Filters
Optimal Design of Bubble Deck Concrete Slabs: Serviceability Limit State
In engineering practice, one can often encounter issues related to optimization, where the goal is to minimize material consumption and minimize stresses or deflections of the structure. In most cases, these issues are addressed with finite element analysis software and simple optimization algorithms. However, in the case of optimization of certain structures, it is not so straightforward. An example of such constructions are bubble deck ceilings, where, in order to reduce the dead weight, air cavities are used, which are regularly arranged over the entire surface of the ceiling. In the case of these slabs, the flexural stiffness is not constant in all its cross-sections, which means that the use of structural finite elements (plate or shell) for static calculations is not possible, and therefore, the optimization process becomes more difficult. This paper presents a minimization procedure of the weight of bubble deck slabs using numerical homogenization and sequential quadratic programming with constraints. Homogenization allows for determining the effective stiffnesses of the floor, which in the next step are sequentially corrected by changing the geometrical parameters of the floor and voids in order to achieve the assumed deflection. The presented procedure allows for minimizing the use of material in a quick and effective way by automatically determining the optimal parameters describing the geometry of the bubble deck floor cross-section. For the optimal solution, the concrete weight of the bubble deck slab was reduced by about 23% in reference to the initial design, and the serviceability limit state was met.
Optimal Design of Bubble Deck Concrete Slabs: Sensitivity Analysis and Numerical Homogenization
The use of layered or hollow floors in the construction of buildings obviously reduces the self-weight of the slab, and their design requires some expertise. In the present work, a sensitivity analysis and numerical homogenization were used to select the most important characteristics of bubble deck floors that have a direct or indirect impact on their load capacity. From the extensive case study, conclusions were drawn regarding the optimal selection of geometry, materials, and the arrangement and size of air voids in such a way as to ensure high stiffness of the cross-section and at the same time maximally reduce the self-weight of the slabs. The conducted analyses showed that the height of the slab and the geometry of the voids had the greatest impact on the load-bearing capacity. The concrete class and reinforcement used are of secondary importance in the context of changes in load-bearing capacity. Both the type of steel and the amount of reinforcement has a rather small or negligible influence on the bubble deck stab stiffness. Of course, the geometry of the voids and their arrangement and shape have the greatest influence on the drop in the self-weight of the floor slabs. Based on the presented results of the sensitivity analysis combined with numerical homogenization, a set of the most important design parameters was ordered and selected for use in the optimization procedure.
Application of the generalized nonlinear constitutive law in numerical analysis of hollow-core slabs
Parametric Optimization of Thin-Walled 3D Beams with Perforation Based on Homogenization and Soft Computing
The production of thin-walled beams with various cross-sections is increasingly automated and digitized. This allows producing complicated cross-section shapes with a very high precision. Thus, a new opportunity has appeared to optimize these types of products. The optimized parameters are not only the lengths of the individual sections of the cross section, but also the bending angles and openings along the beam length. The simultaneous maximization of the compressive, bending and shear stiffness as well as the minimization of the production cost or the weight of the element makes the problem a multi-criteria issue. The paper proposes a complete procedure for optimizing various open sections of thin-walled beam with different openings along its length. The procedure is based on the developed algorithms for traditional and soft computing optimization as well as the original numerical homogenization method. Although the work uses the finite element method (FEM), no computational stress analyses are required, i.e., solving the system of equations, except for building a full stiffness matrix of the optimized element. The shell-to-beam homogenization procedure used is based on equivalence strain energy between the full 3D representative volume element (RVE) and its beam representation. The proposed procedure allows for quick optimization of any open sections of thin-walled beams in a few simple steps. The procedure can be easily implemented in any development environment, for instance in MATLAB, as it was done in this paper.
Numerical and Experimental Validation of Homogenization Techniques for Bubble Deck Slabs
This study investigates the deflection behaviour of Bubble Deck slabs using numerical and experimental approaches. Two techniques—numerical homogenization and 3D cross-sectional integration—are applied to derive equivalent properties for simplified finite element models. A scaled slab specimen (1020×2040×60 mm) with a reinforcement mesh of Ø4 bars spaced at 30 mm (top and bottom) and plastic spheres (Ø40 mm, spaced at 60 mm) is tested under self-weight and a mid-span linear load. The slab, simply supported on two shorter edges, is modelled both in full 3D and using simplified 2D model with homogenized parameters. Experimental deflections are compared with numerical and analytical/theoretical predictions to validate the proposed techniques, demonstrating their effectiveness in simplifying structural analyses while maintaining accuracy.
Elastic Analysis of Three-Layer Concrete Slab Based on Numerical Homogenization with an Analytical Shear Correction Factor
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.
Effective Stiffness of Thin-Walled Beams with Local Imperfections
Thin-walled beams are increasingly used in light engineering structures. They are economical, easy to manufacture and to install, and their load capacity-to-weight ratio is very favorable. However, their walls are prone to local buckling, which leads to a reduction of compressive, as well as flexural and torsional, stiffness. Such imperfections can be included in such components in various ways, e.g., by reducing the cross-sectional area. This article presents a method based on the numerical homogenization of a thin-walled beam model that includes geometric imperfections. The homogenization procedure uses a numerical 3D model of a selected piece of a thin-walled beam section, the so-called representative volume element (RVE). Although the model is based on the finite element method (FEM), no formal analysis is performed. The FE model is only used to build the full stiffness matrix of the model with geometric imperfections. The stiffness matrix is then condensed to the outer nodes of the RVE, and the effective stiffness of the cross-section is calculated by using the principle of the elastic equilibrium of the strain energy. It is clear from the conducted analyses that the introduced imperfections cause the decreases in the calculated stiffnesses in comparison to the model without imperfections.
Shell-to-Beam Numerical Homogenization of 3D Thin-Walled Perforated Beams
Determining the geometric characteristics of even complex cross-sections of steel beams is not a major challenge nowadays. The problem arises when openings of various shapes and sizes appear at more or less regular intervals along the length of the beam. Such alternations cause the beam to have different stiffnesses along its length. It has different bending and shear stiffnesses at the opening point and in the full section. In this paper, we present a very convenient and easy-to-implement method of determining the equivalent stiffness of a beam with any cross-section (open or closed) and with any system of holes along its length. The presented method uses the principles of the finite element method (FEM), but does not require any formal analysis, i.e., solving the system of equations. All that is needed is a global stiffness matrix of the representative volumetric element (RVE) of the 3D representation of a beam modeled with shell finite elements. The proposed shell-to-beam homogenization procedure is based on the strain energy equivalence, and allows for precise and quick determination of all equivalent stiffnesses of a beam (flexural and shear). The results of the numerical homogenization procedure were compared with the existing analytical solution and experimental results of various sections. It has been shown that the results obtained are comparable with the reference results.