Application of Object-Oriented Approach to Earthquake Engineering

Transcription

1 J. of Civil Engrg. Information Processing System, JSCE, Vol.6, 1997 Application of Object-Oriented Approach to Earthquake Engineering Yoshikazu Takahashi 1, Akira Igarashi 2 and Hirokazu Iemura 3 Abstract: A variety of computer programs has been developed in order to analyze complicated structures. As the number of functions in their programs increase, it becomes difficult to manage them. The fundamental problem lies in the fact that they are designed in a computer-oriented manner which is totally different from our intuition. Therefore the object-oriented approach is efficient to overcome the above mentioned problems. In this study, the three-module model for the structural analysis system is proposed. The system is characterized by the structure, load and analysis modules passing messages each other. This model is more flexible and more useful than the conventionally used structure-based model for the earthquake response analysis problem as well as the structure analysis problem. Key Words : object-oriented, class library, earthquake response analysis, structural analysis 1. Introduction 2. Conventional OO Approach to Structural Engineering Recently, Object-Oriented technique (OO) has become popular and it s advantage is being recognized in many field. Some researchers are applying the OO approach to the structural analysis field and a great deal of effort has been made on its application to the finite element method 1)2)3)4). In their articles, the OO technique was only applied to the structure and the other objects were not modeled positively. In earthquake engineering, an earthquake is not only a load. It is an objective of our seismic design, so we would better focus on it in the system. And since we use many method besides the FEM, it is desirable to be able to select a proper method to an objective model. In this paper, we propose a flexible object-oriented analytical system based on modules. Firstly, we summarize the problem domain of the earthquake engineering system and pick up some important items. Secondly, the detailed analysis of each item is described. Finally, through the implementation of the models, we explain the benefits of this approach and the reusage of objects. 1 Member of JSCE, M.Eng., Research Associate, Kyoto Univ. 2 Member of JSCE, Ph.D., Associate Professor, Kyoto Univ. 3 Member of JSCE, Dr. Eng., Professor, Kyoto Univ. (Yoshida Honmachi, Kyoto JAPAN) The most conventional OO approach to a structural analysis is a structure-based modelling, which means that the analytical technique is buried in the structure object. Although it might succeed to properly express the structure, this modelling leads to a serious problem that it has a limitation for extendibility and utility on other fields. Therefore, it is desirable to separate the analytical procedure from the structure object, and to model analytical methods in the same way the structure model is done. 3. OO Analysis of Earthquake Engineering System (1) Definition of System As the basis of this analysis, we define the earthquake engineering analysis, including the structural analysis, as below. Loads, including an earthquake, apply on a structure. The structure responds to it by means of its displacements and inner forces etc.. People trace the response. This procedure is a structural analysis. We can find the important keywords in this paragraph. These are Structure, Load and Response Analysis(trace the response). Of course, Earthquake is also important,

2 Fig. 1 Top Image of Class Diagram of Structure Analysis System but we deal with it as a kind of load on the top image. Although former researchers tried to model only structure positively, we recognize that each one of the three keywords has the same importance and try to model these keywords (modules) independently. This three modules model is shown in Fig. 1 using OMT 8) notations. This is the basic model and we analyze each module more in detail. The definition of each module is showed below. Structure Module This module expresses the specification of a structure. In general, this module is like a database, but when we use it in an analytical problem, its role is to make the information of the structure state, i.e. system matrices. Load Module This is a generalized force. It can generate force data on each time. The earthquake module is a part of this and generate acceleration data. ResponseAnalysis Module This module is generated and initialized when the load object applies to the structure object. The nucleus of this module is the equation module. Its role is to calculate the equation referring to the structure and load modules. The dynamic image model is shown in Fig.2. Three modules communicate each other during the analysis. When the structure object receives the message deform, it also sends message deform to the element objects. After all elements have been deformed, the response analysis module receives back the message deformed. Inside the response analysis module, the equation is generated referring to the structure and load modules, and the solution is obtained, which is sent again to the structure as a new message deform. This message-driven system is flexible and seems to be suitable to our system. (2) Structure Module The structure object has been modeled actively by many researchers. Our approach for a structure object is to have make it available for various analytical Fig. 2 Dynamic Image Model of Structural Analyses System method and also to have a little influence with its extensions. Firstly, we analyze the shape of a structure. A structure is an assembly of elements, in which each element has one section. Both a structure and an element were expressed by a collection of nodes. This idea has much in common with previous research and this object class model is similar to those proposed there. A structure has not only this static characteristic, but also a dynamic one, i.e. deform. When the structure is used in a response analysis, the main role of this module is to make system matrices corresponding to its state. The point of our approach is that methods of making system matrices should be separated from a structure object. If we use only one analytical method, i.e. the finite element method, the best way is to include it into the structure object. However, we try to consider various analytical methods and a hybrid system composed of numerical and experimental method. For this purpose, it is desirable to encapsulate the method of making system matrices and when we want to use another analytical method, we may exchange the proper method object. The method objects have a relation to the element object, which means that we can select an analytical method for each element. It has an advantage to separate the structure into shape and method objects when people try to understand its overview, and what is better, shape objects has a little influence at adding new methods. As the result of our analysis, the object diagram shows in Fig. 3 and Fig. 4.

