with D(φ(·,u)) ⊂ j for all u ∈ = ∏N j=1 j . The existence of an open loop of (1.1), (1.2) with φ independent of the control u, has been established in Ton [7]. With optimal shape design and with inverse problems inmind, we will consider the case when φ depends on the control u as it appears in the top order term of the partial differential operators involved in the problems. Optimal design of d...

A level set based shape and topology optimization framework is used to study the effect of graded interfaces in the optimization process of micro-architectured multi-materials. In contrast to previous studies interfaces are considered as smooth transition between phases instead of a sharp delimitation between two phases. A study on extreme thermoelastic properties of 2D isotropic composites is ...

We consider the optimal design of a machine frame under several stress constraints. The shape optimization is based on a Quasi-Newton Method. We need to solve the plain stress state equations in a complex domain for each evaluation of the objective therein. The complexity and robustness of the optimization depends strongly on the solver for the pde. Therefore, solving the direct problem require...

In this paper an optimization problem for a cylindrical shell is discussed. The aim is to look for an optimal thickness of a shell to minimize the deformation under an applied external force. As a side condition, the volume of the shell has to stay constant during the optimization process. The deflection is calculated using an approach from shell theory. The resulting control-to-state operator ...

1. Abstract In this paper we study concurrent material and structural optimum design of hollow plate with truss-like material based on a micropolar continua representation. The optimization formulation has two classes of design variables, relative density and local aperture distribution of truss-like material, under the given total material volume constraints. Three different objectives, which ...

Solving optimal control problems for real world applications are hard to tackle numerically due to the large size and the complex underlying (partial differential equations based) models. In this paper a structural optimization problem governed by the p-Laplace equation (fine model) is considered. A surrogate optimization is utilized to develop an efficient numerical optimization method. Here t...

We address in this work some theoretical and numerical issues on optimal design problems concerning evolution equation and more specifically the wave equation posed in 1-D and 2-D domain. We compute the gradient of the cost function and then use the level set approach to optimize the location of actuators in order to stabilize or control exactly a given system Copyright c ©2005 IFAC.

Aerodynamic shape optimization plays a fundamental role in aircraft design. However, useful parameterizations of shapes for engineering models often result in high-dimensional design spaces which can create challenges for both local and global optimizers. In this paper, we employ an active subspace method (ASM) to discover and exploit low-dimensional, monotonic trends in the quantity of interes...

Straight elastically supported beams of variable width under the action of a periodic axial force are considered. Two shape optimization problems for reducing parametric resonance zones are studied. In the first problem, the range of resonant frequencies is minimized for a given parametric resonance zone and a fixed amplitude of excitation. In the second problem, the minimal (critical) amplitud...

This paper deals with the existence question in optimal design. We present a general variational technique for proving existence, and give several examples concerning functionals of eigenvalues and of energy type. In particular, we show how the isoperimetric problem for the Dirichlet eigenvalues of an elliptic operator of general order fit into this frame.