A method for the optimization of a nonplanar airplane wing shape with respect to the total of induced and profile wing drags is presented. Optimization is performed subject to the lift constraint and one of the following: fixed span; fixed arc length; or fixed wing root bending moment. A planar wing is demonstrated to be the optimal solution in all cases for which the profile drag contributes most to the total drag. In the cases of fixed span and fixed root bending moment calculations, the emergence of nonplanar wings occurs as the optimal solution when the induced drag becomes the more significant component. This is marked by a break point in which the induced and profile drags are comparable.
COBISS.SI-ID: 3035387
The purpose of the present paper is development of a Non-singular Method of Fundamental Solutions (NMFS) for two-dimensional isotropic linear elasticity problems. The NMFS is based on the classical Method of Fundamental Solutions (MFS) with regularization of the singularities. This is achieved by replacement of the concentrated point sources by distributed sources over circular discs around the singularity, as originally suggested by [Liu (2010)] for potential problems. The Kelvin’s fundamental solution is employed in collocation of the governing plane strain force balance equations. In case of the displacement boundary conditions, the values of distributed sources are calculated directly and analytically. In case of traction boundary conditions, the respective desingularized values of the derivatives of the fundamental solution in the coordinate directions, as required in the calculations, are calculated indirectly from the considerations of two reference solutions of the linearly varying simple displacement fields. The developments represent a first use of NMFS for solid mechanics problems. With this, the main drawback of MFS for these types of problems is removed, since the artificial boundary is not present. In order to demonstrate the feasibility and accuracy of the newly developed method, is the NMFS solution compared to the MFS solution and analytical solutions for a spectra of plane strain elasticity problems, including bi-material problems. NMFS turns out to give similar results than the MFS in all spectra of performed tests. The lack of artificial boundary is particularly advantageous for using NMFS in multi-body problems.
COBISS.SI-ID: 2750203
This paper explores the application of Local Radial Basis Function Collocation Method (LRBFCM) [Šarler and Vertnik (2006)] for solution of Newtonian incompressible 2D fluid flow for a lid driven cavity problem [Ghia, Ghia, and Shin (1982)] in primitive variables. The involved velocity and pressure fields are represented on overlapping five-noded sub-domains through collocation by using Radial Basis Functions (RBF). The required first and second derivatives of the fields are calculated from the respective derivatives of the RBF’s. The momentum equation is solved through explicit time stepping. The method is alternatively structured with multiquadrics and inverse multiquadrics RBF’s. In addition, two different approaches are used for pressure velocity coupling (Fractional StepMethod (FSM) [Chorin (1968)] and Artificial CompressibilityMethod (ACM) [Chorin (1967)] with Characteristic Based Split (CBS) [Zienkiewicz and Codina (1995); Zienkiewicz, Morgan, Sai, Codina and Vasquez (1995)]). The method is tested for several low and intermediate Reynolds numbers (100, 400, 1000 and 3200) and computational node distributions (41x41, 81x81, 101x101, 129x129). The original contribution of the paper represents extension of the LRBFCM to Reynolds number beyond 400 and assessment of the method for two different types of RBFs and two different types of pressure-velocity couplings. The obtained numerical results, in terms of mid-plane velocities, are in a good agreement with the data calculated in several reference publications and by commercial CFD code. Both RBF’s used give approximately the same results. Both pressure-velocity coupling methods give approximately the same results, however the FSM turns out to be slightly more efficient. The advantages of the method are simplicity, accuracy and straightforward applicability in non-uniform node distributions.
COBISS.SI-ID: 2865659
Štore Steel Ltd. is a small flexible steel plant in Slovenia. In 2010, the new continuous rolling mill, which has a technical capacity of 250.000 tons per year, was installed. The new continuous rolling mill, which required a corresponding space, required an urgent relocation of other machinery. The genetic algorithm was used for the optimal rearranging of the other machinery. Two-dimensional or three-dimensional representation of the machines without any kind of geometrical restrictions can be used in the proposed genetic algorithm. The layout efficiency after machinery relocation could be increased by 58.1%, but due to spatial, financial, and practical constraints, the layout efficiency is only 13.58% higher. The paper demonstrates a very successful use of the genetic algorithms for optimizing machine the machine layout problem.
COBISS.SI-ID: 2789115
The purpose of the paper is to extend and explore the application of a novel meshless Local Radial Basis Function Collocation Method (LRBFCM) in solution of a steady, laminar, natural convection flow, influenced by magnetic field. The problem is defined by coupled mass, momentum, energy and induction equations that are solved in two dimensions by using local collocation with multiquadrics radial basis functions on an overlapping five nodded sub-domains and explicit time-stepping. The fractional step method is used to couple the pressure and velocity fields. The considered problem is calculated in a square cavity with two insulated horizontal and two differentially heated vertical walls with magnetic field applied in the horizontal direction. Numerical predictions are calculated for different Grashof numbers, ranging from 10**4 to 10**6, and Hartman numbers, ranging from 0 to 100, at Prandtl numbers 0.71 and 0.14. The results of the method are compared to predictions, obtained by other numerical methods, including FLUENT code. Good agreement has been achieved. The LRBFCM has been used in this kind of problems for the first time. The main advantage of the method is its simple numerical implementation and no need for polygonisation (mesh).
COBISS.SI-ID: 2827003