Optimization and Simulation in CAE Technology

1. Introduction

    The increasingly fierce market competition has made the designers and manufacturers of industrial products more and more aware that if they can launch excellent new products faster than others, they can occupy more markets. For this reason, CAE methods, as a powerful tool to shorten the product development cycle, have been introduced more and more frequently into all aspects of product design and production to improve the competitiveness of products. From simple verification of the performance of designed products, to accurate prediction of product performance, and then to precise simulation of product working processes, people have full trust in CAE methods. However, improving product competitiveness requires not only improving product performance and quality, but also reducing product costs, so people need to find the most reasonable and economical design solution. Although analysts can tirelessly modify design parameters again and again in front of the screen to find the most ideal solution, the pressure to shorten the development cycle usually requires every minute and every second, and people may not have more time to manually adjust data parameters. The introduction of optimization technology into CAE methods has freed people from the heavy work of trial and error, and CAE has also reached a new height.

2. Optimization Methods and CAE

    Under the premise of ensuring that the product reaches certain performance goals and meets certain constraints, by changing certain design variables that are allowed to change, the product's indicators or performance can reach the most desired goals. This is the optimization method. For example, under the premise of ensuring that the structural strength meets the requirements, by changing certain design variables, the weight of the structure is minimized, which not only saves on structural consumables, but also provides convenience in transportation and installation, reducing transportation costs. Another example is changing the installation position of each heating component of electrical equipment to minimize the peak temperature inside the equipment box, which is a typical optimization example of natural convection heat dissipation. In actual design and production, there are countless examples like this. Optimization, as a mathematical method, usually uses the method of finding the extreme value of an analytical function to achieve the purpose of seeking the optimal value. The CAE method based on numerical analysis technology is obviously impossible to obtain an analytical function for our goal, and the result obtained by CAE calculation is only a numerical value. However, spline interpolation technology makes optimization in CAE possible. Multiple numerical points can use interpolation technology to form a continuous curve or surface that can be expressed by a function, thus returning to the extreme value optimization technology in the mathematical sense. The spline interpolation method is of course an approximate method. It is usually impossible to obtain the exact surface of the objective function. However, the result of the last calculation is used to interpolate a new surface. The distance between the two adjacent surfaces will become closer and closer. When their distance is small to a certain extent, it can be considered that the surface at this time can represent the target surface. Then, the minimum value of the surface can be considered as the optimal value of the target. The above is the optimization process in the CAE method. A typical CAE optimization process usually needs to go through the following steps to complete: Parametric modeling: Use the parametric modeling function of the CAE software to define the data (design variables) to be optimized as model parameters, so as to provide the possibility for the software to modify the model in the future. Solution: Load and solve the parametric model of the structure. Post-processing: Extract the state variables (constraints) and the objective function (optimization target) for the optimization processor to evaluate the optimization parameters. Optimization parameter evaluation: The optimization processor compares the optimization parameters (design variables, state variables and objective function) provided by this cycle with the optimization parameters provided by the previous cycle to determine whether the objective function of this cycle has reached the minimum, or whether the structure has reached the optimal state. If it is optimal, the iteration is completed and the optimization cycle is exited. Otherwise, the next step is taken. According to the completed optimization cycle and the state of the current optimization variables, the design variables are corrected and the cycle is re-entered. The following figure is a flowchart of the numerical optimization process

3. Characteristics of optimization technology in CAE method

    From the above process, we may have seen some basic features of the CAE optimization process, such as parameterization of the calculation model, automation of the iterative process, etc. However, as a product of the perfect combination of optimization technology and CAE methods, CAE optimization methods must have richer characteristics than this.

    First of all, the development of modern CAE technology has expanded people's analysis field to every corner of all walks of life. The depth and comprehensiveness of the research problems are gradually improving. Researchers have turned their attention from single-field analysis to multi-field coupling analysis in pursuit of more realistic simulation results. The scope of application of CAE software's optimization technology will inevitably expand accordingly. It is not only required to solve various single-field problems, but also to be able to handle the optimization of multi-field coupling processes. In the design process of automobiles, submarines, aircraft and other equipment, it is often considered to optimize their appearance to make it more conducive to reducing fluid resistance when driving at high speeds, and at the same time, it is necessary to consider whether the change in appearance will damage other mechanical and thermal properties of the equipment. It can be seen that simple fluid dynamics optimization can only solve one aspect of the problem, and only by coupling the mechanical or thermal problems of its internal equipment can the problem be truly and completely solved.

    Secondly, an optimization iteration process usually starts with pre-processing, and goes through modeling, meshing, loading, solving and post-processing, and the optimization problem usually requires more iterations to converge. Therefore, the software has a unified database, which is a prerequisite for an efficient CAE optimization process. This unification means that the pre- and post-processing data and the data used for solving should be in the same database, rather than being transferred through data files, which is bound to reduce the efficiency of the optimization process. In addition, most software that transfers data through files do not fully support the pre-processing and solver, and the pre-processing data files often need to be manually modified before being put into the solver. This is in conflict with the automation of the optimization process. Once this situation occurs and cannot be avoided, either give up or compile an automatic modification program for the data file.
   
    Third, the optimization process is actually a process of continuously and automatically correcting the design parameters. Therefore, in order to ensure the smoothness of the optimization process, CAE software must have a complete and efficient parameter process control technology. In the process control process, not only is it required that the design data to be optimized can be parameterized, but also that this process control has the ability to judge branches and loops so that the software can automatically cope with various complex situations that arise in the optimization process of large problems.

