Uses explanations, word problems, and games to cover some mathematical topics that middle school students need to know, including the invention of numerical notations, basic arithmatical operations, measurements, geometry, graphs, and probability.

The response of a layered elastic half-space to a progressing exponentially decaying normal surface pressure is evaluated for a case in which the constant velocity V of the moving pressure is greater than that of the P and S waves, respectively, in the upper layer (superseismic). It is assumed that a steady-state exists with respect to coordinate axis attached to the moving load. The superseismic-subseismic geometry results in a stress field that extends over the entire plane, with sharp shocks possible only in that portion of the layer that lies behind the front of the progressing normal loading. A computer program for evaluating stresses and velocities at points in the medium is available and results are presented for a typical configuration of interest.

As part of a continuing study of material models for ground shock calculations, some aspects of both rate-dependent and rate-independent models for tensile behavior are examined. In particular, the SRI brittle fracture model is studied and compared with a simple tension cut off procedure. For large-scale problems such as those described in this report, it is important to avoid rate-dependent brittle tensile models, if possible, since rate effects appear to be important only on time scales much smaller than are resolvable in dynamic calculations. On the other hand, rate-independent brittle fracture models are incompatible with current continuum uniqueness-stability theory and hence may not be useable for these problems. It is necessary to examine this situation if tensile modeling techniques are to improve. Some ideas for resolving this conflict are discussed and recommendations for further study are made.

The main purpose of this study is to consider an uncoupling method for analyzing explosively loaded structures embedded in hysteretic media. The method, which is based on wave propagation considerations, can be viewed as the plane wave approximation extended to nonlinear problems. Free-field data (both traction and velocity vectors) must be known in order to apply the method. Accuracy of the approximation is shown to be quite good when applied to a series of one-dimensional soil-structure interaction problems, even when the structure and surrounding soil are both nonlinear. Multi-dimensional problems, and techniques for improving the method, are also discussed briefly.

This report is the first of a continuing study designed to produce more rational tension models for ground shock applications. This document is a review of the state of the art in tensile behavior modeling of earth materials. It contains an historical survey of the field, a discussion of experimental results from various tests and a review of more advanced tensile fracture models, often developed for other applications. In part two of this investigation, it is planned to implement several of the more promising models into the LAYER code to assess their sensitivity and importance for ground shock problems.

A heat pipe was designed for operation in the 100 - 200 K temperature range with maximum heat transport as a primary design goal; another designed for operation in the 15 - 100 K temperature range with maximum flexibility as a design goal. Optimum geometry and materials for the container and wicking systems were determed. The high power (100 - 200 K) heat pipe was tested with methane at 100 - 140 K, and test data indicated only partial priming with a performance limit of less than 50 percent of theoretical. A series of tests were conducted with ammonia at approximately 280 K to determine the performance under varying fluid charge and test conditions. The low temperature heat pipe was tested with oxygen at 85 - 95 K and with methanol at 295 - 315 K. Performance of the low temperature heat pipe was below theoretical predictions. Results of the completed testing are presented and possible performance limitation mechanisms are discussed. The lower-than-expected performance was felt to be due to small traces of non-condensible gases which prevented the composite wick from priming. (NTRL site)