Sei-ichiro Sakata

Structural optimization using kriging approximation

An optimization method using Kriging approximation is applied to a structural optimization problem. The method involves two main processes. The first is a space estimation process that uses the Kriging method, and the second is an optimization process. The use of the Kriging method makes it easier to perform the approximation optimization. As an example of the estimation performed as part of structural optimization, a response surface for layout optimization of beam reinforcement is estimated. To evaluate the applicability of the Kriging method, Kriging estimation is compared with neural network approximation. As a numerical example, the optimization of a stiffened cylinder for an eigenfrequency problem is illustrated. The obtained results clearly show the applicability of the method.

INVERSE TRANSIENT THERMOELASTIC PROBLEM FOR A COMPOSITE CIRCULAR DISK

The present article deals with the application of a piezoelectric material as a sensor of thermomechanical disturbance. We consider a composite circular disk constructed of a transversely isotropic layer onto which a piezoceramic layer of crystal class 6mm is perfectly bonded. An inverse transient thermoelastic problem is solved to determine the unknown transient heating temperature distribution on the surface of the transversely isotropic layer, when the distribution of the electric potential difference across the piezoceramic layer is known. A finite difference method with respect to the time variable is employed to solve this inverse problem. The thermoelastic fields in the transversely isotropic and piezoceramic layers are analyzed by means of a transversely isotropic potential function method and a piezothermoelastic potential function method, respectively. Numerical results are presented for the time variation of the inferred heating temperature distribution and the corresponding distributions of temperature, displacements, stresses, and electric displacements.

Control of Thermal Stress in a Piezo-Composite Disk

This article deals with a stress control problem of a composite circular disk consisting of a structural layer onto which piezoceramic layers are bonded. When a heating temperature distribution acts on the bottom free surface, the maximum thermal stress in the structural layer can be controlled by applying electric potentials to electrodes concentrically arranged on each piezoceramic layer. The applied electric potentials are determined by solving an optimization problem so that the maximum thermal stress in the structural layer is minimized subject to constraints on the stresses in the piezoceramic layers. Finally, numerical results are presented.

Optimum Design of a Piezo-Composite Disk for Control of Thermoelastic Displacement Distribution

This article deals with control of a thermoelastic displacement in a composite disk consisting of a transversely isotropic structural layer and multiple piezoceramic layers of crystal class 6 mm. For various thicknesses of a specified number of layers, a stepwise electric potential distribution applied to each piezoceramic layer is determined by means of a direct optimization technique so that the thermoelastic displacement of the structural layer is controlled to a desired distribution. Based on the obtained results, an approximate optimum design problem of a composite disk is solved in order to minimize the maximum applied electric potential subject to stress constraints.

Optimum Design of a Multilayered Composite Plate Using Neural Networks

An approximate optimum design of a multilayered composite plate constructed of an isotropic structural layer and multiple piezoceramic layers is presented. A thermoelastic displacement distribution on the structural layer surface is controlled by applying appropriate electric potential distributions to the piezoceramic layers. The objective of this study is to determine the thickness of each piezoceramic layer by using neural networks so that the maximum value of the applied electric potential distributions is minimized subject to stress constraints. The quasi-Newton method is employed for an updating formula of connection weights. Numerical results for the approximate optimum design of the composite plate are shown to be in good agreement with those obtained from a direct optimum design using the quasi-Newton method.

Structure Design of a Piezoelectric Composite Disk for Control of Thermal Stress

In order to realize a plan for a hypersonic aircraft, development of a smart heat-resisting plate possible to control a thermal stress has been required because the safety of structural members must be secured even if they are exposed to a severe thermal loading beyond an estimated load. In view of such a background, this paper deals with a control problem of a thermal stress in a multilayer composite circular disk consisting of a structural layer and piezoceramic layers with concentrically arranged electrodes. When a heating temperature distribution acts on the structural layer surface, the maximum thermal stress in the structural layer can be suppressed by applying appropriate voltages to the electrodes. This thermo-elastic problem has been theoretically analyzed by employing the potential function techniques. Utilizing the analytical results, the nonlinear optimization problem for determining the applied voltages is transformed into a linear programming problem and then the optimum solution is successfully obtained. Based on the obtained solutions, the structure of a composite disk has been designed in order to demonstrate the function of stress control to the fullest extent possible. Finally, numerical results for the stresses before and after applying the determined voltages as well as for the structure design of the composite disk and the suppression ratio of the maximum thermal stress are shown in graphical and tabular forms. It is seen from the numerical results that the maximum thermal stress can be reduced by about 34% when the structure of the composite disk is designed optimally.

Control of transient deformation in a heated intelligent composite disk

The problem of sensing and controlling the time-dependent thermoelastic response of a layered circular disk is investigated. An unknown transient temperature distribution acting on the surface of a structural layer of the disk is inferred from the electric potential distribution induced in a piezoelectric sensor layer. A determination is then made of the electric potential that could be applied to an actuator layer in order to control the displacement of the disks heated surface. Solutions are obtained using a potential function approach and a finite difference approximation. Numerical results are illustrated graphically.

Optimum Structure Design of a Multilayer Piezo-Composite Disk for Control of Thermal Stress

This article deals with a control problem of a thermal stress in a composite circular disk consisting of a transversely isotropic structural layer onto which multiple piezoelectric layers with concentrically arranged electrodes are perfectly bonded. When a prescribed heating temperature distribution acts on the structural layer surface, the optimum structure design of the composite disk is performed so that the maximum thermal stress in the structural layer is minimized subject to constraints on stresses in the piezoelectric layers. A hybrid optimization technique combining the particle swarm optimization with the simplex method is employed for solving the optimum design problem. To resolve the difficulty in solving the problem with many optimization variables, three improvements are added to the hybrid optimization technique and an efficient design method is introduced. For a composite disk constructed of a CFRP layer and cadmium selenide layers, the layer thicknesses, the electrode dimensions, and the voltages applied to the electrodes are determined and the numerical results are presented in tabular and graphical forms. Finally, it is shown from the optimum design results that the highest suppression ratio of the maximum thermal stress reaches 40.8% in the case of a five-layer composite disk and is considered to be almost saturated.

A Stochastic Homogenization Analysis for a Thermoelastic Problem of a Unidirectional Fiber-Reinforced Composite Material with the Homogenization Theory

This article describes a stochastic homogenization analysis on a thermoelastic problem of a composite material. A basic formulation of the stochastic homogenization method with the homogenization theory for the thermoelastic properties is introduced at first. Next, the stochastic properties of the homogenized thermal expansion coefficient of a unidirectional fiber reinforced composite material for a microscopic random variation is analyzed. In addition, from the numerical results, accuracy of the perturbation-based approach for the stochastic homogenization analysis on the thermoelastic properties is investigated. Also, an example of stochastic thermal stress analysis of a composite material considering a microscopic random variation is provided.

Control of Temperature-Induced Plate Vibrations Based on Speed Feedback

Piezoelectric control of thermally induced vibrations of rectangular and circular plates exhibiting strain-rate damping is investigated. The plates consist of a thermoelastic structural layer bonded to two outer piezothermoelastic layers. Electric pulses are applied to the piezoelectric layers in order to suppress the vibration. The initiation and termination times of the pulse voltages are calculated according to a procedure similar to a method proposed earlier by the authors; amplitudes of the pulses are determined by various control strategies, including those based on speed feedback. Numerical results are presented for aluminum/PZT ceramic plates.