Shape and volume optimization of industrial parts

In the present time, there are many challenges in the production of industrial parts. Due to the constantly rising prices of materials and energy, it is necessary to constantly look for ways to optimize production costs and optimize material consumption. There is great pressure on economical production, i. to produce products with the lowest costs given the expected and necessary properties. With the introduction of additive manufacturing technologies into practice and the production of parts for end use comes the introduction of methods for optimizing the shape of the part and the required amount of material for its production. We call this method Topological Optimization. The presented article describes the preparation of topologically optimized parts and a comparison of their strength properties with respect to the original and the original part.

Finite Element Calculation of the Polymer Stamp Material Redistribution under Restrictions on Fatigue Life

The numerical method of stamp topological optimization taking into account fatigue strength is presented in the work. It is proposed to take into account the restrictions on the stress state in accordance with the curve of the dependence of the maximum stresses on the number of loading cycles in the ESO topological optimization method. An approach to the selection of the evolutionary coefficient with a step-by-step increase in the rejection coefficient is proposed when constructing an iterative scheme for the rejection of elements by the method of topological optimization. The calculation of the stamp optimal topology with a decrease in volume due to the removal and redistribution of material was carried out in the study. The new geometric model of the optimal topology stamp is based on the predicted distribution of elements with a minimum stress level. The verification calculation of the stress state of the stamp of optimal topology with an assessment of fatigue strength was carried out in the work. The numerical calculation was carried out using the finite element method in the Ansys software package. The minimized stamp volume decreased by 35% according to the calculation results. The results of the study can be further applied in the development of topological optimization methods and in the design of stamping tools of optimal topology.

Binary optimal control by trust-region steepest descent

We present a trust-region steepest descent method for dynamic optimal control problems with binary-valued integrable control functions. Our method interprets the control function as an indicator function of a measurable set and makes set-valued adjustments derived from the sublevel sets of a topological gradient function. By combining this type of update with a trust-region framework, we are able to show by theoretical argument that our method achieves asymptotic stationarity despite possible discretization errors and truncation errors during step determination. To demonstrate the practical applicability of our method, we solve two optimal control problems constrained by ordinary and partial differential equations, respectively, and one topological optimization problem.

Topological Optimization of the Strength Element of the Aircraft Compartment Made of Metal-Matrix Composite Material

At present, in order to increase the weight efficiency of parts and structures of promising aircraft and rocket-space vehicles, various types of additive technologies and topological optimization methods are being actively introduced. Their purpose is a significant reduction in time and financial costs in the manufacture and creation of fundamentally new geometric solutions. The article considers approaches to selecting the geometric parameters of the strength elements of the flight vehicle body made of a metal-matrix composite material based on VT6 titanium alloy, reinforced with a finely dispersed silicon carbide powder, which is produced by direct laser growth technology. On the basis of numerical simulation, the dependences of the metal-matrix composite material physicomechanical and thermophysical characteristics on the volume fraction of silicon carbide have been determined. It was found that the use of a metal-matrix composite material and the optimization of geometric parameters with adaptation to the direct laser growth technology allows reducing the weight of the strength element of the flight vehicle body by more than 30% (depending on the overall dimensions).

THE IMPROVEMENT MECHANICAL BRAKE SYSTEM OF THE PASSENGER СAR

A set of theoretical scientific researches is carried out in the work, which proves that with the use of different types of brake pads in passenger cars some elements of the typical design of the mechanical brake system need to be modernized. Analytical calculations of the brake lever transmission of passenger cars are performed on the basis of the 2D scheme-model. Due to this, ways to improve the most important elements of lever transmission in passenger cars under the conditions of composite pads are proposed. The analysis of the forces acting in the typical design of the lever transmission of a passenger car for different types of pads is performed. The strength of important elements of the mechanical brake system is calculated by applying the finite element method. It is proposed to use the capabilities of the software package Femap Siemens PLM Software, which allows you to optimize the elements of the mechanical system of passenger cars. An example of topological optimization of some elements of brake lever transmission of a passenger car is given. By improving the elements of the mechanical brake system for the use of composite pads in passenger cars, greatly simplifies their design, facilitates maintenance and repair, also reduces the weight of the system as a whole and cost and significantly increases the level of traffic safety.

Mathematical model of structural and topological optimization of logistics networks

The subject of research in the article is the topological structures of closed-loop logistics networks. The goal of the article is to increase the efficiency of centralized logistics networks by developing a mathematical model for a two-criteria problem of optimizing topological structures in the process of their reengineering. The article solves the following tasks: analysis of the current state of the problem of structural and topological optimization of logistics networks; formalization of the problem of optimization of logistics networks as geographically distributed objects; synthesis of objective functions of the mathematical model of a two-criterion optimization problem for centralized three-level topological structures of closed logistics networks at the reengineering stage; development of a system of constraints of the mathematical model of the problem of optimizing centralized three-level topological structures of closed logistics networks; a function for evaluating the overall utility of options based on the Kolmogorov-Gabor polynomial is offered. The following methods are used: methods of systems theory, methods of utility theory, optimization and operations research. The following results were obtained: the analysis of the current state of the problem of system optimization of logistics networks, mathematical models and methods for its solution was carried out; formalization of the problem of structural and topological optimization of logistics networks as geographically distributed objects; a mathematical model of a two-criterion task of reengineering of three-level topological structures of logistics networks in terms of costs and efficiency with integrated points of production and processing has been developed (originality). Conclusions: Based on the results of the analysis of the problem of optimizing the topological structures of logistics systems, it has been established that the problems of direct and reverse logistics are still considered as conditionally independent, which does not allow obtaining effective global solutions. In the context of expanding the network of consumers, changes in delivery volumes, the introduction of environmental restrictions, it is proposed to reengineer the networks, which provides for their radical redesign. The formulated statement and the developed mathematical model of a two-criterion (in terms of cost and efficiency) optimization problem for three-level topological structures for combined production and processing points will increase the efficiency of logistics networks with reverse flows by reducing the cost of reengineering (practical value).

Bifurcated Topological Optimization for IVIM

In this work, we shed light on the issue of estimating Intravoxel Incoherent Motion (IVIM) for diffusion and perfusion estimation by characterizing the objective function using simplicial homology tools. We provide a robust solution via topological optimization of this model so that the estimates are more reliable and accurate. Estimating the tissue microstructure from diffusion MRI is in itself an ill-posed and a non-linear inverse problem. Using variable projection functional (VarPro) to fit the standard bi-exponential IVIM model we perform the optimization using simplicial homology based global optimization to better understand the topology of objective function surface. We theoretically show how the proposed methodology can recover the model parameters more accurately and consistently by casting it in a reduced subspace given by VarPro. Additionally we demonstrate that the IVIM model parameters cannot be accurately reconstructed using conventional numerical optimization methods due to the presence of infinite solutions in subspaces. The proposed method helps uncover multiple global minima by analyzing the local geometry of the model enabling the generation of reliable estimates of model parameters.