The need for quick and easy deflection calculations of various prefabricated slabs causes simplified procedures and numerical tools to be used more often. Modelling of full 3D finite element (FE) geometry of such plates is not only uneconomical but often requires the use of complex software and advanced numerical knowledge. Therefore, numerical homogenization is an excellent tool, which can be easily employed to simplify a model, especially when accurate modelling is not necessary. Homogenization allows for simplifying a computational model and replacing a complicated composite structure with a homogeneous plate. Here, a numerical homogenization method based on strain energy equivalence is derived. Based on the method proposed, the structure of the prefabricated concrete slabs reinforced with steel spatial trusses is homogenized to a single plate element with an effective stiffness. There is a complete equivalence between the full 3D FE model built with solid elements combined with truss structural elements and the simplified homogenized plate FE model. The method allows for the correct homogenization of any complex composite structures made of both solid and structural elements, without the need to perform advanced numerical analyses. The only requirement is a correctly formulated stiffness matrix of a representative volume element (RVE) and appropriate formulation of the transformation between kinematic constrains on the RVE boundary and generalized strains.

The interest in passive construction that has low demand for thermal energy continues to grow every year. It is related to both the reduction in maintenance costs of buildings and the growing environmental awareness in societies. Passive houses are characterised by very good thermal insulation properties of their external partitions. This paper presents the results of tests on the thermal conductivity for three different types of building materials, assuming their use as thermal insulation. The materials were subjected to water absorption tests during long-term immersion. The purpose of this study was to simulate water absorption caused by long-term water exposure. The tests were carried out on a perlite concrete block, a sheet of polyurethane foam applied by spraying and expanded clay in a loose form in three different fractions. The tested insulation materials were selected due to their different form, structure, and porosity characteristics, which largely determined the value of the thermal conductivity. A perlite concrete block is a new, innovative product, of which manufacturer’s data are not yet available as the product is currently at the stage of detailed research. The results were analysed statistically and used in graphs to show the dependence of the value of the thermal conductivity on moisture content of the samples. The purpose of this study was to indicate the importance of the proper incorporation of insulation materials into buildings, their storage before construction and use in the post-construction phase. Building standards for passive houses place high demands on materials used. In order to fully enjoy the advantages of passive buildings, i.e., lower energy consumption and benefits for the natural environment due to lower consumption of energy generated from non-renewable energy sources, it is necessary to use certified building materials and ensure proper use of objects. The studies quoted in this paper indicate to what extent the influence of moisture content negatively affects the properties of insulation materials in external partitions.

Moisture transport in building materials significantly influences their durability, mechanical integrity, and thermal performance. This study presents an experimental investigation of moisture permeability in a range of traditional and modern wall elements, including autoclaved aerated concrete (ACC), ceramic blocks, silicate blocks, perlite concrete blocks, and concrete units. Both vapor diffusion and capillary transport mechanisms were analyzed under controlled climatic conditions using gravimetric and hygrometric methods. Among the tested materials, autoclaved aerated concrete (AAC) was selected for detailed numerical modeling because of its high porosity, strong capillarity, and widespread use in modern construction, which make it especially vulnerable to moisture-related degradation. Based on the experimental findings, a digital twin was developed to simulate hygrothermal behavior of walls made of ACC under various environmental conditions. The model incorporates advanced moisture transport equations, capturing diffusion and capillary effects while considering real-world variables, such as relative humidity, temperature fluctuations, and wetting–drying cycles. Calibration demonstrated strong agreement with experimental data, enabling reliable predictions of moisture behavior over extended exposure scenarios. This integrated approach provides a robust engineering tool for assessing the long-term material performance of AAC, predicting degradation risks, and optimizing material selection in humid climates. The study illustrates how coupling experimental data with digital modeling can enhance the design of moisture-resistant and durable building envelopes.

