OPTIMUM THERMOELASTIC DESIGN OF LAMINATED PLATES

A thermoelastic optimization procedure is proposed for the design of symmetric. laminated, fiber-reinforced plates. A maximum stiffness criterion is employed, wherein the ply orientations are found by minimizing the complementary strain energy. Approximate solutions for the thermoelastic response are obtained using the Rayleigh-Ritz procedure. Optimization is performed via a quasi-Newton method, with the initial point selected using a random jump routine. Numerical results are presented for simply supported plates subject to a temperature distribution that varies linearly in the thickness direction. Results are given for various composite materials, and the optimum thermoelastic solutions are compared with designs for mechanically loaded laminated plates.     

PUBLICATIONS ON THERMAL STRESSES

In this section, publications on thermal stresses that have appeared elsewhere are listed. In order to make the list as complete as possible, authors are requested to submit two copies of their publications to the Editor-in-Chief. Publications in languages other than English should be accompanied by the English translation of their titles.     

Thermal buckling of clamped symmetric laminated plates

The buckling behavior of moderately thick symmetric angle-ply laminates having clamped edges and subject to a uniform temperature rise is investigated. Transverse shear deformation is accounted for by employing the Reissner-Mindlin theory. The exact solution to the coupled differential equations is obtained using the general double Fourier series approach. Calculated values of the critical temperature are compared with corresponding finite element results.     

THERMOELASTIC ANALYSIS OF AN ORTHOTROPIC SEMI-INFINITE SLAB

The stationary thermoelastic problem for an orthotopic semi-infinite slab undergoing plane deformation is investigated. The top and bottom faces of the slab are presumed to be free of traction and subject to arbitrary symmetrical distributions of temperature, while the end of the slab is taken to be rigidly fixed and thermally insulated. By using Fourier transforms the heat conduction problem is solved and the corresponding stress problem is reduced to a singular-integral equation. Numerical results are presented for both the temperature and stresses along the fixed end of the slab caused by different prescribed surface temperature distributions.     

PIEZOTHERMOELASTIC RESPONSE OF A CIRCULAR PLATE WITH THERMAL RELAXATION

Transient response of a piezothermoelastic plate subject to axisymmetric surface heating is investigated. The Laplace transform is employed to determine the temperature field satisfying the heat conduction equation that includes a relaxation time. Resulting thermally induced displacements, stresses, electric potential, and electric displacements are obtained based on a potential function formulation derived earlier by the authors. Numerical results calculated for a cadmium selenide plate with thermal relaxation are compared with those for a plate without thermal relaxation.     

TRANSIENT PLANE-STRESS RESPONSE OF A PIEZOTHERMOELASTIC CIRCULAR DISK

The transient plane-stress response of a piezothermoelastic circular disk to axisymmetric heat input is investigated. Solutions to the equations of equilibrium and electrostatics are obtained using a potential function approach. The disk is assumed to exhibit hexagonal material symmetry of crystal class 6 mm. Initially the disk is at zero temperature; thereafter one face is exposed to linear heat transfer, while the opposite face is kept at zero temperature. Both faces are taken to be traction-free. The cylindrical edge of the disk is thermally insulated, electrically charge-free, and constrained against radial deformation. Numerical results are obtained for the induced elastic displacements, stresses, electric potential, and electric displacements in a cadmium selenide disk; and the results are compared with those based on an exact three-dimensional solution.     

Control of thermoelastic deformation in a smart composite disk by a stepwise applied electric potential distribution

Summary This paper deals with a smart composite disk for control of a thermoelastic deformation resulting from an unknown thermal load. The disk consists of a structural layer onto which piezoelectric sensor and actuator layers are bonded. First, an unknown heating temperature distribution is inferred from a sensor output. The thermoelastic displacement on the bottom free surface is then controlled by applying electric potentials to electrodes on the actuator layers. For a composite disk with one actuator layer, applied electric potentials are determined by solving a direct optimization problem with and without stress constraints, respectively. The introduction of the stress constraints leads to a deterioration in the effectiveness of the displacement control. In order to resolve this issue, an approximate optimum design problem of a composite disk with two actuator layers is solved under stress constraints. As a result, the thermoelastic displacement is satisfactorily controlled to the desired distribution. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

THERMOELASTIC ANALYSTS OF LAMINATED PLATES. 2: ANTISYMMETRIC CROSS-PLY AND ANGLE-PLY LAMINATES

Thermal deformations and stress resultants in rectangular, antisymmetric cross-ply and angle-ply laminates are investigated. Exact solutions are obtained for the response of simply supported plates to general three-dimensional temperature variations. To illustrate the thermoelastic behavior, deflections are computed for fiber-reinforced laminates undergoing constant and linearly varying temperature fields. Thermal membrane-bending coupling is found to be significant when the total number of layers is small, but it rapidly becomes unimportant as the number of layers within a plate of a given thickness increases.