A stability problem for a low-height curvilinear porous arch under random loading

Classical mechanics of deformable bodies is based on the continuity hypothesis. However, many structural elements are made of porous materials. Porous natural materials (soil, rocks) have invariable porosity. Porous synthetic materials (ceramics, concrete, graphite, and pressed powder metals) have controlled porosity. To calculate the strength and hardness of the structure, the material is assumed to be conditionally continuous with the adjusted porosity. Nowadays, there are many available works presenting mechanical characteristics of materials with different porosities. This paper proposes a new class of problems in mechanics of deformable solids. Considering a low arch stability problem, which is important in construction practice, the problem of optimal arch design is solved by controlling the properties of the material. The solution to the problem of stability of the low arch made of porous material is presented. The flat arch with a rectangular crosssection is exposed to equally distributed loading. The near-rational law of the porosity distribution over the cross-section is used. The load is considered as a random variable. The solution to the problem is obtained using the theory of stationary random processes. A comparative analysis of the reliability and material consumption is carried out for the arch with continuous and porous sections. The calculation shows that the porous structure of the arch reduces the material consumption by 13.3% without stability and reliability losses.