The paper discusses the problem of designing the stiffest truss with a given and fixed number of joints and element connections. The design variables are the cross sectional areas of the bars or/and the nodal points locations. In each case a maximal volume of a truss, constituting an isoperimetric unilateral condition is prescribed. The nodal force vector is assumed to be independent of the design variables, hence fixed during the optimization process. The equilibrium problems of the trusses are modeled by the conventional linear as well as nonlinear finite element analyses taking into account large nodal displacements and small deformations of members. New optimal layouts of plane and space trusses are presented. These new layouts are found by using the moving asymptotes algorithm, the simplex method and the optimality criteria method.

A. Garstecki, Z. Pozorski. Sensitivity analysis for variable dynamic load parameters. CAMES 2003 (10)

The paper is concerned with a class of generalized structural optimization problems for which not only stiffness, damping and mass parameters but also loading and support parameters are unspecified and subject to sensitivity analysis and optimization. Both, viscous and complex modulus damping models are used. Single concentrated force and coupling of a force with a concentrated moment, which lags by *pi*/2, are considered. The latter case corresponds to an excitation induced by a rotational machine with eccentricity. Steady-state periodic vibrations are studied. Response functionals in the form of displacement amplitudes are discussed. Numerical examples of beam and plate structures illustrate the theory and demonstrate the accuracy of the derived formulae for sensitivity operators.
*Keywords:* sensitivity analysis, optimal design, structural dynamics, vibrations.

M. Hintermüller, W. Ring. Numerical aspects of a level set based algorithm for state constrained optimal control problems. CAMES 2003 (10)

Numerical aspects of a level set based algorithm for state constrained linear-quadratic optimal control problems for elliptic partial differential equations are discussed. The speed function needed in the level set equation is derived from shape sensitivity analysis. The discretization operates on a fixed grid and additional boundary points representing the discrete interface between the coincidence set and the set where the bound to the state is not active. The discretization of the hyperbolic level set equation, the shape gradient of an appropriate penalty functional and an useful extension of this gradient (naturally defined only on the interface) to the whole computational domain are discussed.

L. Jackowska-Strumillo, J. Sokolowski, A. Zochowski. Topological optimization and inverse problems. CAMES 2003 (10)

The topological derivative of an arbitrary shape functional is introduced in [1] for 2D elasticity. The optimality conditions for general shape optimization problems are established in [2] using the shape variations including boundary and topology variations. The topology variations result in the presence of topological derivatives in the necessary conditions for optimality. In the present paper we derive the necessary optimality conditions for a class of shape optimization problems. The topological variations of shape functionals are used for the numerical solution of inverse problems. The numerical method uses neural networks. The results of computations confirm the convergence of the method.
[1] J. Sokolowski, A. Zochowski. On topological derivative in shape optimisation. INRIA-Lorraine, Rapport de Recherche No. 3170, 1997.
[2] J. Sokolowski, A. Zochowski. Optimality conditions for simultaneous topology and shape design, to appear in SIAM Journal on Control and Optimization, 2003.
*Keywords:* topological derivative, shape optimization, optimality conditions, artificial neural network, shape inverse problem, nucleation of openings.