Current trends towards saving energy and designing sustainable buildings result in most designers focusing on achieving the best thermal parameters, thereby neglecting a careful moisture analysis. Excessive moisture content in building partitions degrades the mechanical properties of materials, reduces thermal insulation properties (which leads to an increase in the demand for thermal energy) and worsens the microclimate in rooms. Modern digital solutions help create appropriate models of partitions that work for many years in good environmental conditions. According to the analysis of air parameters, 1 m³ of air at 20 °C contains approx. 17.3 g of water. When the temperature of the air reaches the dew point temperature, water vapour condenses. The dew point depends on air temperature and relative air humidity; for instance, at the same air temperature of 20 °C, the dew point temperature at 40% relative air humidity is 6 °C, whereas at 90% relative humidity, it is over 18 °C. This means that the higher the value of relative humidity in the room at a certain temperature, the lower the temperature that will cause condensation. The article presents a numerical analysis of the insulation work of flexible materials within the layers of ventilated partitions in an 8-year simulated period of varying environmental conditions. The aim of the article is to analyze different models and variants of ventilated partition operation with respect to the advisability of using a vapour barrier to avoid the problem of destruction of thermal insulation and finishing layers of a ventilated roof.

Sandwich structures are widely used in construction, as well as in the aviation, spaceship, and electronics industries. The interesting result, among others, is the fact that individual layers can be freely selected to meet the planned requirements. In the case of sandwich structures in construction, they must meet the requirements of load-bearing capacity, thermal, and acoustic insulation, and additionally, they must be resistant to biological and chemical corrosion. The paper presents calculation algorithms for Hoff’s three-layer panels. In the first case, the well-known and proven method of finite differences in variation terms was used, assuming actual geometrical and material parameters. In the second case, the numerical homogenization method of the layered panel was used, replacing the stiffnesses of individual layers with a homogeneous equivalent plate with substitute stiffness corrected in shearing by an analytically derived shear correction factor. A comparative analysis of the results of the calculations with the use of both approaches was carried out. A good agreement between the displacement values and the calculated cross-sectional forces was obtained. On this basis, it can be assumed that the static analysis of a slab by simplified methods using numerical homogenization with an analytical shear correction factor is appropriate and can be applied to layer structures.

The method to calculate rectangular tanks as a system of bi-directionally bent plates with the use of separated plates methodology is a widely known and currently most often used approach to verify numerical calculations obtained from computer software supporting the design process, in which spatial operation of tanks is taken into account. In these calculations, due to their static scheme, it is possible to distinguish supported plates, plates fixed on four edges and plates with one edge free and three fixed. The subject literature contains publications on plates or tanks with walls of a constant thickness, however, there are very few references on plates or tanks with walls of linearly variable thickness. The wall plate of a tank is subject to hydrostatic load or soil pressure and might be exposed to thermal load in the case of, i.e. filling it with hot liquid or during climate action. The article presents the results of static calculations for rectangular plates with a linearly variable thickness, a trapezoidal cross-section, three fixed edges and one edge free, subjected to permanent and thermal loads. Trapezoidal cross-section walls are optimal when used in structures where load distribution is triangular in shape (hydrostatic load). For tanks recessed in the ground, the load on walls increases along with the depth of foundations and obtains the highest value in the bottom part of the wall. Trapezoidal or triangular load distribution causes that the highest values of bending moments in the vertical cross-section occur at the point where a wall connects to the bottom, while the upper free edge of the tank takes zero value. The above statements lead to the conclusion that structural and economic considerations should determine the choice of walls with a thickness increasing along with the tank depth, since it is more economical in terms of material usage. The impact of thermal load is often neglected in the design process, which may cause operational problems and even pose a threat to the safety of use. In addition to the numerical analysis, the article presents the results of model tests for a plate with a linearly variable thickness made of resin, subjected to thermal load. The convergence of the obtained results proves the correctness of calculations and tests performed. This also contributes to the recognition of statics in rectangular plates of a trapezoidal cross-section.