We obtained the solution of the optimization problem for the step-parallel beam with constant width of the cross-section. The problem was solved by minimizing the strain energy while the volume of beam is constant. The solution was made for the case of simple support at the ends and evenly distributed along the length load. We introduced the parameter α, which is the ratio of height of the average part to a height of side parts. The optimal value of α was found. At this value the stiffness of the beam is maximum at constant volume. The obtained beam of maximum stiffness is not equal strength.

Keywords: optimization, speed-prismatic beam, the strain energy, variable stiffness, minimum

We solved the problem of optimizing the gable beam by minimizing the strain energy at constant volume. The problem reduced to an integral equation for determining the optimum angle of the beam. This equation was solved numerically by the method of bisection. Integral was calculated using the method of trapezoids. Solution was made in software package Matlab. The optimum angle depends on the width of the cross section b, and the volume of the beam. It was found that with increasing of width of the cross section the optimum tilt angle decreases. Also the volume increases by increasing the width of the beam.

Keywords: optimization, gable beam, strain energy, variable rigidity, minimum volume, method of bisection

This article is related to technological problems of cavities with kamufletnyh explosions, during which the temperature in the cavity greatly exceeds the initial temperature of the array. Often these cavities are created in an array of rock salt. Because the salt even at light loads demonstrate expressive flow properties, it is interesting solution to the problem of creep salt massif with a cavity under the action of a force (pressure inside the cavity and the pressure of the soil), and thermal loads.

Keywords: heterogeneity, creep, highly elastic deformation, hydrochloric array coupling equation, the integral relations