Boundary Condition Simulation for Structural Local Refined Modeling Using Genetic Algorithm

Transcription

1 2016 Internatonal Conference on Artfcal Intellgence: Technques and Applcatons (AITA 2016) ISBN: Boundary Condton Smulaton for Structural Local Refned Modelng Usng Genetc Algorthm Zhong ZHANG 1, We LIU 2, Nng GUO 2, Hao CHENG 1 and Le WANG 2,* 1 Scence and Technology on Relablty and Envronment Engneerng Laboratory, Bejng Insttute of Structure and Envronment Engneerng, Bejng, , Chna 2 School of Aeronautcs, Northwestern Polytechncal Unversty, X an , Chna *Correspondng author Keywords: Structural local refned modelng, Boundary condton smulaton, Genetc Algorthm (GA), Dynamc strength evaluaton. Abstract. Structural dynamc strength evaluaton s pad more attentons n aeronautcs and astronautcs engneerng, and the structural local refned modellng technque whch can be utlzed to precsely calculate the dynamc strans n the crtcal local stes of the structure s the key ssue n the structural dynamc strength evaluaton. Frstly, four common methods,.e. global / local two-step method, substructure method, transton element method and mult-pont constrant (MPC) method, used n structural local refned modelng was revewed. Then, a structural local refned modelng method, whch uses smple physcal models to smulate the effect of the surroundng structure on the local structure, s proposed based on Genetc Algorthm (GA). Fnally, the proposed structural local refned modelng method was llustrated by smulatve example of a four edges fxed alumnum rectangular plate. Introducton Wth the rapd development n aeronautcs and astronautcs engneerng, the safety of the complex aeronautcs and astronautcs structures cannot be satsfed by the tradtonal statc strength based desgn, and the dynamc strength of such structures to complex dynamc forces must be nvestgated. Consequently, the structural dynamc strength evaluaton was pad more attentons n the feld of aeronautcs and astronautcs engneerng n recent years. In the structural strength analyss, stran analyss s base for evaluatng the loadng capacty, servce lfe, relablty of the structure and performng the optmzaton desgn of the structure [1]. Therefore, the structural fnte element modelng technque whch can be utlzed to precsely calculate the dynamc strans s the crtcal ssue n the structural dynamc strength evaluaton. However, the global fnte element model of the complex aeronautcs and astronautcs structures bult by mesh refnement technque wll always have huge elements, and cannot be utlzed for common analyss. Meanwhle, the structural damages are always occurred n the local ste of the complex aeronautcs and astronautcs structures, and t s no need to perform the stran analyss usng the global model. Consequently, the structural local refned modelng and analyss mght be a useful technque for the dynamc strength analyss of the complex aeronautcs and astronautcs structures. The Common Methods Used n Structural Local Refned Modelng and Analyss Structural local refned modelng s one of the mult-scale analyss technque utlzed for balancng the precson and effcency of the calculaton, and can be used to obtan the precse results wth low computatonal costs. In the development of the fnte element analyss, there are many technques developed for balancng the precson and effcency of the calculaton, ncludng: 1) Global / local two-step method,.e. performng the local analyss after the global analyss. Such as, Tanaka et al. [2] nvestgated a hybrd global / local two-step method usng shell sold element for three dmensonal weldng structure wth crack, and verfed ther method by smulatve analyss 184

