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Topology optimization design of bus roof structure

in this paper, the static finite element analysis of a bus body is carried out with ANSYS software. On this basis, using the homogenization method, taking the total flexibility of the frame as the objective function and the volume as the constraint condition, the topology optimization design of the roof under several working conditions is carried out. In the process of topology optimization design, the basic model establishment, optimization region selection, optimization process control, optimization result analysis and application are discussed. The application of topology optimization in the initial design of automobile structure is realized

I. Introduction

the research of structural optimization is divided into three levels: sizing optimization, shape optimization and topology optimization. Structural size optimization is basically mature, structural shape optimization is more difficult than structural size optimization, and it is still in the development stage, while structural topology optimization is very difficult, which is considered to be the most challenging topic, and it is still in the exploratory stage in engineering design

The basic idea of structural topology optimization is to transform the problem of finding the optimal topology of the structure into the problem of finding the optimal material distribution in a given design area. [1] Through topology optimization analysis, designers can fully understand the structure and functional characteristics of products, and can design the overall structure and specific structure pertinently. Especially in the early stage of product design, it is not enough to design parts only by experience and imagination. Only under appropriate constraints, making full use of topology optimization technology for analysis, combined with rich design experience, can we design products that meet the best technical conditions and process conditions. The biggest advantage of topology optimization of continuum structure is that it can determine a more reasonable structure form according to the known boundary conditions and load conditions without knowing the topology shape of the structure. It does not involve the specific structure size design, but can put forward the best design scheme. Topology optimization technology can provide designers with new designs and optimal material distribution schemes. Topology optimization is based on the idea of conceptual design, and the resulting design space needs to be fed back to the designer and made appropriate modifications. The optimal design is often lighter in structure and better in performance than the conceptual design. The design scheme modified by designers can get a better scheme through shape and size optimizationSecond, the mathematical model of topology optimization design

2.1 selection of optimization methods

at present, the commonly used topology optimization methods of continuum structures are: variable thickness method, variable density method and homogenization method. The mathematical model of variable thickness method is simple, but the optimization object is greatly limited. The variable density method is to artificially establish a relationship between material density and material properties. After topological optimization calculation, the density value of the element is 0 or 1, and the topological optimization structure is relatively clear [2,3]. Homogenization method is the most popular method. After topology optimization, the density of cells is a continuous value between 0 and 1, resulting in a relatively fuzzy topology. The optimal topological structure only considers the strength of the structure, and the design of the structure also needs to meet the design requirements of manufacturing process and assembly relationship. People need to carry out structural design on the basis of topological optimization. The fuzzy topological structure provides a value range, which is more conducive to subsequent design

2.2 mathematical model of homogenization method

the basic idea of homogenization method is to introduce microstructure into the materials that make up the topological structure - the unit cell at the junction of the large bottom sidewall and the upper is not obvious enough (Fig. 1). In the optimization process, the unit cell size of microstructure is used as the topological design variable to establish the relationship between material density and material properties, and the growth and decline of unit cell size is used to realize the addition and deletion of microstructure, And produce composite materials composed of intermediate size cells to expand the design space, so as to realize the structural topology optimization model and size optimization model, which has a strict mathematical foundation, and is a good method 4]

Figure 1 Single cell (unit cell) of microstructure

where:

η-- Density of microstructure cells

l (U) -- structural compliance

l (V) -- virtual work of equivalent volume force and boundary load on virtual displacement V

p, T -- equivalent volume force and boundary load on structure

u-- node displacement

v-- virtual displacement of node

p> ε Ij (U) -- strain caused by node displacement u

ε KL (V) -- virtual strain caused by node virtual displacement V

eijkl (a) -- assumed material properties, and density η And the material characteristics E0 of the actually used materials

e0-- the material characteristics of the actually used materials

α-- Undetermined coefficient

v-- initial volume of the structure

Ω -- indicates the integration on the volume domain with volume force

Г-- Means to integrate on the boundary domain with area force

in the above model, formula (2) takes the minimum total flexibility of the structure as the optimization objective, and the cell size a of the microstructure as the optimization design variable; Constraint conditions (3) according to the principle of virtual work, the static balance of the structure is taken as the constraint condition; Constraint condition (4) considers that the optimized volume must not be greater than the initial volume, and constraint condition (5) assumes the relationship between material properties and density

III. finite element analysis of bus body

as the key assembly of the bus, the body frame must have sufficient strength and static stiffness to ensure its fatigue life, assembly and use requirements, and also have reasonable dynamic characteristics to achieve the purpose of controlling vibration and noise. Application practice has proved that [5], using the finite element method to analyze the body structure can have a full understanding of its stiffness, strength, natural frequency and vibration mode before the design drawing becomes a product, so as to understand the stress and deformation of the body, and improve the deficiencies in time, so that the product can meet the use requirements in the design stage, so as to shorten the design test cycle and save a lot of test and production costs, It is one of the economic and applicable methods to improve the reliability of products

