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As part of the Mathematical Problem Solving Project, MPSP, the goals and purposes of miniprojects are explored. Various conjectures are presented which are based partially upon observation of children working on projects and partially upon the opinions of mathematicians who have observed how problem-solving processes are used in real-world situations. Four miniprojects are outlined and a report on one project is given. (MP)

An overview of the Mathematical Problem Solving Project, MPSP, is given. The goals, organization, and history of the project are described and the progress toward those goals is discussed. The outcomes of the project are stated, a brief diary of activities given, and a listing of technical reports made. (MP)

Tests were performed measuring the locations and geometries of delaminations in Fiberite T300/976 graphite/epoxy, Fiberite IM7/977-2 graphite-toughened epoxy, and ICI APC-2 graphite/PEEK plates subjected to transverse impact loads. The data provide specific information on the effects of impactor velocity, impactor mass, material, thickness of back ply group, difference in fiber orientation between adjacent ply groups, plate thickness, and impactor nose radius. The data were compared to the results of the Finn-Springer model. The model was found to describe the data with reasonable accuracy.

A method is presented for calculating the locations, shapes, and sizes of delaminations which occur in a fiber reinforced composite plate subjected to transverse static or dynamic (impact) loads. The plate may be simply supported, clamped, or free along its edges. A model of the delamination formation was developed. This model was then coupled with a finite element analysis. The model and the finite element analysis were implemented by a computer code which can be used to estimate the load at which damage is initiated as well as the locations, shapes, and sizes of the delaminations.

Tests were performed measuring the damage initiation loads and the locations, shapes, and sizes of delaminations in Fiberite T300/976 graphite/epoxy, Fiberite IM7/977-2 graphite-toughened epoxy, and ICI APC-2 graphite-PEEK plates subjected to transverse static loads. The data were compared to the results of the Finn-Springer model, and good agreements were found between the measured and calculated delamination lengths and widths.

Tests were performed assessing the effectiveness of repair in restoring the mechanical properties of damaged, solid composite plates made of Fiberite T300/976 graphite-epoxy. Some (75%) or all (100%) of the damaged zone was cut out, and the plate was repaired by plugging and patching the hole. The effectiveness of the repair was evaluated by measuring the compressive strengths of undamaged plates, damaged plates with no cutout, damaged plates with a cutout, and plates that had been repaired.

The behavior of elliptical sublaminates created by delaminations in composite plates was investigated for plates subjected to in-plane compressive, shear, and thermal loads. The axes of the ellipse may be arbitrarily oriented with respect to the applied loads. A model was developed which provides the stresses, strains, and displacements of the sublaminate, and the loads applied to the plate at which the sublaminate buckles and at which it grows in size. A series of experiments was conducted on sandwich plates made of Fiberite T300/976 graphite-epoxy laminates bonded to an aluminum honeycomb core. Teflon film in either a circle or an ellipse was embedded in the laminate, simulating the presence of a delamination. Each plate was loaded in compression, and the load-strain history of the sublaminate, the sublaminate buckling load, and the sublaminate growth load were measured. The predictions of the model agreed reasonably well with the data.

The present volume on impact damage in composite plates presents an extensive compendium of visual and graphic data regarding a variety of material and impactor parameters. The photographs are taken with X-ray and C-scan imaging in conjunction with a dye penetrant to show matrix cracks and delaminations. Impact and static-loading tests are performed on plates of graphite-epoxy, graphite-toughened epoxy, and graphite-PEEK materials. The images are presented to yield specific visual data regarding such parameters as impactor velocity, thickness of the back ply group, impactor nose radius, and the effects of multiple delaminations. The images are grouped in eight subsets that correspond to parameters including plate length, material, and the difference in fiber orientation between adjacent ply groups. This substantial volume represents a systematic effort to study the effects of several material parameters on impact damage.

A method is presented for calculating the locations, shapes, and sizes of delaminations which occur in a fiber reinforced composite plate subjected to non-penetrating (low velocity) impact of a solid object. The plate may be simply supported, clamped, or free along its edges. A failure model of the delamination formation was developed. This model was then coupled with a finite element analysis. The model and the finite element analysis were then implemented by a computer code (IMPACT-ST) which can be used to estimate the damage initiation load and the locations, shapes, and sizes of the delaminations. Tests were performed measuring the geometries of the delaminations in graphite-epoxy, graphite-toughened epoxy, and graphite-PEEK plates impacted by a projectile with a spherical tip having masses ranging from 0.355 lbm to 0.963 lbm and velocities from 50 in/sec to 225 in/sec. The data were compared to the results of the model, and good agreements were found between the measured and the calculated delamination lengths and widths.

A model was developed which describes the filament winding process of composite cylinders. The model relates the significant process variables such as winding speed, fiber tension, and applied temperature to the thermal, chemical and mechanical behavior of the composite cylinder and the mandrel. Based on the model, a user friendly code was written which can be used to calculate (1) the temperature in the cylinder and the mandrel, (2) the degree of cure and viscosity in the cylinder, (3) the fiber tensions and fiber positions, (4) the stresses and strains in the cylinder and in the mandrel, and (5) the void diameters in the cylinder.

Analytical and experimental studies were performed to validate the model developed by Lee and Springer for simulating the manufacturing process of filament wound composite cylinders. First, results calculated by the Lee-Springer model were compared to results of the Calius-Springer thin cylinder model. Second, temperatures and strains calculated by the Lee-Springer model were compared to data. The data used in these comparisons were generated during the course of this investigation with cylinders made of Hercules IM-6G/HBRF-55 and Fiberite T-300/976 graphite-epoxy tows. Good agreement was found between the calculated and measured stresses and strains, indicating that the model is a useful representation of the winding and curing processes.

By using the Lee-Springer filament winding model temperatures, degrees of cure, viscosities, stresses, strains, fiber tensions, fiber motions, and void diameters were calculated in graphite-epoxy composite cylinders during the winding and subsequent curing. The results demonstrate the type of information which can be generated by the model. It is shown, in reference to these results, how the model, and the corresponding WINDTHICK code, can be used to select the appropriate process variables.

A model was developed for simulating he manufacturing process of filament-wound cylinders made of a thermoset matrix composite. The model relates the process variables (winding speed, fiber tension, applied temperature) to the parameters characterizing the composite cylinder and the mandrel. The model is applicable to cylinders for which the diameter is large compared to the wall thickness. The model was implemented by a user-friendly computer code suitable for generating numerical results.

The conceptual evolution of waverider configurations and their applications to hypersonic air vehicles are examined in the context of evolving mission requirements and technological advances. The fundamental objective of employing configurations which tend to maximize the payload fraction is emphasized, and the achievement of this objective over the time period of interest is reviewed, starting with high drag ballistic vehicles through low lift-drag ratio lifting bodies to the revived interest in high lift-drag ratio configurations. Practical applications of research in the area of lifting waveriders are discussed with particular reference to the B-70 Valkyrie and the Space Shuttle.