The Development of Log Aesthetic Patch and Its Projection onto the Plane

In this work, we introduce a new type of surface called the Log Aesthetic Patch (LAP). This surface is an extension of the Coons surface patch, in which the four boundary curves are either planar or spatial Log Aesthetic Curves (LACs). To identify its versatility, we approximated the hyperbolic paraboloid to LAP using the information of lines of curvature (LoC). The outer part of the LoCs, which play a role as the boundary of the hyperbolic paraboloid, is replaced with LACs before constructing the LAP. Since LoCs are essential in shipbuilding for hot and cold bending processes, we investigated the LAP in terms of the LoC’s curvature, derivative of curvature, torsion, and Logarithmic Curvature Graph (LCG). The numerical results indicate that the LoCs for both surfaces possess monotonic curvatures. An advantage of LAP approximation over its original hyperbolic paraboloid is that the LoCs of LAP can be approximated to LACs, and hence the first derivative of curvatures for LoCs are monotonic, whereas they are non-monotonic for the hyperbolic paraboloid. This confirms that the LAP produced is indeed of high quality. Lastly, we project the LAP onto a plane using geodesic curvature to create strips that can be pasted together, mimicking hot and cold bending processes in the shipbuilding industry.

NUMERICAL MODELING OF THE DISTRIBUTION OF SNOW LOAD ON A HYPERBOLIC PARABOLOID. THEORETICAL BASIS

The paper discusses the choice of a method for studying the distribution of snow loads on a biconcave roof of a hyperbolic paraboloid and its theoretical justification. It is noted that the numerical modeling of the aerodynamic characteristics of buildings and structures is a difficult and resource-intensive task due to the design features of building objects, which, as a rule, have a complex geometric shape, as well as due to a complex unsteady flow resulting from their flow around them. In addition, the task becomes more complicated due to the interference of vortex structures between different objects. Overcoming these objective difficulties became possible with the advent of modern specialized software systems, primarily ANSYS Fluent. Opportunities have appeared for accurate modeling with verification of the results obtained, which implies the use of an effective, well-tested mathematical apparatus. To implement the theory of two-phase flow, two methods based on numerical modeling are mainly used: the Euler-Lagrange method and the Euler-Euler method. The second method is used in the work. Comparative analysis, which investigates two-phase flow around different structures using different turbulence models (including RSM model, SST k-ω model, k-ε model and k-kl-ω model), shows that the k-kl-ω model is the best fit with experiment. ANSYS Fluent supports four multiphase models, i.e. VOF model, Mixture model, Wet Steam and Euler model. Compared to the other three models, the Mixture model provides better stability and lower computational costs, while the Euler model provides better accuracy, but at a higher computational cost . With a rather complex geometry and flow conditions, the use of the RANS approach does not lead to reliable simulation results. Moreover, unsteady turbulent flows cannot be reproduced. In real situations, landslides, saltations, and the suspended state of snow particles are closely related to the real effects of microbursts and bursts present at the surface of the boundary layer. Therefore, in further research, it is advisable to apply alternative approaches to RANS, which include Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), and the hybrid RANS-LES approach to turbulence modeling, which combine efficiency LES techniques in tear-off free zones and the cost-effectiveness of RANS in near-wall areas.

Influence of the concrete strength and the type of supports on the stress-strain state of a hyperbolic paraboloid shell footbridge structure

Relevance. This work is the first in a series of publications on the selection of a suitable analytical surface for implementation as a self-supporting structure for a thin shell footbridge. The study on the influence of concrete strength, live load position and support types on the stress-strain state of a hyperbolic paraboloid (hypar) shell is presented. Objective - to define the initial design parameters such as the appropriate concrete strength and the support type that generates the best structural behaviour to perform the subsequent structural design of a thin shell footbridge. Methods. The static finite element analysis was performed for 4 compressive strengths of concrete (28, 40, 80, 120 MPa) which correspond normal, high and ultra-high resistance concrete, 5 different live load arrangements and 3 different support conditions. Results. The shell model with pinned (two-hinged) supports shows the same vertical displacements as the model with fixed supports (hingeless). For the studied shell thickness, in terms of stress behaviour, the model with pinned ends is more efficient. The combination of two-hinged supports with 80 MPa concrete strength shows a better structural performance.

Inverted Umbrella-type Hyperbolic Paraboloid Reinforced Concrete Shell Structures (Inverted Umbrella HP RC Shells)

The inverted umbrella HP RC shells became a predominant type of single column structure during the 1950s and 1960s. The paper provides a historical overview of architecturally most attractive inverted umbrella HP structures made out of reinforced concrete. It starts in the second quarter of the 20th century with the world’s oldest umbrella structures, designed by three pioneers: F. Aimond, A. Williams and K. Hruban. The most notable master in designing was F. Candela, as he constructed a number of this structures in Mexico between 1953-68. During the 1960s this form became widely used all over the Western world but suddenly disappear after 1975. The results of the paper are presented in three figures where the inverted umbrella HP RC shells are analysed according to several criteria (number of built elements, roof dimensions with shapes, use of the structures in relationship to year of completion). The similarities and differences between elements of the analysed buildings are compared and discussed. In the conclusion, the advantages and disadvantages are briefly exposed.