Vol 21, No 5 (2025)

An analysis of a number of published materials regarding four types of developable surfaces with two director (supporting) algebraic curves of the second order lying in parallel or in intersecting planes has been conducted. Three types of developable surfaces are shortly described with references to sources, and visualizations of each type of developable surface are presented. For the developable surfaces with two supporting curves with intersecting axes in intersecting planes, the construction technique and the method of obtaining parametric equations are given. This method is illustrated with three examples. It is established that to date, there are no studies on the strength of thin shells in the form of the presented developable surfaces defined in curvilinear conjugate non-orthogonal coordinates that coincide with the external contour of the shells. It is shown that there are suggestions of application of the studied surfaces in architecture, shipbuilding, and agricultural machine engineering.

In this study, thin shells in the form of algebraic surfaces defined by a geometric frame of three plane superellipses lying respectively in three coordinate planes are considered. As the main focus of the study, the case when the horizontal superellipse is a circle is examined. It is shown that depending on the type of the other two superellipses, it is possible to obtain a conical surface, or a surface of negative Gaussian curvature, including conoids, or surfaces of positive Gaussian curvature. The construction of 12 particular cases of such surfaces with a circular base is illustrated. Six of them are investigated in detail using the methods of differential geometry, i.e. expressions of the fundamental quadratic forms are obtained, for the first time. Out of the 12 presented shell shapes, two ruled shells of zero and negative Gaussian curvature (conical and cylindroidal respectively) with the same geometric frame were selected for comparative static analysis. The two shells were analyzed for uniform distributed load using displacement-based FEM implemented in the SCAD software. It is shown that despite the two shells having identical geometric frames, the conical shell demonstrated better performance over the most strength parameters.

A quasilinear representation of a nonlinear rheological equation of concrete state has been established, derived on the basis of the concept of statistical strength distribution of individual fractions combined to form a structural element. In the nonlinear formulation for ageless concrete, L. Boltzmann’s well-known principle of superposition of creep deformations is realized by increments of structural stress of fractions capable of force resistance under non-decreasing loading. For aging concrete, in contrast to previous approaches, the superposition of partial increments of deformations generated by increments in stress levels is implemented. This leads to the correct consideration of concrete aging, clarifying the type of known rheological equations. Quasilinear forms of rheological equations that are convenient in applications are given. The concept of the strength structure of concrete and the identity of the aging functions of strength, modulus of elasticity and creep make it possible to reduce the creep equation to a linear differential equation with constant coefficients. This simplifies, in particular, the solution of stress relaxation problems, which are important in the calculations of structures for long-term safety.

This study presents an advanced layered triangular finite element method for modeling reinforced concrete (RC) slabs, incorporating material nonlinearity based on a refined global-local plate theory. The RC slab's cross-section is discretized into concrete and steel layers, each modeled as an individual plate element with distinct material properties. The proposed formulation independently considers displacement field variables and out-of-plane stress components, enabling precise nodal stress determination through constitutive relationships. A three-node triangular element maintaining C1-continuity is employed for spatial discretization, with governing equations derived using a triangular layered plate theory. Benchmark verification studies confirm the method’s computational accuracy and efficiency, with ultimate deflection predictions exhibiting errors ranging from 2.59% (minimum) to 11.2% (maximum). Comprehensive numerical tests demonstrate that the proposed triangular layered finite element approach delivers high-precision solutions while significantly reducing computational expense.

This research covers and compares the thermomechanical behavior of steel and recycled aluminium plates under concentrated loading and buckling conditions in several thermal conditions simulating the tropical savanna (Aw) climate. The study aims to explore their structural behavior as a function of temperature and evaluate their applicability in heat-sensitive applications. Finite element analysis (FEA) was used to model the buckling and deformation behavior of the two materials at temperatures from 0°C to 44°C and uniaxial loading of up to 100 MPa. The analytical and numerical solutions were compared; their results would differ no more than 5%, thus validating the FEA model. The steel plates generally buckled less (greater critical buckling load) in hotter thermal conditions than the aluminium. The buckling load of steel reduced by approximately 40% in Mode 1 when it went from 33°C to 44°C, while the buckling load of aluminium reduced by just 4.71%. The same trend was observed in Mode 2. These findings validate that recycled aluminium possesses superior thermomechanical stability to tropical thermal fluctuation and can be a good alternative as a material for structures in applications of high thermal fluctuation, which will be beneficial towards maximum utilization of resources in building engineering.