K. Kolanek, T. Lewinski. Circular and annular two-phase plates of minimal compliance. CAMES 2003 (10)

The paper deals with optimal design of thin plates. The plate thickness assumes two possible values: *h*1 and *h*2 and the plate volume is given. The problem of minimizing the plate compliance needs relaxation. The relaxed formulation was found by Gibiansky and Cherkaev in 1984 [1]. In the present paper a finite element approximation of this problem is presented in the framework of rotationally symmetric bending of circular and annular plates.
The problem is composed of a nonlinear equilibrium problem coupled with a minimum compliance problem. The aim of the present paper is to analyze the forms of the optimal solutions, in particular, to look into the underlying microstructures. It is proved that in some solutions a ribbed microstructure occurs with ribs non-coinciding with both the radial and circumferential directions. Due to non-uniqueness of the sign of an angle of inclination of ribs the appearance of this microstructure does not contrasts with the radial symmetry of the problem. In the degenerated problem when the smallest thickness *h*1 vanishes the above interpretation of the inclined ribbed microstructure becomes incorrect; in these regions one can assume that the plate is solid but with a varying thickness. The degenerated case of *h*1=0 was considered in the papers by Rozvany et al. [2] and Ong et al. [3] but there such a microstructure was not taken into account. One of the aims of the paper is to re-examine these classical and frequently cited results.
[1] L.V. Gibiansky, A.V. Cherkaev. Designing composite plates of extremal rigidity In: A.V. Cherkaev, R.V. Kohn, eds., Topics in the Mathematical Modelling of Composite Materials, Birkhäuser, Boston 1997.
[2] G.I.N. Rozvany, N. Olhoff, M.P. Bendsoe, T.G. Ong, R. Sandler, W.T. Szeto. Least-weight design of perforated elastic plates. I,II. Int. J. Solids. Struct., 23: 521-536, 537-550, 1987.
[3] T.G. Ong, G.I.N. Rozvany, W.T. Szeto. Least-weight design of perforated plates for given compliance: non-zero Poisson's ratio. Comp. Meth. Appl. Mech. Eng., 66: 301-322, 1988.

B. Mohammadi and J. Santiago. Incomplete sensitivities in design and control of fluidic channels. CAMES 2003 (10)

We would like to show how to perform shape optimization and state control at a cost comparable to the one of analysis. To this end, we propose to only use informations available for cost function evaluation and incomplete sensitivities not requiring the solution of the linearized state equation. The application of the method is presented for microfluidic MEMs design and control.

W.M. Paczkowski, A. Badower, E. Silicka, A. Silicki. A quasi-evolutionary identification attempt to modelling of steel frames. CAMES 2003 (10)

The work presents a process of analytical identification via a standard steel frame example. Some experimental tests are made to verify the identification process. Under controlled external loadings the values of displacements and strains are recorded and an approximate FEM-based model is formulated. The polyoptimization approach is employed to analyze that model. The compatibility criteria for comparison of theoretical and experimental models are assumed as square sums of differences between displacements and strains. The whole problem is proceeded in three cycles of evolution suggested by the authors.

P. Tauzowski, M. Kleiber. Sensitivity analysis for viscoelastic bodies in object-oriented finite element environment. CAMES 2003 (10)

In this paper the constitutive model of thermoviscoelastic model is presented. To obtain the parameter sensitivity equations the direct differentiation method is applied. The paper also deals with the finite element for equilibrium and sensitivity analysis problems. Consistent tangent operator for the model is derived. To integrate the creep evolution equation the backward-Euler scheme is efficiently applied. The thermoviscoelastic model with parameter sensitivity analysis is implemented in object-oriented finite element system. Many advantages of the object-oriented approach in FE programming are described in the paper. Two numerical examples are solved. Very good agreement between the FE and analytical results is observed.
*Keywords:* viscoelasticity, transient heat transfer, sensitivity analysis, object-oriented approach.

B. Wilczynski, Z. Mróz. Topology and shape optimization of structural components with fracture constraints. CAMES 2003 (10)

In this paper a numerical design algorithm is described which enables the minimization of the stress intensity factor in a machine component by introducing the defense notch system into the component (weakening of the component) or/and by introducing stiffeners into the component (stiffening of the component) and selection of the shape of its boundary. The paper starts with the extensive review of literature devoted to the optimal design of machine parts with fracture constraints. The design procedure used is the combination of mathematical methods of computer graphics, the Boundary Element Method or the Finite Element Method used for the analysis of the stress field, the sensitivity analysis for the response gradient computations assisted by the Sequential Linear Programming. Also the concept of stop holes drilled at the crack tip, to crack arrest, is discussed. That means replacement of singular stress filed problem (cracks) by quasi-singular one (notches) and optimal design of stop holes becomes notch shape optimization problem.
*Keywords:* stress intensity factor, optimization, BEM, FEM, SLP, defense notch system, stop holes.