    Fourth, high-precision mesh is one of the key factors for successful finite element analysis. A good CAE software must have an intelligent mesher to solve the mesh singularization problem when the shape parameters of the model change dramatically in order to handle the optimization process well, especially the shape optimization problem.

    Fifth, modern CAE software usually has and should have the ability to handle nonlinear problems, and the convergence control of nonlinear problems has made countless heroes bow down. Usually, the means to improve the convergence of nonlinear problems should be determined according to the specific situation, and the optimization process of a nonlinear problem is often affected by various factors. However, the optimization process is automatically controlled and iterated by the program, and people cannot participate too much. Therefore, the intelligent control technology of nonlinear convergence is indispensable for nonlinear optimization problems. When talking about nonlinearity, people may think of a solution technology called explicit integration. This technology is usually used to solve high-speed deformation and highly nonlinear problems, and it complements the implicit solution technology commonly used to solve static or slow dynamic problems. For most problems, we can only choose a suitable one to solve, but not all problems can be separated so clearly. For example, the simulation of stamping and springback processes usually uses explicit methods to simulate the stamping process and implicit methods to simulate the springback process. Then there must be a switching process from explicit to implicit. If it is just to simulate these two processes, it is OK to do this switching manually. However, for the optimization process that does not involve too much human involvement, if this switching cannot be done automatically, then the optimization analysis of this type of problem cannot be completed. When the software application level reaches a certain level, people may think of trying a cooperative optimization method, that is, multiple networked work machines in the same work group work together to optimize the same problem. Usually, the models, brands and even operating systems of each work machine in the same work group may be different, so the incompatibility of databases on different platforms may make such a creative attempt come to nothing. Of course, not all software has this problem. Today, a popular CAE software - ANSYS has the best technology on this issue, and some of its other features make it a role worth mentioning in the current topic. ANSYS is a CAE software that integrates structural, thermal, electromagnetic and fluid analysis capabilities and can perform multi-field coupling analysis; it has powerful pre- and post-processing capabilities, especially in intelligent meshing; it has strong explicit or implicit nonlinear solution capabilities, and the explicit and implicit modes can be switched automatically at will; the nonlinear convergence control is intelligent, and for most engineering problems, the convergence of nonlinear problems can be completed without human intervention; it also has a parametric design language ━ APDL, which is highly praised by its users as "all-powerful". This language has high-level language elements such as parameters, mathematical functions, macros (sub-procedures), judgment branches and loops, and is an ideal program flow control language; the uniformity of its pre- and post-processing and solution databases and the compatibility of databases on different platforms make it very suitable for advanced optimization analysis.

4. A CAE Optimization Example

    The turbine unit of Ertan Power Station is the largest unit in my country so far, with a volute diameter of 20 meters. The shape of the underground structure is shown in the figure. It consists of two parts: one is a seat ring structure welded by two annular plates and 20 fixed guide vanes, which constitutes the support of the shell part; the other is a shell structure welded by 25 sections of cones. Each section of the cone has a different diameter and thickness. At the same time, each section is not a complete cone, but a part is cut off along the axial direction, and the axial straight edge of the remaining part is welded to a certain position of the upper and lower ring plates along the circumference. The choice of this position plays a key role in the stress distribution in the entire volute. If this position is well selected, the stress distribution in the volute can be uniform, reducing the maximum stress in the entire structure. In this way, the thickness of the volute shell and the upper and lower ring plates of the seat ring can be reduced to a certain extent, so as to reduce its volume or weight and thus reduce the cost of materials, processing, transportation and installation. Therefore, the purpose of this analysis is to select the welding positions of the shell and the upper and lower seat rings and the thickness of the seat ring plate and shell materials to make the weight of the whole structure the lightest, while ensuring the hydraulic characteristics of the flow channel and the maximum stress of the whole structure does not exceed the allowable stress (the equivalent stress value of the whole structure provided by the manufacturer should not exceed 160MPa). The optimizable parameters (a total of 18) of the volute underground structure shape problem are 13 shell thicknesses, 1 ring plate thickness, and 4 welding positions (the other positions are linear interpolations of the four points). It is a fluid-solid coupling optimization problem with many design variables. At the same time, the hydraulic characteristics of the flow channel need to be considered, that is, the cross-sectional area of ​​the flow channel must not be reduced. The modeling process makes full use of the parametric modeling function of ANSYS, and the parametric model of this problem is established using the APDL language. The ring plate and shell wall are segmented using SHELL63 (shell unit), the guide vane is segmented using SOLID45, and the fluid model is segmented using Fluid142 units. The objective function of this problem is the total volume of the structure. By comparing the data before and after optimization, it is found that the total volume of the structure is reduced from 56.84 before optimization to 52.26, which is 8% of the original design. In addition, after optimization, the water pressure on the shell wall tends to be smooth, and the stress distribution in the structure tends to be uniform.

5. Developing CAE Optimization Methods

    With the development of CAE technology, the optimization technology in CAE will also continue to develop. In addition to the above-mentioned features, which will become more and more obvious, there will be many new features, such as optimization problems of discrete quantities and multi-objective optimization problems. In modern CAE optimization technology, a new method called topology optimization has emerged. This method has been adopted to a certain extent by some CAE software (including ANSYS). As its theoretical basis gradually matures, its practicality will gradually improve. It is believed that topology optimization will be a good supplement to the classical optimization method.