Michael W. Hyer

Some Observations on the Cured Shape of Thin Unsymmetric Laminates

This paper discusses the fact that the cured shape of thin unsymmetric laminates do not conform to the predictions of classical lamination theory. Rather than being saddle shaped, as predicted by the classical theory, the paper shows that thin unsymmetric laminates cure into a shape of a right circular cylinder. This anomalous behavior has been observed by many but the paper serves to quantify the effect and to inspire investigators to begin thinking about using the phenomenon to advantage. The paper indicates that the anomalous behavior is repeatable and that thicker laminates con form to the predictions of the classical theory. Laminates of the [0/902 /θ ] T, [02 /θ2 ] T and [04 /θ4 ] T families are investigated for this be havior and it is shown the principal curvature directions of the cylindrical shapes are predictable.

Calculations of the Room-Temperature Shapes of Unsymmetric Laminatestwo:

The cured shape of unsymmetric laminates do not always conform to the predictions of classical lamination theory. Classical lamination theory predicts the room-temperature shapes of all unsymmetric laminates to be a saddle. Experimental observations, however, indicate some unsymmetric laminates have cylindrical room-temperature shapes. In addition, some unsymmetric laminates exhibit two stable room-temperature configurations, both cylindircal. This paper presents a theory which explains these characteristics. The theory is based on an extension of classical lamination theory which accounts for geometric nonlinearities. A Rayleigh-Ritz approach to minimizing the total potential energy is used to obtain quantitative information regarding the room-temperature shapes of square T300/5208 [02/902] T and [04/904] T graphite-epoxy laminates. It is shown that, depending on the thickness of the laminate and the length of the side of the square, the saddle shape configuration is actually unstable. For values of length and thickness that render the saddle shape unstable, it is shown that two stable cylindrical shapes exist. The predictions of the theory are compared with existing experimental data.

The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes

The gains in buckling performance are explored that can be achieved by deviating from the conventional straightline fiber format and considering the situation whereby the fiber orientation in a layer, or a group of layers, can vary from point to point. The particular situation studied is a simply supported square plate with a centrally located hole loaded in compression. By using both a sensitivity analysis and a gradient-search technique, fiber orientation in a number of regions of the plate are selected so as to increase the buckling load relative to baseline straightline designs. The sensitivity analysis is used to determine which regions of the plate have the most influence on buckling load, and the gradient search is used to find the design that is believed to represent the absolute maximum buckling load for the conditions prescribed. Convergence studies and sensitivity of the final design are discussed. By examining the stress resultant contours, it is shown how the curvilinear fibers move the load away from the unsupported hole region of the plate to the supported edges, thus increasing the buckling capacity. The tensile capacity of the improved buckling design is investigated, and it is shown that both tensile capacity and buckling capacity can be improved with the curvilinear fiber concept.

Thermally-induced deformation behavior of unsymmetric laminates

A methodology is presented to predict the displacements, particularly the out-of-plane component, of flat unsymmetric epoxy-matrix composite laminates as they are cooled from their elevated cure temperature. Approximations to the strain fields are used in the expression for the total potential energy and the Rayleigh-Ritz technique is applied. Curvatures of the originally flat laminate as a function of temperature are predicted, as are the shapes of the laminates at room temperature. As geometrically nonlinear effects occur, stability is studied. As such, stability and the existence of multiple solutions, which are interpreted as multiple shapes, are prominent features of the problem. Experimental results are presented which confirm the predictions of the theory regarding the existence of multiple solutions, and the magnitude of the displacements. Results are compared with those of several other investigators, and limited finite element analyses are used to further study the problem.

The room-temperature shapes of four-layer unsymmetric cross-ply laminates

A previous approximate theory for predicting the room-temperature shapes of unsymmetric laminates is examined in light of the assumptions regarding the inplane strains. The previous theory, which was a geometrically nonlinear extension of classical lamination theory, was felt to be restrictive and this paper develops a new theory in which these restrictions are relaxed. It is shown that despite the previous concern, there is little difference between the previous theory and this theory. This paper presents numerical results for the inplane residual strains of unsymmetric laminates which have cooled from curing into a cylindrical room-temperature shape. It is shown that the residual strains are compressive and practically independent of spatial loca tion on the laminate. In another facet of the paper, the room-temperature shapes of all four-layer unsymmetric cross-ply laminates are predicted. There are only four unique stacking arrangements for this category of laminates and it is shown that their room-temperature shapes are a strong function of their size and their stacking arrangement. Depending on these parameters, the room-temperature shape of a four-layer cross-ply unsymmetric laminate can be a unique saddle shape, a unique cylindrical shape, or a cylindrical shape that can be snapped through to another cylindrical shape.

