Abstract
The results of a comparative analysis of numerical solutions of problems of determining the form of the body of minimal resistance and maximal depth of penetration into a plastic soil are presented. Optimal forms of the bodies of the assigned length and cross-section radius with a piecewise-linear presentation of the generatrix are obtained in the framework of one of the modifications of the local variation method. A binomial quadratic model of local interaction including inertial and strength components is used. The difference between the resistance forces and penetration depths of cones and those of the obtained optimal forms for various initial impact velocities has been analyzed. For a medium with assigned parameters, critical velocities have been determined for which the radius of the frontal flat end of an optimal body comes to be equal to zero, whereas the cone of an assigned length and cross-section area is an absolutely optimal body. A considerable difference between the forms for velocity values close to critical is noted, as well as the approach of the generatrices with the increasing velocity. Keywords: soil medium, body of revolution, minimal total resistance, maximal penetration depth, local interaction model, optimization, local variation method.
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