László P. Kollár

Shape Control of Composite Plates and Shells with Embedded Actuators. II. Desired Shape Specified

The changes in shapes of fiber-reinforced composite beams, plates and shells affected by embedded piezoelectric actuators were investigated. An analytical method was developed to determine the voltages needed to achieve a specified desired shape. The method is formulated on the basis of mathematical models using twodimensional, linear, shallow shell theory including transverse shear effects which are important in the case of sandwich construction. The solution technique is a minimization of an error function which is a measure of the difference between the deformed shape caused by the application of voltages and the desired shape. A computationally efficient, userfriendly computer code was written which is suitable for performing the numerical calculations. The code, designated as SHAPE2, gives the voltages needed to achieve specified changes in shape. To validate the method and the computer code, results generated by the code were compared to existing analytical and experimental results. The predictions provided by the SHAPE2 code were in excellent agreement with the results of the other analyses and data.

Shape control of composite plates and shells with embedded actuators. I. Voltages specified

The changes in shapes of fiber-reinforced composite beams, plates and shells affected by embedded piezoelectric actuators were investigated. An analytical method was developed which can be used to calculate the changes in shapes for specified applied voltages to the actuators. The method is formulated on the basis of mathematical models using two-dimensional, linear, shallow shell theory including transverse shear effects which are important in the case of sandwich construction. Solutions to the governing equations were obtained via the Ritz method. A computationally efficient computer code with a user-friendly interface was written which is suitable for performing the numerical calculations. The code, designated as SHAPE1, provides the change in shape for specified applied voltages. To validate the method and the computer code, results generated by the code were compared to existing analytical and experimental results and to test data obtained during the course of the present investigation. The predictions provided by the SHAPE1 code were in excellent agreement with the results of the other analyses and data.

Lateral-torsional buckling of composite beams

Abstract This paper presents the stability analysis of simply supported and cantilever, thin walled, open section, orthotropic composite beams subjected to concentrated end moments, concentrated forces, or uniformly distributed load. In the analysis, both the transverse shear and the restrained warping induced shear deformations are taken into account. An explicit expression is derived for the lateral-torsional buckling load of composite beams. A simple expression is also presented, which shows the approximate reduction in the buckling load due to shear deformation. It enables us to decide whether the effect of shear deformation is negligible.

A Model of Embedded Fiber Optic Fabry-Perot Temperature and Strain Sensors:

A model was developed for embedded intrinsic and extrinsic Fabry-Perot fiber optic sensors. This model relates the strains and the temperature changes in the material surrounding the sensor to the reflected light intensity. The model consists of three parts. Submodel I relates the temperature and the strains in the material to the temperature and the strains inside the sensor. Submodel 2 relates the temperature and the strains inside the sensor to the change in sensor length and to the changes in the optical properties of the sensor. Submodel 3 relates the changes in sensor length and optical properties to the changes in the intensity of the reflected light. On the basis of the model, a computer code SENSOR1 was written which can be used to calculate the reflected light intensity for specified strains and temperature changes inside the material. The model and the code were verified by measuring changes in the light in tensity of an intrinsic Fabry-Perot sensor embedded in a graphite-epoxy composite plate subjected to loads varying with time. The changes in light intensities were measured and were also calculated by the code. The measured and calculated light intensities were found to be in good agreement.

Analysis of building structures by replacement sandwich beams

Abstract In this paper replacement beams of building structures are developed, and the stiffnesses of the replacement beams are derived. The analysis is robust and can be used for slender and wide structures consisting of frames, trusses, shear walls, or coupled shear walls. The utility of the derived replacement beam is demonstrated through the examples of the in plane and flexural–torsional buckling and vibration analyses of high-rise buildings.

Flexural–torsional buckling of open section composite columns with shear deformation

Abstract The paper presents the stability analysis of axially loaded, thin-walled open section, orthotropic composite columns. Vlasovs classical theory is modified to include both the transverse (flexural) shear and the restrained warping induced shear deformations. In addition to the bending stiffness matrix a (3×3) shear stiffness matrix is introduced. A closed form solution is derived for the flexural–torsional buckling load of composite columns. A simplified, approximate solution is also presented, in which the effect of the shear deformations is included using Foppls theorem.

Flexural–torsional vibration of open section composite beams with shear deformation

The paper presents the analysis of the natural frequency of thin-walled open section composite beams. Vlasovs classical theory of thin-walled beams is modified to include both the transverse shear and the restrained warping induced shear deformations. A simplified, approximate solution is also presented, in which the effect of the shear deformations are considered by Foppls theorem.

Stress analysis of anisotropic laminated cylinders and cylindrical segments

Abstract A stress analysis of fiber-reinforced composite cylinders and cylindrical segments is presented. The analysis applies to thin as well as to thick walled cylinders with no restriction on fiber orientation, other than that an individual fiber must remain at the same radial distance from the axis. The cylinder may be subjected to hygrothermal and mechanical loads which may vary in the radial and circumferential, but not in the axial directions. Equations are derived which can be used to calculate the displacements, strains and stresses inside the material.

Analysis of Thin-Walled Composite Beams with Arbitrary Layup

A beam theory for open and closed section, thin-walled, composite beams is presented. The layup of each wall segment is arbitrary, the effects of shear deformation and restrained warping are neglected. Closed form expressions are developed for the calculation of the 4×4 stiffness matrix. It is also shown that the local bending stiffnesses of the wall segments may be neglected when the laminate is either symmetrical or orthotropic.

Calculation of the Stresses and Strains in Embedded Fiber Optic Sensors

Embedded fiber optic sensors operating on interferometric principles have recently been considered for measuring strains and temperature inside isotropic and orthotropic (composite) materials. Owing to the complex interactions between the sensor and the material surrounding it, the relationship between the sensor output and the strains and temperature inside the material cannot be determined by simple tests. In general, the relationships providing the bridge between the sensor output and the engineering values of strain and temperature must be established via analytical models. Once arrived at, the relationships between the sensor output and the engineering values of the strains and temperature can be inverted to provide the values of the strains and temperature in terms of the sensor output. The scope of this article is limited to the relationship between the strains and temperature in the material, far from the sensor, and the strains and temperature in the sensor. Closed form expressions are derived which relate the strains and temperature in the composite to the strains inside the optical sensor. The sensor may be either circular or elliptic. The sensor and the material surrounding it are considered to be orthotropic.