SMA-induced snap-through of unsymmetric fiber-reinforced composite laminates

A theory is developed and experiments designed to study the concept of using shape memory alloy (SMA) wires to effect the snap-through of unsymmetric composite laminates. The concept is presented in the context of structural morphing, that is, a structure changing shape to adjust to changing conditions or to change operating characteristics. While the specific problem studied is a simplification, the overall concept is to potentially take advantage of structures which have multiple equilibrium configurations and expend power only to change the structure from one configuration to another rather than to continuously expend power to hold the structure in the changed configuration. The unsymmetric laminate could be the structure itself, or simply part of a structure. Specifically, a theory is presented which allows for the prediction of the moment levels needed to effect the snap-through event. The moment is generated by a force and support arrangement attached to the laminate. A heated SMA wire attached to the supports provides the force. The necessary SMA constitutive behavior and laminate mechanics are presented. To avoid dealing with the heat transfer aspects of the SMA wire, the theory is used to predict snap-through as a function of SMA wire temperature, which can be measured directly. The geometry and force level considerations of the experiment are discussed, and the results of testing four unsymmetric laminates are compared with predictions. Laminate strain levels vs. temperature and the snap-through temperatures are measured for the these laminates. Repeatability of the experimental results is generally good, and the predictions are in reasonable agreement with the measurements.

Snap-through of unsymmetric fiber-reinforced composite laminates

Abstract An approximate theory based on assumed strain and displacement fields, the Rayleigh–Ritz technique, and virtual work is used to predict the snap-through forces and moments for three families of unsymmetric fiber-reinforced composite laminates. Unsymmetric laminates generally have two stable equilibrium configurations when cooled from their elevated cure temperature, and it is the moment required to snap the laminate from one stable configuration to the other that is the subject of this paper. A simple force-controlled experiment is described which is used to measure the snap-through moment and the characteristics of the configuration change, by way of strains, in four laminates. The correlation between predicted results and experimental measurements is quite good, both in terms of moment levels and in terms of strain response.

Snap-Through of Unsymmetric Cross-Ply Laminates Using Piezoceramic Actuators

The paper discusses the concept of using a piezoceramic actuator bonded to one side of a two-layer unsymmetric cross ply [0/90] T laminate to provide the moments necessary to snap the laminate from one stable equilibrium shape to another. The results presented are considered an alternative to existing morphing concepts wherein actuators are used to elastically warp structures into a shape other than their natural and unique equilibrium shape. These existing concepts require the continuous application of power to maintain the warped shape. With the concept discussed here, the actuators are used only to change from one equilibrium shape to another, so continuous power is not needed. The paper discusses several phases of modeling, including bonding the actuator to the laminate and applying voltage to the actuator to effect the shape change, and experimental work. Two models are developed, a simple model and a more refined one. Both are based on the Rayleigh-Ritz technique and the use of energy and variational methods. The experimental phase of the study is discussed, particularly the measurement of the voltage level needed to snap the laminate. The voltage measurements are compared with predictions and the agreement between measurements and the predictions of the refined model are reasonable, both qualitatively and quantitatively. Suggestions for future activities are presented.

Thermal buckling and postbuckling of symmetrically laminated composite plates

The thermal buckling and postbuckling response of symmetrically laminated composite plates are discussed. Using variational methods in conjunction with a Ray-leigh-Ritz formulation, thermal buckling and postbuckling are investigated for two laminates, a ( ±45/0/90) s and a ( ± 45/02 ) s, under two different simple support conditions, fixed and sliding. These laminates are subjected to the condition of a uniform temperature change. The effects of the principal material axes not being aligned with the edges of the plate, referred to here as material axis skewing, are also investigated. Although differences between buckling temperatures for the two support conditions were small, support conditions can have a large influence on thermal postbuckling response. In general, plates with fixed simple supports defied more than plates with sliding simple supports. In addition, support conditions can influence modal interaction. Skewing of the material axis decreases the buckling temperatures of both laminates and, li...

Contact stresses in pin-loaded orthotropic plates

Abstract A study to determine the effects of pin elasticity, friction, and clearance on the stresses near the hole in a pin-loaded orthotropic plate is described. The problem is modeled as a contact elasticity problem, the pin and the plate being two elastic bodies interacting through contact. This modeling is in contrast to previous works, by other investigators, which have assumed that the pin is rigid or that it exerts a known cosinusoidal radial traction on the hole boundary. Neither of these approaches explicitly involves a pin. A complex variable series, a collocation procedure, and iteration were used to obtain numerical results for a variety of plate and pin elastic properties and various levels of friction and clearance. Collocation was used to enforce the boundary conditions at a finite number of points around the hole boundary and iteration was used to find the contact and no-slip regions on the boundary. Details of the numerical scheme are discussed. The study shows that pin elasticity is not as important as clearance, friction, or the elastic properties of the plate in determining contact stresses.