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The plated structures are one of the most frequently used engineering structures. The object of this research work is the optimal design of curved folded plates. This work is an ongoing investigation. There are various solution methods to analyze this type of structures. Here the finite strip method is used. At first single load condition is consid...

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... expression (55) K g means ∂ t g t g . As usual, the box constraints are treated separately from the compliance inequality constraint, as they are not involved in the formulation of the La- grangian function, but examined at every iteration cycle. Therefore, if a thickness happens to fall outside of the feasible set, in the next cycle it is forced to start with the boundary value ( t max or t ) of the box. In the following, sample problems are introduced to illustrate the above explained methods. As already mentioned, the Finite Strip Method is used for the evaluation of the state variables, which excels in the calculation of structures with constant cross section. These include the following examples: At each run, quadratic base functions were used in the cross section. The boundary conditions are also the same, according to the rules of the classical finite strip method (CFSM). This means that hinged supports were prescribed by choosing the proper trigonometric functions, while no additional boundary conditions were imposed. Here we note, that in all cases, the cross sections should be understood in the x-z plane, therefore in Fig. 5 size ‘a’ means the width of the plate and size ‘b’ means it’s width and accordingly the thickness is the size in the ‘z’ direction. The introduced plate was subjected to various loads, which positions are given with coordinates relative to the upper left corner, as seen in Fig. 7. The first load case is a single concentrated force F 100 kN pointing downwards, acting in the geometric middle of the structure, so according to the notation of Fig. 7, ξ = 3 m and η = 4 m in this case. The obtained thickness distribution can be seen on the left of Fig. 8. The result for the same setup, but with a hor- izontal load is presented on the right of the same picture. With two concentrated forces of both 100 kN placed at ξ = 2 m and 4 m , η = 4 m : The setup of these examples is the same as at the straight plate, with the di ff erence, that the loads positions should be understood with the same value, but in a cylindrical relative coordinate system, illustrated on the next figure. The geometry of this example is presented on Fig. 12. On the next figure (Fig. 13), the loads are always placed at the mid-span on the top flange at the position of the webs, so according to the notation of Fig. 11: ξ = 2 m and / or 4 m , η = 5 m . The geometry of this example shows no di erence to the pre- vious one, except that the bridge has a curved geometry around the vertical axis. Only one load case was investigated, which can be put into comparison with the upper left picture of Fig. 13. The position of the concentrated forces should be understood as before. A numerical procedure and computer program were elaborated for optimization of folded plates subjected to multiple loadings. The computational method is based on the finite strip method. The elaborated procedure with a slight modification can be suitable for the case of stochastic loading and / or multiple loading cases, as well. The surrogate loading system is problem dependent. To make more appropriate models it is needed to make some additional investigations on the topic. The present study was supported by the Hungarian National Scientific and Research Foundation (OTKA) (grant K ...

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... The MOP was used to modify the shape of buildings like corners, slots, setbacks, pedestrian level wind comfort, thermal comfort, and many more situations (Wang et al. 2019, Xie and Yang 2019, Paul and Dalui 2020. Space structures, R.C.C., and steel structural frame, dome structures are also optimized for better aerodynamic performance and cost minimization approach (Kaveh and Raeissidehkordi 2002, Balogh and Lógó 2014, Gholizadeh 2015, Kaveh and Kooshkbaghi 2019). In Fig. 9 (a) Flow chart of Genetic Algorithm (GA), (b) flow diagram of the multi-objective minimization process this study, MOP was used to minimize the drag and lift of the setback building models using their best combination of geometric parameters. ...

This paper highlights the minimization of drag and lift coefficient of different types both side setback tall buildings by the multi-objective optimization technique. The present study employed 48 number both-side setback models for simulation purposes. This study adopted three variables to find the two objective functions. Setback height and setback distances from the top of building models are considered variables. The setback distances are considered between 10-40% and setback heights are within 6-72% from the top of the models. Another variable is wind angles, which are considered from 0° to 90° at 15° intervals according to the symmetry of the building models. Drag and lift coefficients according to the different wind angles are employed as the objective functions. Therefore 336 number population data are used for each objective function. Optimum models are compared with computational simulation and found good agreements of drag and lift coefficient. The design wind angle variation of the optimum models is considered for drag and lift study on the main square model. The drag and lift data of the square model are compared with the optimum models and found the optimized models are minimizing the 45-65% drag and 25-60% lift compared to the initial square model.

