Ansys programı ile dizayn optimizasyonu

Abstract

Mühendislik bilimi, analiz, dizayn, fabrikasyon, satış, araştırma ve geliştirme gibi birçok faaliyet alam içermektedir. Bunlardan biri olan "sistem dizaynı", mühendislikte büyük bir yer kaplamaktadır. Hızla gelişmekte olan dünyada, sadece çalışan bir sistem geliştirmek artık tatmin edici olmaktan uzaklaşmaktadır. Önemli olan "e« iyi " sistemi geliştirmektir. "En iyi" kavramına, gördüğü işlevlere göre en hafif, en ucuza mal olmuş en verimli, en hızlı, çok fonksiyonlu, dayanıklı vb. manalar atfedilebilir. Böyle bir sistemin dizaynı, "optimizasyon problemi" olarak formüle edilip çözümlenebilir. En basit tabiri ile bir optimizasyon problemi, "en iyi" den kastedilen manaları hedef olarak alıp, matematiksel fonksiyonla temsil ettirilerek, belirtilen sınırlar dahilinde bu fonksiyonun minimum (bazen maksimum) değerinin bulunmasıdır. Böyle bir problemin üç önemli bileşeni vardır:. Dizayn değişkenleri: Genellikle uzunluk, kalınlık, çap vb. gibi modeli tanımlayan geometrik büyüklüklerdir. Bunlar bağımsız değişkenlerdir.. Dizayn sınırlamaları: Dizayn değişkenlerine bağımlı olarak tanımlanan ve sisteme ait gerilme, frekans, boyut, deformasyon, sıcaklık vb. büyüklüklerdir sınırlarını belirten değişkenlerdir.. Hedef fonksiyonu: Dizayn değişkenlerine bağımlı olarak tanımlanan ve dizayn sınırlamaları dahilinde minimum veya maksimum yapılmaya çalışılan fonksiyondur. Optimizasyon problemlerin çözümünde analitik ve sayısal yöntemler kullanılmaktadır. Analitik yöntemlerin, çözüm yolunda belirli bir aşamadan daha ileriye geçememesi birçok sayısal yöntemin geliştirilmesine zemin hazırlamıştır. Sayısal yöntemlerde da tekrarlı (iteratif) işlemlerin çokça yapılması, çağımızın en önde gelen vazgeçilmezlerinden olan bilgisayarları devreye sokmuştur. CAD, CAM, CAE programları üreten bazı büyük yazılım şirketleri, geliştirdikleri bu programlara dizayn optimizasyonu yapan modüller de eklemişlerdir. Bu tezde dizayn optimizasyonunun teorisi ve ANSYS programı ile nasıl yapılacağı ele alınmıştır.

