In this study, a different coupling strategy is used for the coupling of finite element (FE) and boundary element (BE) methods. In the literature, the coupling is done by transforming nodal forces into nodal tractions using distribution matrix at the interface line. In this study, however, the stress-traction equilibrium is used at the interface line for coupling of both methods. A finite and boundary element program is written using FORTRAN 95 and ordinary and developed coupling methods are adapted to this program. The results of both methods are compared with each other, ANSYS, FE, BE and analytical solution whenever possible. It has been seen that the developed method supply more efficient results against the ordinary method.
*Keywords:* coupling, FEM, BEM, distribution matrix, stress-traction equilibrium.

G. Domokos, I. Szeberényi. A hybrid parallel approach to one-parameter nonlinear boundary value problems. CAMES 2004 (11)

This paper presents a global algorithm for parallel computers, suitable to solve nonlinear boundary value problems depending on one parameter. Our method offers a mixture of path continuation and scanning. The former is well-known, the latter is a novel approach introduced a few years ago, capable to find *all* equilibria in a given domain. The hybrid method combines the speed of path continuation with the robustness and generality of scanning, offering a transition between the two methods which depends on the choice of some characteristic control parameters. We introduce the algorithms on a small example and test it on large-scale problems.

H. A. Attia. Equations of motion of serial chains in spatial motion using a recursive algorithm. CAMES 2004 (11)

In the present study, a recursive algorithm for generating the equations of motion of serial chains that undergo spatial motion is presented. The method is based on treating each rigid body as a collection of constrained particles. Then, the force and moment equations are used to generate the rigid body equations of motion in terms of the Cartesian coordinates of the dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotation matrices. For the open loop case, the equations of motion are generated recursively along the serial chains. Closed loop systems are transformed to open loop systems by cutting suitable kinematic joints and introducing cut-joint constraints. The method is simple and suitable for computer implementation. An example is chosen to demonstrate the generality and simplicity of the developed formulation.
*Keywords:* multibody system dynamics, equations of motion, system of rigid bodies, mechanisms, machine theory.

K. Bana¶, M. F. Wheeler. Preconditioning GMRES for discontinuous Galerkin approximations. CAMES 2004 (11)

The paper presents an implementation and the performance of several preconditioners for the discontinuous Galerkin approximation of diffusion dominated and pure diffusion problems. The preconditioners are applied for the restarted GMRES method and test problems are taken mainly from subsurface flow modeling. Discontinuous Galerkin approximation is implemented within an hp-adaptive finite element code that uses hierarchical 3D meshes. The hierarchy of meshes is utilized for multi-level (multigrid) preconditioning. The results of numerical computations show the necessity of using multi-level preconditioning and insufficiency of simple stationary preconditioners, like Jacobi or Gauss-Seidel. Successful preconditioners comprise a multi-level block ILU algorithm and a special multi-level block Gauss-Seidel method.

E. Kita, T. Tamaki, H. Tanie. Topology and shape optimization of continuum structures by genetic algorithm and BEM. CAMES 2004 (11)

This paper describes the topology and shape optimization scheme of continuum structures by using genetic algorithm (GA) and boundary element method (BEM). The structure profiles are defined by using the spline function surfaces. Then, the genetic algorithm is applied for determining the structure profile satisfying the design objectives and the constraint conditions. The present scheme is applied to minimum weight design of two-dimensional elastic problems in order to confirm the validity.
*Keywords:* topology and shape optimization, genetic algorithm (GA), boundary element method, spline function, two-dimensional elastic problem.

J. M. Fragomeni, S. Pochampally. Effect of extrusion processing deformation and heat treating on the plastic flow, microstructure, and mechanical behavior of an aluminum alloy. CAMES 2004 (11)

The extrusion temperature, extrusion ratio and ram speeds were varied and finite element simulations of the extrusion process were conducted to determine the effect of these extrusion parameters on temperature transients, strain rate, and metal flow uniformity for the high temperature plastic deformation of an aluminum-lithium alloy billet. The finite element simulations were important in determining temperature transients, metal flow patterns, and the distributions of strain and strain rate during the extrusion process. The contours showed that the strain, strain rate and metal flow were not uniform but varied as the billet was extruded; this might be due to the non-uniform distribution of temperature during the extrusion of the billet. The microstructure of the aluminum-lithium alloy was computer simulated and correlated to the processing parameters and flow stress based on the heat treating times and temperatures. The extrusion processing variables were correlated to the Zener-Hollomon parameter temperature compensated strain rates. Extrusion temperature and extrusion ratio were found to have very little effect on the strength or ductility. The as-extruded section geometry was found to have the largest effect on the strength and ductility.

H. J. Antúnez, M. Kowalczyk. Combined shape and non-shape sensitivity for optimal design of metal forming operations. CAMES 2004 (11)

Shape and non-shape optimization is carried out for metal forming processes. This means a unified treatment of both shape parameters and other process parameters which are assumed to be design variables. An optimization algorithm makes use of the results of the analysis problem and of the sensitivity parameters obtained as a byproduct of the basic solution, in the context of the direct differentiation method. The shape sensitivity stage is formulated within the domain parametrization approach. Two alternative mappings are proposed to obtain the required derivatives with respect to the shape parameters. The behaviour of different functionals considered and the effect of the boundary conditions on the optimal design are discussed.