This paper gives a review of the new Bejan's constructal theory and its various applications to design and optimization. According to Bejan, the objective and constraints principle used in engineering is the same mechanism from which the geometry in natural flow systems emerges. This observation is the basis of the new constructal theory. The topics covered in this review are: mechanical structure, thermal structure, heat trees, and structure in transportation and economics. In the conclusion, remarks on possibility of coupling this approach with computational mechanics are given.
*Keywords:* optimization, constructal theory, constructal design, review.

A. Aiad, I. Tawfiq. Finite element models updating by means of a global approach. CAMES 2007 (14)

Analytical models are often used to analyse behaviour of structures, particularly in the field of structural dynamics. The application of such models demands that they must predict the effects of structural modifications with a reasonable accuracy. Unfortunately, lacks of correlation between initial analytical predictions and experimental results are usually observed so that the analytical model needs to be updated with respect to an experimental reference. Many updating methods, involving two main categories of techniques, have been developed in recent years. In the first group of methods, the model to be adjusted is modified by means of correcting parameters associated with the regions containing dominant errors in modelling. The techniques require a localization of modelling errors and are essentially iterative. The second category involves one-step algorithms to globally correct the model in terms of its representative mass and stiffness matrices. These methods have come to be called direct or global methods. Each class of methods presents advantages and disadvantages. The main disadvantage of the iterative methods is the errors localization phase that may require an extensive amount of computational efforts. In addition, the convergence is not ensured for all iterative algorithms. The present paper deals with a direct approach to correct the whole mass and stiffness matrices of a derived finite element model. A modal analysis and a quantitative study of matrix changes are performed to evaluate the capability of the proposed algorithm and to investigate its potential usefulness in model updating.

A. Ambroziak. Application of elasto-viscoplastic Bodner?Partom constitutive equations in finite element analysis. CAMES 2007 (14)

A finite element implementation of the unified elasto-viscoplastic theory of Bodner-Partom for non-linear analysis is investigated in detail. Description of the Bodner-Partom constitutive equations is presented. Proposed UVSCPL procedure has been applied into MSC.Marc system and can be introduced into wide range of different finite elements (e.g. shell, solid, truss). For the validation of the proposed FE procedure the numerical simulations are presented. Additionally, the first part of the paper gives brief characterization of the engineering applications of the Bodner-Partom constitutive equations used for the different modelling of materials.
*Keywords:* elasto-viscoplastic constitutive model, Bodner-Partom, FEM.

M. Radwańska. An overview of selected plate and shell FE models with graphic presentation of governing relations. CAMES 2007 (14)

A survey of three forms (strong, weak and variational) of mathematical models is presented using expressive diagrams [1,2]. The primary and intermediate variables, governing field equations, constraint equations and variables specified by boundary conditions are components of the graphic representation of various FE (finite element) formulations. The attention is focused on linearly elastic plate element QUAD for Mindlin-Reissner theory and shell elements EAS4-ANS, EAS7-ANS based on CBRST (Continuum Based Resultant Shell Theory). In both cases the mixed FE models with the EAS (enhanced assumed strain) and ANS (assumed natural strain) concepts are used. [1] C. Fellippa, Advanced Finite Element Methods (ASEN 5367), Course materials, 2003 [2] Commun. Numer. Methods Engng., 11: 105-115, 1995

R. Wieteska, J. Majewski, J. Rokicki. Investigation of WENO schemes for 3D unstructured grids. CAMES 2007 (14)

This paper paper discusses accuracy of WENO reconstruction used for unstructured grids and applied to two common discretization approaches within Finite Volume Method (FVM). They are Cell Centered and Vertex Centered methods. The numerical results are shown for 3D supersonic flow in a channel and for ONERA M6 wing. The comparison of computational performance of both methods is included.

