The aim of this paper is to derive a reduced model for a piezoelectric plate and to study its actuator and sensor capabilities. In the first part, we focus on the asymptotic modeling for thin plates formed by stacking layers of different piezoelectric materials. In the asymptotic model, the mechanical and electric unknowns are shown to be partly decoupled. In the second part, we study the actuator and sensor capabilities of this model. We use two discrete non-differentiable multi-objective optimization problems, which are solved by genetic algorithms. Several numerical results are reported.
In this work the flexible multibody dynamics formulations of complex models are extended to include elastic components made of laminated composite materials. The only limitation for the deformation of a structural member is that it must be elastic and linear when described in a body fixed frame. A finite element model for each flexible body is obtained such that the nodal coordinates are described with respect to the body fixed frame and the inertia terms involved in the mass matrix and gyroscopic force vector use a diagonalized mass description of the inertia terms. The coupling between the flexible body deformation and its rigid body motion is described using only standard finite element parameters obtained with a commercial finite element code. These elements include composite material shells and beams. For composite material beam elements, the properties of their sections are found using an asymptotic procedure proposed by Hodges. The component mode synthesis is used to reduce the number of generalized coordinates to a reasonable dimension for complex shaped structural models of flexible bodies. The kinematic constraints between the different system components are introduced and the equations of motion of the flexible multibody system are solved using an augmented Lagrangean formulation. Finally, the methodology is applied to the analysis of the deployment of a synthetic aperture radar (SAR) Antenna and the results are discussed.
The paper presents a general optimization methodology for flexible multibody systems which is demonstrated to find optimal layouts of fiber composite structures components. The goal of the optimization process is to minimize the structural deformation and, simultaneously, to fulfill a set of multidisciplinary constraints, by finding the optimal values for the fiber orientation of composite structures. In this work, a general formulation for the computation of the first order analytical sensitivities based on the use of automatic differentiation tools is applied. A critical overview on the use of the sensitivities obtained by automatic differentiation against analytical sensitivities derived and implemented by hand is made with the purpose of identifying shortcomings and proposing solutions. The equations of motion and sensitivities of the flexible multibody system are solved simultaneously being the accelerations and velocities of the system and the sensitivities of the accelerations and of the velocities integrated in time using a multi-step multi-order integration algorithm. Then, the optimal design of the flexible multibody system is formulated to minimize the deformation energy of the system subjected to a set of technological and functional constraints. The methodologies proposed are first discussed for a simple demonstrative example and applied after to the optimization of a complex flexible multibody system, represented by a satellite antenna that is unfolded from its launching configuration to its functional state.
In this paper an application of a genetic algorithm to a material-and sizing-optimization problem of a plate is described. This approach has obvious advantages: it does not require any derivative information and it does not impose any restriction, in terms of convexity, on the solution space. The plate optimization problem is firstly formulated as a constrained mixed-integer programming problem with a single objective function. An alternative multiobjective formulation of the problem in which some constraints are included as additional objectives is also presented. Some numerical results are included that show the appropriateness of the algorithm and of the mathematical model for the solution of this optimization problem, as well as the superiority of the multiobjective approach.
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