Fumihiro Ashida

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.

Developments in thermopiezoelasticity with relevance to smart composite structures

A review of theoretical developments in thermopiezoelasticity having relevance to smart composite structures is presented. The equations governing linear response of piezothermoelastic media are outlined, and a general solution procedure based on potential functions is described. Sensor applications aimed at predicting thermal loads and corresponding responses from measurements of electric potential distributions are described; studies on the control of composite structures (beams, plates and shells) via piezoelectric actuation are reviewed.

GENERALIZED THERMOELASTICITY IN AN INFINITE SOLID WITH A HOLE

This paper deals with one-dimensional generalized thermoelasticity based on the theories of Lord and Shulman and of Green and Lindsay. A formulation of generalized thermoelasticity that combines both generalized theories is derived. The generalized thermoelastic problems for an infinite solid with a cylindrical hole and an infinite solid with a spherical hole are analyzed by means of the Laplace transform technique. Numerical calculations for temperature, displacement, and stresses under the generalized formulation are carried out and compared with those of classical dynamic coupled theory.

A general plane-stress solution in cylindrical coordinates for a piezothermoelastic plate

A general solution procedure is proposed for plane-stress problems of circular plates constructed from piezothermoelastic material. Potential functions are introduced in order to uncouple the equations governing equilibrium and electrostatics. The present formulation is applicable to plates having arbitrary edge conditions. Solutions are derived for plates having either radially constrained or traction-free edges and subjected to axisymmetric surface heating. Numerical results illustrate the effects of plate thickness and variations in material properties upon the induced elastic displacements, stresses, electric potential and electric displacements.

An Inverse Problem for Determination of Transient Surface Temperature From Piezoelectric Sensor Measurement

The time-varying ambient temperature on the face of a piezoelectric disk is inferred from a knowledge of the thermally induced electric potential difference across the disk thickness. The temperature-sensing disk has a circular planform, possesses hexagonal material symmetry properties, and is constrained by a rigid, thermally insulated, electrically charge-free ring. A potential function approach, together with Laplace transforms, is employed to solve the inverse problem for a particular form of electric potential difference. Also presented is a finite difference formulation which does not require specification of an analytical form for the potential difference. Numerical results are given for the predicted transient ambient temperatures corresponding to various combinations of disk thickness-to-radius ratios and surface heat transfer coefficients. Through-thickness distributions of temperature, stresses, and electric field intensities are shown, and a comparison of the exact and finite difference results is provided.

CONTROL OF TRANSIENT RESPONSE IN INTELLIGENT PIEZOTHERMOELASTIC STRUCTURES

Investigations on sensing and controlling thermally induced transient structural deformations by means of piezoelectric elements are reviewed in this article. Past research in the field of thermopiezoelasticity having relevance to smart structures is discussed briefly. Equations governing the linear response of piezothermoelastic media are outlined; and solution procedures for determining the thermal, elastic, and electric fields in composite structures constructed of thermoelastic and piezothermoelastic layers are discussed. Applications of the solution techniques to direct problems (prescribed transient thermal loadings), control problems (applied electric potentials), inverse problems (determination of thermal loadings from knowledge of induced electric potentials), and intelligent problems (piezoelectric layers serve both to sense thermal loadings and suppress deformations) are addressed.

APPLICATION OF THE POTENTIAL FUNCTION METHOD IN PIEZOTHERMOELASTICITY: SOLUTIONS FOR COMPOSITE CIRCULAR PLATES

Developments in piezothermoelasticity having relevance to intelligent structures are discussed briefly. The equations governing the axisymmetric behavior of a piezoelastic body with hexagonal material symmetry of class 6 mm are reviewed. A general solution procedure based upon potential functions is presented for the analysis of transversely isotropic thermoelastic and piezothermoelastic bodies. The method is used to derive exact solutions to problems involving the response of a composite circular plate consisting of a piezoelectric material attached to a layer of structural material. Numerical results are presented for cases of: (i) a prescribed thermal loading; (ii) an inverse problem in which the thermal loading is determined from knowledge of induced electric potential; (iii) a control problem in which an electric potential is applied to control thermally induced deformation; and (iv) an intelligent plate problem, where the piezo electric layer serves both to sense the thermal loading and to suppress ...

Control of transient thermoelastic displacement in a composite disk

Control of displacement in a composite disk subjected to axisymmetric heating is investigated. The disk consists of a transversely isotropic structural layer to which is bonded a layer of piezoceramic material of crystal class 6mm. First, a solution procedure based on potential functions is used to analyze the elastic and electric fields induced in the disk when a transient ambient temperature acts on the free surface of the structural layer. Then a transient distribution of electric potential across the piezo-electric layer is determined such that the resultant displacement at the surface of the structural layer has a prescribed distribution. Numerical results are obtained for the resulting thermal, elastic, and electric fields.

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.

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.