M.M. Abdelkhalek. Thermal radiation effects on hydromagnetic flow. CAMES 2007 (14)

Numerical results are presented for the effects of thermal radiation, buoyancy and heat generation or absorption on hydromagnetic flow over an accelerating permeable surface. These results are obtained by solving the coupled nonlinear partial differential equations describing the conservation of mass, momentum and energy by a perturbation technique. This qualitatively agrees with the expectations, since the magnetic field exerts a retarding force on the free convection flow. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, Prandtl number, Grashof number and Schmidt number on the profiles of the velocity components and temperature. The effects of the different parameters on the velocity and temperature profiles as well as the skin friction and wall heat transfer are presented graphically. Favorable comparisons with previously published work confirm the correctness of numerical results.
*Keywords:* heat and mass transfer, hydromagnetic flow, perturbation technique.

S. Jendo, W.M. Paczkowski, E. Silicka. Discrete multicriteria reliability-based optimization of spatial trusses. CAMES 2007 (14)

The paper presents problem of discrete multicriteria optimization of two-layer regular orthogonal spatial trusses. Three criteria of evaluation are taken into account, namely: minimum of weight, maximum of reliability and maximum of stiffness of the structure. To simplify the problem, decomposition techniques are applied. The decision variables are cross-sections of the truss members. The best possible cross section is selected for each bar from a discrete catalogue. Other decision variables (coordinated variables) describe also the geometry of the structure. The multicriteria reliability-based algorithm allows for evaluating the objective functions values and then finding sets of nondominated evaluations and solutions. Reliability of the structure is expressed by the Hasofer-Lind reliability index *beta*.

E. Pabisek. Neural analysis of elastoplastic plane stress problem with unilateral constraints. CAMES 2007 (14)

The paper is a development and continuation of paper [1] where the Panagiotopoulos approach was extended for the elastoplastic analysis. In case of elastic analysis the parameters of the Hopfield?Tank Neural Network (HTNN) are calibrated only once but the updating of the elastoplastic stiffness matrix needs an iteration of HTNN and FE system. The main problem is the matrix condensation repeated for each iteration step of the Newton-Raphson method. Besides all the improvements proposed in [2], a new interacting program has been implemented which enables a significant decrease of the processing time (number of iterations) in comparison with the time achieved in [1]. The results of the extensive numerical analysis are discussed for a tension perforated strip with a rigid bolt placed frictionlessly in a circular hole in the middle of the strip.
[1] E. Pabisek, Z. Waszczyszyn, in: *B.H.V. Topping, ed., Computational Engineering Using Metaphors from Nature*, pp. 1-6, Civil-Comp Press, 2000
[2] Z. Waszczyszyn, E. Pabisek, CAMES, 7: 757-765, 2000
*Keywords:* neural network, finite element method, elastoplastic problem, unilateral constraints.

K.V. Pagalthivarthi, A. Mittal, P. Goyal, G.R. Gupta Applications of improved SVM framework in modeling in mechanics. CAMES 2007 (14)

The problem of empirical data modeling is pertinent to several mechanics domains. Empirical data modeling involves a process of induction to build up a model of the system from which responses of the system can be deduced for unobserved data. Machine learning tools can model underlying non-linear function given training data without imposing prior restriction on the type of function. In this paper, we show how Support Vector Machines (SVM) can be employed to solve design problems involving optimizations over parametric space and parameter prediction problems that are recurrent in engineering domain. The problem considered is diffuser design where the optimal value of pressure recovery parameter can be obtained very efficiently by SVM based algorithm even in a large search space. In addition, locating the position of points on a string vibrating in a damped medium serves as an appropriate prediction problem. A grid-searching algorithm is proposed for automatically choosing the best parameters of SVM, thus resulting in a generic framework. The results obtained by SVM are shown to be theoretically sound and a comparison with other approaches such as spline interpolation and Neural Networks shows the superiority of our framework.
*Keywords:* conical diffuser, turbulent flow, string vibration, support vector machine, parameter grid searching, optimal pressure recovery, neural networks.