We consider the problem of finding a geometrical form of a body in a thermal radiation field, for which the thermal balance between the body and the surrounding air is minimal. The case of a point source of heat is investigated. To consider an analogous problem for buildings, one must know the value of incoming thermal energy to a unit square in relation to its orientation. We develop an application package in MATLAB that represents this relation in table form and takes into consideration the direct, diffuse, ground-reflected solar radiation and the thermal radiation of atmosphere.

Abstract. The two-dimensional concrete elements under the action of one-sided central crushing often occurs. For them, the strength problems are solved on the basis of the concrete ideal plasticity theory variational method with application of discontinuous velocities functions. The method takes into account the influence on concrete elements strength the compressive strength and tensile strength of concrete. It also takes the ratio of a sample height to the crushing platform length and friction coefficient between a surface of element and a load punch if it′s necessary. The results of experimental researches were confirmed the assumed in the theoretical solution the kinematical schemes of elements failure. Higher convergence of theoretical strength with tested is received. The calculation sequence of the concrete element under one-sided central crushing is described. The joint calculation of all factors that determine the strength opens the possibility of more accurate assessment and improvement on its basis of structural solutions of concrete elements under the local compressive load.

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The central one-sided concrete element crushing is considered when the loading platform width is less than the element width (in three-dimensional stress state conditions). A variational method in the concrete plasticity theory, which is developed in the Poltava National Technical Yuri Kondratyuk University, is proposed to calculate the strength. The formula for determining the ultimate load is based on the destruction kinematics, which is observed in the experiments, and takes into account the loading platform size ratio and the element, both concrete strength characteristics, the frictional forces between the support surface and the element. The calculation dependence is rather precise during the cubes central crushing when the element height ratio and the loading platform greater than 4. With other geometric parameters the kinematic scheme changes, which must be taken into account when deriving the formulas for calculating the strength by the variational method. The proposed method allows considering all possible calculation schemes and determining its application limits.

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