3.1 generation of finite element model

geometric model is the basis of finite element model. This paper uses Unigraphics software system, according to the AutoCAD two-dimensional design drawings of the body frame structure, establishes its three-dimensional space geometric model, and imports the model into ANSYS with the self-made interface program. After importing the geometric model, you need to make some necessary modifications to divide the lattice. In order to check the built finite element model, after the node constraint of the model in the suspension assembly part, give a certain acceleration to the three coordinate axis directions respectively, check the connection between the beams, and modify it. The final finite element model is shown in Figure 2. Scale information of the model: 1288 key points, 2150 straight lines, 31216 nodes, 16044 units. The mass of the body frame of this model is 4388.5kg, the on-board mass is 5911.6kg, the front axle carries 3721.8kg, and the rear axle carries 6578.3kg. [6]

Figure 2 finite element model of body frame

3.2 static finite element load case analysis of body structure

the body bears a lot of loads when the bus is running. In terms of its load nature, the main loads the body receives are bending, torsion, lateral load and longitudinal load. The bending load mainly comes from the mass of vehicle body, on-board equipment, passengers and luggage; The torsional load is produced by the asymmetric support of the vehicle body caused by the road roughness. As a comparative calculation, the static maximum possible torque can be used, that is, to simulate the limit state of a suspended front wheel; The lateral load is mainly produced by the centrifugal effect during steering; The longitudinal load is generated by the inertia force during acceleration and braking. In order to comprehensively understand the stress distribution of the body frame under the actual working conditions, the finite element simulation calculation is carried out for the horizontal bending condition (no-load + full load), the limit torsion condition (left and right front wheels suspended), the emergency turning condition (left and right turns), and the emergency braking condition (full load) to analyze the strength and stiffness of the body structure, so as to provide a reference basis for further optimization design. [6]

IV. roof topology optimization

topology optimization refers to shape optimization, also known as shape optimization. The purpose of topology optimization is to find the best material distribution scheme for objects bearing single or multiple loads. This optimization is expressed as "maximum stiffness" design in topology optimization. Different from traditional optimization design, topology optimization does not need to give the definition of parameters and optimization variables. The objective function, state variables and design variables are predefined. Users only need to give the parameters of the structure (material properties, models, loads, etc.) and the percentage of materials to be omitted. [6] The objective function of topology optimization is to reduce the deformation energy of the structure while meeting the structural constraints. Reducing the deformation energy of the structure is equivalent to improving the stiffness of the structure. This technique is achieved by using design variables to give the pseudo density of each finite element element

4.1 define topology optimization problem

topology optimization analysis, like other finite element analysis, the first thing is to establish its optimization model according to the basic structure of the analysis object. Due to the complexity of the body frame structure and the diversity of the loads it bears, it is almost impossible to optimize the topology of the whole body frame. The above-mentioned static analysis results show that the deformation of the roof under various working conditions is second only to that of the rear engine layout of the body frame; Modal analysis shows that the vibration amplitude of the ceiling is large in the medium and high frequency range, which is related to the layout of the ceiling. In order to reduce the scale of the optimization problem, the results of the static analysis are taken as the constraints of the roof optimization, and the topology optimization technology of ANSYS is used to optimize the topology of the roof of the body frame

4.2 select the unit type

through the analysis of the structure and stress characteristics of the body skeleton and its ceiling, according to the setting of the properties of the topology optimization design unit by ANSYS, and considering the calculation capacity of the computer, the convenience of the actual operation of the topology optimization process and the processing of the optimization results, shell93 [6] unit is selected to simulate the body skeleton ceiling for analysis

4. There is an approximate conversion relationship between the hardness value and the tensile strength value of the material. 3 basic structure

the so-called basic structure is the initial structure before optimization. The basic structure should not only conform to the characteristics of stress and support, but also facilitate the optimization calculation. Due to the default provisions of the ANSYS program, only the unit with the unit number specified as 1 can be topologically optimized. This rule can be used to control the optimized and non optimized parts of the model 8] for example, the layout position of the roof rail sector pipe is fixed and cannot be changed; There are also some beams whose main bearing sections are welded into one, so they cannot be changed; In addition, there are two longitudinal beams that are the main bearing components of the ceiling and cannot participate in the optimization. The unit number of these beams can be specified as 2 or greater, and the area that needs to determine the layout form through topology optimization calculation can be achieved by specifying its unit number as 1. In order to be faithful to the actual structure and function, some real constants should also be assigned to the unit. The materials used in the body frame are isotropic materials 16Mn, the material size is mm, and others are kg mm s unit system, as shown in Table 2. The established topology optimization model is shown in Figure 3, where gray is the optimization area and black is the non optimization area. Table 1 materials and their characteristic parameters

Figure 3 roof topology optimization model

4.4 definition and control of load conditions

since the topology optimization does not consider the skin, it is necessary to

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