The goal of many engineers is to design systems for automotive, aerospace, mechanical, civil, chemical, industrial, electrical, biomedical, agricultural, naval and nuclear engineering applications. In the highly competitive world today, it is no longer sufficient to design a system that performs the required task satisfactorily. It is essential to design the best system. "Best" means an efficient, versatile, unique and cost effective system. To design such systems, proper analytical, experimental and numerical methods are needed. Optimum design concepts and methods provide some of the needed tool. The design of systems can be formulated as problems of optimization where a measure of performance is to be optimized while satisfying all the constraints. In recent years, numerical methods of optimization have been developed extensively. Many of the methods have been used to design better systems. Any problem in which certain parameters need to be determined to satisfy constraints can be formulated as an optimum design problem. Once this has been done, optimization methods can be used to solve the problem. Figure 1 shows the optimum design process. In an optimization problem, there are three basic terms: 1. Design variables 2. Objective function 3. Design constraints ( "State variables" in ANSYS terminology) Xlll Stop Figure 1- Optimum design process Design variables: Parameters chosen to describe the design of a system are called the design variables. These variables are independent, so designer can assign any value to them. If the specified values do not satisfy all constraints, the design is not feasible, which is called an infeasible design. If the constraints are satisfied, we have a feasible (workable or usable) design. All design variables for a problem are represented in the vector x. Objective function: There can be many feasible designs for a system and some are better than others. To make such a claim we must have some criterion to compare various designs. The criterion must be a scalar function whose numerical value can be obtained once a design is specified i.e. it must be a function of the design variables. The objective function is represented byf, oxf(x) to emphasize its XIV dependence on design variables. Numerical methods was developed to minimize the objective function. If the function is desired to be maximum, it is converted from f(x) to -f(x). Then -f(x) is minimized by the same methods. Design constraints: All restrictions placed on a design are collectively called constraints. Each constraints must be influenced by one or more design variables. Some constraints are quite simple, such as minimum and maximum of design variables, while more complex ones may be indirectly influenced by design variables. Design problem may have equality as well as inequality constraints. For example, to perform the desired operation, a machine component must move precisely by A, so we must treat this as an equality constraint. A feasible design must satisfy precisely all the equality constraints. Also, there are inequality constraints in most design problems. Examples of such constraints are that calculated stresses must not exceed allowable stress of the material, deflections must not exceed specified limits, resources must not be exceeded, etc. The standart design optimization model is defined as follows: Find an n- vector x={xi,X2,....,xn} of design variables to minimize a cost function f(x)=f(xi,x2,....,xn} subject to p equality constraints ht{x) = h,{xxtx2,,x") = 0 j=ltop and m inequality constraints g,(x)Bg,(Xi,x2,,xn)<0 i=l torn Analytical methods for solving some problems are not applicable at all. For that reason many numerical methods are developed. The design of complex systems requires large calculations and data processing. Today's computers can perform complex calculations and process large amounts of XV data efficiently. Better systems can now be designed by analysing various options in a short time. When optimization problems are properly implemented into a software, they give powerful numerical tools for designing best systems. This thesis focuses on optimization module of ANSYS software program. Furthermore, some theory of analytical and numerical methods are mentioned to understand the sense of optimization better. The ANSYS program offers two optimization methods to accomodate a wide range of optimization problems. The "subproblem approximation method' is an advanced zero-order method that can be efficiently applied to most engineering problems. The "first order method" is based on design sensitivities and is more suitable for problems that require high accuracy. For both the subproblem approximation and first order methods, the program performs a series of analysis-evaluation-modification cycles. That is, an analysis of the initial design is performed, the results are evaluated against specified design criteria, and the design is modified as necessary. This process is repeated until all specified criteria are met. In addition to the two optimization techniques available, the ANSYS program offers a set of strategic tools that can be used to enhance the efficiency of the design process. For example, a number of random design iterations can be performed. The initial data points from the random design calculations can serve as starting points to feed the optimization methods mentioned above. There are basically two ways to approach an ANSYS optimization: as a batch run or interactively through the Graphical User Interface (GUI). XVI The usual procedure for design optimization consists of the following main steps. These steps may vary slightly, depending on whether you are performing optimization interactively (through the GUI) or in batch mode. 1. Create an analysis file to be used during looping. This file should be represent a complete analysis sequence and must do the folloing: a. Build the model parametrically ( in PREP7 module) b. Obtain the solution(s) (SOLUTION) c. Retrieve and assign to parameters the responce quantities that will be used as state variables (design constraints) and objective functions (PQST1/PQST26) 2. Establish parameters in the ANSYS database which correspond to those used in the analysis file; this step is typical but not required (Begin or OPT) 3. Enter OPT and specify the analysis file (OPT) 4. Declare optimization variables (OPT) 5. Choose optimization tool or method (OPT) 6. Specify optimization looping controls (OPT) 7. Initiate optimization analysis (OPT) 8. Review the resulting design sets data (OPT) and postprocess results (POST1/POST26) The optimization module (/OPT) is an integrated part of the ANSYS program that can be employed to determine the optimum design. Design configurations that satisfy all constraints are referred to as feasible designs. Design configurations with one or more violations are termed infeasible. As design sets are generated by methods or tools and ifan objective function is defined, the best design set is computed and its number is stored. The subproblem approximation method can be described as an advanced zero-order method in that it requires only the values of the dependent variables, and not their derivatives. There are two concepts which play a key role in the subproblem approximation method: the use of approximations for the objective function and state variables, and the conversion of the constrained optimization problem to an XVll unconstrained problem. The conversion is done by adding penalties to the objective function approximation to account for the imposed constraints. Because approximations are used for the objective function and SVs, the optimum design will be only as good as approximations. Like the subproblem approximation method, the first order method converts the problem to an unconstrained one by adding penalty functions to the objective function. The first order method uses gradients of the independent variables with respect to the design variables. For each iteration, gradient calculations are performed in order to determine a search direction, and a line search strategy is adopted to minimize the unconstrained problem.