... Problem 1 used to find the optimal tall building cross-section to reduce the drag force due to wind and problem 2 used to found the optimal cross-section to reduce the wind lateral vibration. The optimization tool already takes a large role and used to predict the interference effect minimization (Kar et al. [16]), folded curve plate design (Balogh and Lógó [17]), truss optimization with multiple natural frequency constraints (Kaveh and Kooshkbaghi [18]) and many multi-disciplinary types of researches. Dhote and Varghese [19] analyzed the bending moment and shear force variation on tall buildings by ANN method, and validated with IS 875 (Part-3) [20]. ...

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The wind load on an irregular plan shape tall building is quite different compared to a conventional plan shape tall building. Especially the aerodynamic parameters have extreme change due to the variety of setbacks at one or more the disparity of level. This paper highlights the prediction of pressure coefficient on square, single (20 %) setback and double (10 %) setback buildings for any wind incidence angle by CFD simulation and validated with Artificial Neural Network (ANN) and fast Fourier transform. The ANN is a widely used and efficient tool for different types of analyses. The 0° to 180° wind incidence angles (WIAs) considered as input data and respective face wise pressure coefficient (Cp) used as target data. The Levenberg-Marquardt training function and Mean Square Error (MSE) performance function used to train the target data. The face wise graphs of CFD, ANN and FFT are plotted in a single graph and the Cp of the surface checked by any random WIAs. Amazingly, the C p of random WIA by ANN is almost similar to CFD. Furthermore, the error of ANN is 0.6 % to 2.5 %, which is negligible. According to this predicted graph, the design C p of any WIA can be easily calculated and implement directly in the design.

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The long-span structure of the San Nicolás church was designed in 1959 by the renowned engineer E. Torroja. His innovative solution consists of two Z-shaped folded plates mutually independent spanning 29 m. In this paper the technical advances used by the engineer to carry out its daring structure are explained. A series of ribs provide stiffness to the slabs facing biaxial bending and torsion and support cantilevered roof. The set of post-tensioned tendons contribute to the strength capacity of the slabs as well as avoid the cracking of concrete. Rotation and the horizontal displacement of the plates are released by the twofold articulation of the main frame. The simplified structural design carried out by the engineer is explained and his results are compared with the structural analysis obtained by a virtual finite element model. The aggressive environment caused corrosion in reinforced concrete elements, but not in the post-tensioned concrete plates.

The transverse behavior of a long span three-plate precast roof element is investigated by means of an experimental and numerical research. The performed study highlights that the failure mode of this folded-plate element is strongly influenced by the amount of transverse reinforcement in the wings. This latter is usually designed through simplified methods, which often lead to over-dimensioning in terms of steel welded mesh. To avoid excessive costs for the producers, transverse reinforcement optimization should be required. In this work, a non-linear FE modelling was applied for this purpose. The reliability of the followed numerical procedure was first verified by an initial type testing (i.e. experimental load test up to failure). The agreement between numerical and experimental results showed the efficiency of the model in simulating all the main sources of non-linearity related to both material behavior and element geometry. Numerical analyses were so used to perform a parametric study as a function of transverse reinforcement amount, aimed at determining a coefficient of “model inaccuracy”. This coefficient should be used as a correction factor for the element design in routine calculations based on beam theory.

There is an additional new fact that topology optimization has started its career more than hundred years ago by Maxwell and only a few years later by Michell. The classical solutions of the different type of plate or shell problems can be followed by the works of Mroz, Prager and Shield. This paper overviews these almost forgotten results. In addition to the conspectus of this hidden period, the optimal design of curved folded plates is presented. The finite strip method is used for the analysis. At first, a single load case is considered, but later multiple load cases are used for the design. The base formulation is a minimum volume design with displacement constraint, which is represented by the strain energy. For the multiple loading cases two topology optimization algorithms are elaborated: minimization of the maximum strain energy with respect to a given volume and the minimization of the weighted sum of the compliance of the connected load cases with respect to a given volume. The numerical procedures are based on iterative formulae, which are formed by the use of the first order optimality condition of the Lagrangian-functions. The application is illustrated by numerical examples.