3 Fig. 3 Class Diagram of Structure Shape Module Fig. 5 Overview of Class Diagram of Earthquake Fig. 4 Class Diagram of Analytical Method Module (3) Load Module This module deals with not only seismic load, but also static load. The earthquake object is modeled as an inheritance of a generalized load, therefore, static load may be modeled in the same way and in the parallel position to the earthquake object. Since in earthquake engineering, an earthquake is the main item, which can be used on different analysis, it is a good idea to model the earthquake as an object. a) Concept of Earthquake Object People might think that an earthquake is only a set of data. Therefore, opinions may vary as to regard it as an object. In the earthquake engineering field, however, an earthquake is a key concept, so it is convenient to look upon it as an object. Is an earthquake able to be qualified as an object, indeed? Here, we recognize that an object is a selfcontained entity composed of data and procedures. Then let us examine further analysis about it. An earthquake has a set of data that is acceleration etc.. Using this data, we can calculate Fourier spectra and response spectra, which indicate specificity of the earthquake. Each earthquake has its own characteristic, therefore, these calculation are regard as methods of an earthquake. It follows from what has been said that an earthquake is qualified as an object. Because an earthquake is expressed by acceleration etc., it is not said strictly that it is a load. But in the earthquake engineering field, it is common to think of it as a kind of load since it has a relation to inertia forces of a structure. Therefore, we define that an earthquake object inherits a generalized load object because of its extendibility and utility. This earthquake object must have a response analysis procedure. Since the response analysis is to solve dynamic linear/nonlinear equation of motion, we can reuse the equation module that is described later. Fig. 5 is an object diagram of the earthquake object. (4) Equation Module The fundamental component of a response analysis is an equation, for example the equation of motion. Before the response analysis module, we include the equation module which plays an important role in the response

4 Fig. 6 Class Diagram of Equation analysis module. a) Feature of Equation Module We solve the equation to get the unknown variables. On the procedural system, the stiffness matrix or displacement vector, which are part of the equation, can be expressed using a procedure type programming language, like FORTRAN. But we cannot express the whole equation suitably in the program. An equation is always used in the structural analysis, so it has its advantage to think of an equation as an object An equation changes its feature by problem domain, for example linear / nonlinear equation and static / dynamic equation. But every equation has the same aim that is to get unknown variable. Accordingly, we change an equation into one that get unknown variable using known information, for example a stiffness matrix etc.. b) Analysis of Equation Module An equation has two type, static and dynamic, in term of number of unknown variable. The aim of this module is to solve itself using known matrices of which it is composed. To solve an equation, it is necessary to have information about a solution method. We make this model so as not to have this information inside the module, but to refer to an information object outside it. This is why this module can have no influence if a new solution method is added. Of course, it seems that static / dynamic and linear / nonlinear equations have different characteristics, however we can find its similarity by analyzing them carefully. Generally, an equation can be expressed by the equation below. ˆK U = t+ t ˆR On a linear equation, the displacement can be derived from the equation directly. On the other hand, on a nonlinear equation, it is necessary to use a iterative calculation. The question it arises is how to deal with the left-hand side of the equation because it may update. On a structural analysis, a stiffness matrix, and etc. are decided referred to structure for its analysis. Therefore, if a structure object may be modelled, the equation module can cope with this difficulty using the structure object. But this give rise to serious limitation for the equation module. Since the equation is a very general one, the equation module should not use a concrete object directly. Therefore this nonlinearity of solution method is also separated from the other part, and we make an interface object that make possible to deal with the nonlinearity. For performing the above separation, we use the strategy and bridge patterns of Design Patterns 9). Fig. 6 shows the object diagram of this equation module. This diagram indicates that this equation module is available for various purposes if it refer to proper Nonlinearity object. The dynamic diagram(fig. 7) shows how the Equation object in Fig. 6 can solve itself. The Equation object can use the same expression in either linear or nonlinear problem, because the SolutionMethod object that deals with linear / nonlinear solution method is modelled independent of the Equation object. This independency induces a great advantage, because the

