture energy are explained based on the plastic slip (strain) induced in different slip systems during deformation. A qualitative comparison of the crystal plasticity analysis with the experiments of [2,3] is also been presented.
[1] A. Siddiq, S. Schmauder. Steel Grips: J. Steel Rel. Materials, 3: 281-286, 2005.
[2] D. Korn, G. Elssner, R.M. Cannon, M. Rühle. Acta Materialia, 50: 3881-3901, 2002.
[3] R.M. Cannon, D. Korn, G. Elssner, M. Rühle. Acta Materialia, 50: 3903-3925, 2002.
*Keywords:* crystal plasticity, finite element methods, fracture, metal-ceramic interface.

M. Dhanasekar, J.-J. Han, Q.H. Qin. Interaction of surface and internal cracks in railhead. CAMES 2007 (14)

This paper presents a two-dimensional model for the analysis of interaction between surface and internal cracks in the railheads subjected to wheel loading. The shape of the railhead, the surface crack and the internal crack are modelled as curved cracks defined by the theory of continuous distribution of dislocation in an infinite body. From the boundary conditions along these cracks, a system of singular integral equations is deduced. Influence functions in these singular integral equations are first expanded into the Cauchy kernel multiplying normal functions and later are reduced to a system of linear equations and solved numerically. Stress intensity factors (SIFs) of the surface crack tip are calculated from the numerical solution of distribution function along these cracks directly, eliminating need for any indirect integral method. The method does not require meshing and hence idealisation of the shapes of the cracks, thereby improving accuracy and reducing pre- and post processing efforts. Interaction between the internal crack and the surface crack is examined in detail through several examples.
*Keywords:* railhead, surface crack, internal crack, curved crack, SIF, crack angle.

H. Shimizu, A. Hara, T. Tamaki, E. Kita. Simulation of traffic flow through a toll gate. CAMES 2007 (14)

This paper describes the simulation of the traffic flow through toll gate. A two-lane road is considered as the object domain and then, the local rules are defined to control the vehicle behavior. First, one simulates the traffic flows through the road with two non-ETC gates or the road with two ETC gates. The maximum traffic amount on the roads with two ETC gates is less than that on the road without gates by about 10%, while, in the case of the roads with two non-ETC gates, the maximum traffic amount decreases by 80%. Next, one simulates the traffic flows through the road with one non-ETC gate and one ETC gate. The traffic amount depends not only on the vehicle occupancy but also on the percentage of ETC vehicles among all driving vehicles.
*Keywords:* traffic flow, toll gate, traffic cognition, stochastic velocity model, cellular automata.

L. Zhang, W. Dai, R. Nassar. A numerical algorithm for obtaining an optimal temperature distribution in a 3D triple layered cylindrical skin structure. CAMES 2007 (14)

In recent years, there has been interest in research related to hyperthermia combined with radiation and cytotoxic drugs to enhance the killing of tumors. The objective is to control laser heating of the tumor so that the temperature of the normal tissue surrounding the tumor remains low enough so as not to cause damage to the tissue. To achieve this objective, it is important to obtain an optimal temperature field of the entire treatment region. In this paper, we develop a numerical algorithm for obtaining an optimal temperature distribution in a 3D triple layered cylindrical skin structure by pre-specifying the temperatures to be obtained at the center and perimeter of the treated region on the skin surface. The method is comprised of designing a laser irradiation pattern, solving a 3D Pennes' bioheat equation by a numerical scheme, and optimizing the laser power.

R. Stocki, P. Tauzowski, M. Kleiber. Efficient sampling techniques for stochastic simulation of structural systems. CAMES 2007 (14)

One of the main obstacles in making stochastic simulation a standard design tool is its high computational cost. However, this problem can be significantly reduced by using efficient sampling techniques like optimal Latin hypercube (OLH) sampling. The paper advocates this kind of approach for scatter analysis of structural responses. After explaining the idea of the OLH sampling the principal component analysis method (PCA) is briefly described. Next, on numerical examples it is shown how this technique of statistical postprocessing of simulation results can be used in the design process. Important improvements of the estimation quality offered by OLH design of experiments are illustrated on two numerical examples, one simple truss problem and one involving finite element analysis of elastic plate. Based on numerical experiments an attempt is made to propose the sample size which for a given number of random variables provides an acceptable estimation accuracy of statistical moments of system responses and which enables more advanced statistical post-processing.