METHODOLOGY OF OPTIMAL DESIGN OF MECHANICAL STRUCTURES

ABSTARCT

This article proposes an optimal design methodology for structures based on constructive and parametric optimization methods. Includes software systems, materials, technologies, and data that implement this methodology and allow these targets to predict product design in terms of product operational and technological constraints.

АННОТАЦИЯ

В данной статье предлагается оптимальная методология проектирования конструкций на основе методов конструктивной и параметрической оптимизации. Включает программные системы, материалы, технологии и данные, которые реализуют эту методологию и позволяют этим целям прогнозировать конструкцию продукта с точки зрения операционных и технологических ограничений.

Keywords: design, model, CAD, CAE, CAO, composite, design, optimal design, integration, finite elements.

Ключевые слова: конструкция, модель, CAD, CAE, CAO, композит, проект, оптимальная проектирование, интегрированный, конечные элементы.

Introduction. It is known that in traditional design, the designer develops a CAD model of the structure, then compares the tests and creates a CAE model with loads, taking into account the circumstances that make it impossible to perform in real conditions. In this case, the system acts as an auxiliary and plays an important role in optimizing the design parameters. For example, increasing the thickness of the block elements reduces the load on them [1].

However, for the optimal design of structures, the reorganization of the order of use of these systems and the development of the project should be based on topological and parametric optimization and, accordingly, the CAO system. The general concept of optimal constructive design methodology is shown in Figure 1.

Experience. The traditional approach to structural design, taking into account in part the achievements in mathematical modeling, is that the designer, knowing the working conditions and based on his own experience, sketches a future product, which then becomes a CAD (Computer-Aided Design) model.

Figure 1. Methods of optimal design of structures

The structured methodology is general, and the technical implementation of each item of the methodology depends on the industry, the software package, and the problem being addressed. The number of targets for a modern constructive assembly (for example, for a car) can reach tens of thousands. However, it may be known at the beginning of the project that no more than 30% of the targets will be met, the rest will be known during the design process. However, despite the generality, this method allows the identification of key components of the software tool that can be used to design structures for targets. The software system should include a database of materials, a database of technologies, a database of structures and computing tools associated with that database, and tools for solving the optimization problem.

The following calculations can be performed in an automated design and engineering system to achieve optimal design [8]:

- Engineering calculations (CAE system)

- topological optimization

- Form optimization

- topographic optimization

- parameter optimization

Determining the area of ​​optimization.

There are two requirements to follow when determining the area of ​​optimization:

1) The optimization area should include all points where the presence of the material can significantly affect the stiffness of the structural element under given loads

2) The optimization area should not go beyond the boundaries defined by the location of adjacent structural elements.

One of the requirements for topological optimization of a structural element is to keep the connecting parts between the given structural element and the surrounding structural elements unchanged [6]. Preserving the spatial location and geometric properties of the connecting parts allows you to replace this element with an optimized element without further design solutions, without changing the surrounding structural elements.

Identify target functions, technological and operational constraints during optimization, as well as loading conditions.

The target function is the mass of the structure calculated as the sum of the masses of all finite elements. It should be minimized.

- the value of the imaginary density in the selected finite element, - the column of imaginary densities of all finite elements. In this case, the variable parameters are the imaginary density values ​​in all finite elements [5].

The result of topological optimization depends on the average size of the finite element in the model, strictly speaking, by reducing this size we achieve more complex (and at the same time, more precise) geometric structures. Therefore, in order to be able to produce the final product, the optimization process uses a filtering method that prevents the occurrence of an increase in density in two adjacent finite elements and thus limits the minimum material thickness in the optimized part.

                              (2)

Parametric optimization problem and solution.

Topological optimization provides a qualitative view of the distribution of material in the structure. In order to more accurately assess the geometric properties of the resulting sternal sections, it is necessary to perform a parametric optimization of the structure called “bionic”.

Figure 2. Sterile model based on topological optimization results

To do this, on the basis of the obtained topology, a finite element model is constructed on a newly parameterized rod, in which the cross sections of the rods are selected based on the results of topological optimization (Figure 2). The model includes fasteners modeled using shell finite elements. This task is also a nonlinear programming problem. To solve it, a modified Neoder Mead algorithm is used (Figure 3).

Figure 3. The result of parametric optimization

It should be noted that the shape of the cross-sections of the sternum elements is selected based on the results of topological optimization, the use of circular cross-sections where the sternal elements have a rectangular cross-section may also lead to the desired result. The general formula for the parametric optimization problem is to use the moments of inertia of each stem element section as design variables. Nevertheless, the obtained results allow to accurately estimate the section size of the optimized part [4].

The article uses methods of the theory of elasticity and plasticity, mechanics of composite materials, computational mechanics, methods of parametric and structural optimization. For the numerical solution of problems, the modern theoretically based finite element method was used. The variable asymptote method is used to solve topological optimization problems [8].

The problem of topological optimization is, in the classical formula, the problem of finding the optimal distribution of material in terms of stability in a given field. As a result, for each point in the region, we have to answer the question of whether there is material in a particular place. To permanently reduce this initial discrete problem, the SIMP (Solid Isotropic Material with Penalization) method is used, which allows the elastic properties of the material to be related to the auxiliary parameter of the “false density” of the material:

                                                   (3)

 the parameter is called the additional coefficient because this interval prevents the occurrence of false density: if the false density is  <1, then the elastic properties of the material for a sufficiently large value are obtained, and at this point the use of the material becomes very expensive. This is an important aspect of topological optimization because the presence of points in the optimal solution with a false density value of 0 to 1 makes it difficult to interpret the resulting solution from a physical point of view.

Conclusion. Topological optimization is software that uses algorithms to determine the optimal shape design for a given detail. Using an optimal design methodology designed to optimally design a structure into an integrated automated design and engineering system, the organization of design according to target indicators given at different hierarchical levels is also achieved through the use of the world’s best solutions in CAD, CAE and CAO .

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