5 Fig. 7 Dynamic Model of Equation Fig. 8 Functional Model of Equation Equation object has nothing to do with a change of the SolutionMethod object, therefore, this module becomes stable. Fig. 8 is a functional model of a solution process. As this diagram indicates, the SolutionMethod object operates to make ˆK and ˆR using matrices of the Equation object and gets unknown variables, and the Nonlinearity object gets them and updates stiffness matrix, etc.. Fig. 9 Functional Model of Making R vector Fig. 10 Dynamic Model of Response Analysis (5) Response Analysis Module The response analysis module uses the equation module. What we have to analyze about this module is how to transfer an information of a deformation to the structure object and how to make a stiffness matrix and a load vector as components of the equation module. In terms of making a stiffness matrix, the earthquake object gets the hysteresis information through the equation object. Since the structure module makes the matrix, we only add an interface object between the structure module and the equation object, and we do not have to modify any part of the equation object. Also the load vector is calculated based on the information contained in the load module. Because there are two type object, a static load and a seismic load, the method of building them is different. While a static load, whose unit is a force, is applied directly, a seismic load, whose unit is an acceleration, needs data of a structure to make the load vector. Therefore the response analysis module must include a methodology to make the load vector (Fig. 9). A real analysis runs by solving an equation. In the procedure, since the equation object has the information of an iteration, the response analysis module only mentions about a time step calculation (Fig. 10). Like this module, a reuse of objects has a good effect on not only a reduction of code but its readability. As the result of this analysis, the object diagram of this module is shown in Fig. 11.

6 Fig. 11 Class Diagram of Response Analysis Module 4. Implementation (1) Object-oriented language In order to implement the objects as mentioned above, the C++ language 10) was chosen. Although the SmallTalk language is very famous as the objectoriented language, the C++ language is designed with the purpose of combining the advantages of objectoriented programming with the computational efficiency of the C language and is likely to be the most commonly used object-oriented language in the coming years, due to its compatibility. (2) Equation class library At the first step of implementation, the equation module is selected, since it is the fundamental object of the earthquake object and the response analysis module. When objects are implemented, basically we only translate the analysis models into program code. A example of usage of the equation class library is shown in Fig.12. This shows that the same expression can be used to perform a linear and a nonlinear analysis. It has a great advantage to use it. When we make some program using this object, we don t have to take care of its linearity. (3) Earthquake Module According to the analytical model, the earthquake object reuses the equation object. Since the solution methods of equations are coded in the equation object, /* example of Equation Object */ #include <fstream.h> #include "equation.h" void main() { Equation *eq; /* omission */ /* set up for Linear Problem */ eq = new Equation( new NLHyst(new HysLinear(2.0),new LinearSolutionMethod,new StaticSolutionMethod); /* */ /* solve linear equation */ eq->solve(); /* */ /* set up for Nonlinear Problem */ eq = new Equation( new NLHyst(new HysBilinear(2.0),new NewtonRaphson,new StaticSolutionMethod); /* */ /* solve nonlinear equation */ eq->solve(); Fig. 12 Example program of Equation Object the earthquake object takes care of only its specific function. The code in Fig. 13 is a program using the earthquake object. At first, the earthquake object is generated and after that, various analysis of the earthquake are operated to the same object by sending messages. When calculating nonlinear response spectrum, we only define it hysteresis object. This hysteresis object is used by

7 /* example program of Earthquake Object */ #include <fstream.h> #include "earthq.h" void main() { Earthquake earthq; earthq.setonedirloaddatawithtime(ns, "kobe_ns.data"); /* calculate linear response spectra */ earthq.calcresponsespectra(ns, "response.data", 0.05); /* calculate nonlinear response spectra using BILINEAR model */ earthq.calcnonlinearresponsespectra (new HMBilinear(0.1,196.0), NS, "response2.data", 0.05); /* calculate nonlinear response spectra using TAKEDA model */ earthq.calcnonlinearresponsespectra (new HMTakeda(0.5, 40.0, 0.1,196.0), NS, "response3.data", 0.05); Fig. 13 Example program of Earthquake Object in C++ the equation object inside the earthquake object. Because the equation is concealed, the expression of the analysis becomes clear. (4) Structure Module The structure object has the element objects as a list. The purpose of this object is to make structural matrices. In order to make them, the structure object gets an element from the list using iterator. It must be taken care that the structure object doesn t have to know what kind of element it is. The calculation of the element matrices is different of its shape and method. Since element objects know their kind, they can calculate matrices by their specific method and return them when they receive the message deform. Fig.14 shows the code mentioned above. In Fig.14, no concrete calculation method appears. The definite method exists in the method object. Because, as long as the element matrices are calculated, the function of the element object is satisfied, it is no problem that the calculation method is a blackbox. It have a great benefit that one expression can deal with every element s function and even if a new method is adopted in the system, the code won t be changed at all. In the code of the structure module, element objects // In Element Object, KL matrix is made // using MtdMtx Object Gen_matrix<double> LineElement::makeKL() { method->makekl(); return KLmatrix; // In MtdMtx Object, KL matrix is made // acutually Gen_matrix<double> SGAxial::makeKL() { int i, j; Gen_matrix<double> *matrix; matrix = &(ownerelement->getklmatrix()); Col_vector<double> tmpu(6); tmpu = ownerelement->getuvector() +ownerelement->getdeltau(); double disp = tmpu[1] - tmpu[4];; double mat11 = hyst->getk(disp); (*matrix)[1][1] = mat11; (*matrix)[1][4] = -mat11; (*matrix)[4][1] = -mat11; (*matrix)[4][4] = mat11; return *matrix; Fig. 14 Implemental Code of Element Object appear as we image. We can deal with the structure object as the assembly of elements, which are a similar expression of real world. (5) Earthquake Engineering System Like the equation and the structure module, we implement all modules as class libraries. Because most of all function of the system has been implemented in each object, the main function of the earthquake engineering system is the relation among objects. In Fig.15, the actual analysis code is shown. At first, the structure object is generated (constructed). This object has not only the same name (Structure), but the similar information of real structures (not only data but also deformation). So we can request the information from the structure object directly, i.e. the modal shape. Besides the structure object, the earthquake object is generated. At this time, there is no relation between the structure and the earthquake objects. When there is a message that the load applies to the structure, the response analysis module is generated and initialized. This procedure is as same as the definition of the system. And finally, we command the analysis to the response analysis object. As the result of object-oriented analysis, since we can

8 /* program for Dynamic Analysis */ #include <fstream.h> #include "structure.h" #include "r_analysis.h" void main() { Structure *structure = new Structure; structure->construct("struct.data"); structure->showstructuredata(cout); structure->plotmodeshape() Earthquake *load load = new Earthquake("kobejma.data"); load->showinfo(cout); ResponseAnalysis problem; problem = structure->applied(load); RAPrototypeFactory factory( new NLGeometric,new NewtonRaphson,new NewmarkBeta(0.25)); problem.setanalysistype(factory); problem.setdirection(ns, UD); problem.analyze(); Fig. 15 Example program of Earthquake Response Analysis express the intuitive object in the program, we can have the consistent idea through analysis, design and implementation. 5. Conclutions We give in this paper an object oriented analysis for an earthquake response analysis. Our analysis leads to the conclusion below. We analyze and arrange the knowledge of an equation. It follows from this analysis that we can express the same way on various solution methods. Next we make the model of the earthquake object using the equation object. The earthquake object has not only numerical data but also methods that express its characteristic. This fusion between data and method suggests that people can read the program included earthquakes easily and can develop an intuitive program. Finally, we try to model the whole analysis system. We propose a three module model that is more flexible than the structurebased model. This model runs by the message passing among the three modules, and the structure and load module can be also used independently. The three module model gives the extendibility and the stability for the analysis system. The reuse of object has a great advantage for the reduction of codes and programming. Our objects we made are high-level class library for the analysis, for example the structure module, the hysteresis module etc.. Therefore we prove clearly that arranging class libraries for the analysis leads to supply effective tools and methods. REFERENCES 1) Bruce W.R. Forde, Ricardo O.Foschi and Siegfried F. Stiemer, Object-oriented finite element analysis, Computers & Structures, Vol.34, , ) Thomas Zimmermann, Yve Dubois - Pèlerin and Patrica Bomme, Object-oriented finite element programming : I. governing principles, Computer Methods in Applied Mechanics and Engineering, Vol.98, , ) Yve Dubois-Pèlerin and Thomas Zimmermann, Object - oriented finite element programming : III. An efficient implementation in C++, Computer Methods in Applied Mechanics and Engineering, Vol.108, , ) E. Ishida et al., Object-oriented programming of dynamic finite-element analysis using substructure method, Proceeding of Numerical Analysis Method on Structural Engineering (in Japanese), Vol. 17, , ) R.M.V. Pidaparti and A.V. Hudli, Dynamic Analysis of structures using object-oriented techniques, Computers & Structures, Vol.49, No.1, , ) Ziga Turk, Tajana Isaković and Matej Fischinger, Object-oriented modeling of design system for RC buildings, Journal of Computing in Civil Engineering ASCE, Vol.8, No.4, , ) N. Fukuwa et al., Object oriented analysis on the earthquake response problem of soil-structure system, The 43rd Nat. Cong. of Theoretital & Applied Mechanics (in Japanese), , ) J. Rumbaugh et al., Object-oriented modeling and design, Prentice Hall, Inc., ) E. Gamma et al., Design Pattern, Softbank, ) B. Stroustrup et al., The C++ programming language, Second Edition, Addison Wiley, 1991.