2 of the three dmensonal fracture; Langhe et al. [3] proposed a structural fatgue lfe evaluaton usng the global / local two-step method, and demonstrated the advantages of ther method by comparng the results calculated usng the proposed method and the super element method. 2) Substructure method,.e., decomposng the complex structure nto several smple substructures, and performng the analyss n each substructure. Such as, L et al. [4] proposed a mult-scale modelng strategy and method for long span brdge based on the substructure method, and fulflled the mult-scale analyss for the structural damage analyss of the long span brdge; Bao et al. [5] utlzed the substructure method to reduce the order of the whole vehcle dynamcs model, and obtaned the rgd flexble couplng model for vehcle system dynamc analyss. 3) Transton element method,.e., connectng the local fne mesh element wth the global coarse mesh element usng the transton element. Such as, Surana [6] formed a seres transton elements usng for connectng the shell element and sold element based on reduced ntegral method, and then proposed the geometrcally nonlnear transton element [7] and axal symmetry transton element [8]; accordng the moton constrans between dfferent degree of freedom, Gong [9] extracted the transton stffness matrx from the stffness matrxes of the shell element and sold element, and fulflled the connecton of shell elements and sold elements. 4) Mult-pont constrant (MPC) method,.e. formng the constrants between dfferent degree of freedom usng MPC equatons, and solvng the ncoordnate between the dfferent dmensonal elements. Such as, McCune et al [10] and Shm et al [11] proposed an MPC equaton deducton procedure for connecton dfferent elements based on the work recprocal theorem n the nterface; accordng to the global analyss results of a long span brdge, L et al. [4] ndcated that the mult-scale model usng MPC can be utlzed to calculate the local thermal stress. Boundary Condton Smulaton Usng Genetc Algorthm (GA) The above four menton methods can be utlzed to solve the calculaton effcency for the complex structure analyss. However, the purpose for the dynamc strength analyss of the complex aeronautcs and astronautcs structure s to obtan the dynamc stran characterstcs of the local crtcal structures, and there s no need to perform the global model analyss usng the above methods. Usually, the structural local refned modelng technque can be utlzed. In the structural local refned modelng technque, the local structure should be extracted frstly, and then the effect of the surroundng structure on the local structure can be smulated by the equvalent boundares, fnally the local structure model can be formed by the extracted local structure and ts equvalent boundares. Ban [12] proposed a structural local refned modelng technque based on structural dynamc condensaton method, and llustrated the hgh precson of the proposed method usng smulatve examples. Accordng to the deducton procedure of the method, t can be seen that: 1) the matrx nverse calculaton are requred,.e., t s mpossble for calculatng the model wth huge degree of freedom; 2) both the stffness and mass matrxes of the obtaned equvalent boundary are full matrxes,.e. the obtan equvalent boundary s a mathematc model, and the correspondng physcal model cannot be manufactured for expermental valdaton of the proposed method. To overcome the above shortages of the structural local refned modelng technque, a boundary condton smulaton method n whch the equvalent boundary are smulated by some smple physcal models (such as short beams and short plates) wll be proposed n ths paper. The key ssue for structural local refned modelng s the smulaton of the equvalent boundary for the local structure,.e. how to smulate the constrants of the surroundng structure on the local structure usng some smple physcal models (such as short beams and short plates). Usually, t s dffcult to obtan the equvalent boundary by smplfyng the global model drectly. Thus, an ntal equvalent boundary should be bult frstly, and then the parameters of the ntal equvalent boundary wll be updated by some optmzaton technques to fulfll the demands of the local model. However, the classcal senstvty based optmzaton technque cannot be adopted for the complex aeronautcs and astronautcs structure as the calculaton effcency for senstvty analyss wll be huge. 185

3 Consderng the advantages of GA n optmzaton and the usage of the commercal fnte element analyss software MSC Nastran n aeronautcs and astronautcs engneerng, a boundary smulaton method for structural local refned modelng s proposed usng both GA and MSC Nastran, the optmzaton procedure s as follows (shown n Fg. 1): 1) Select and ntalze the desgn parameters n the ntal equvalent boundary; 2) Modfy the values of desgn parameters n MSC Nastran nput fle; 3) Analyze the local structural model usng MSC Nastran; 4) Extract the results for constructng the objectve functon; 5) Output the values of the desgn parameters f the optmzaton satsfed the stop crteron; otherwse, update the values of the desgn parameters usng GA and go to step 2). Select and Intalze Desgn Parameters Modfy Nastran Input Fle (BDF Fle) Analyze Usng Nastran Extract Results Update the Values of Desgn Parameters Usng GA Satsfy the Stop Crteron? No Yes Obtan the Optmum Values for Desgn Parameters Fgure 1. Flowchart of boundary condton smulaton usng GA. Smulatve Example A four edges fxed alumnum rectangular plate shown n Fg. 2 (a) s adopted to verfy the proposed structural local refned modelng method. The dmenson of the plate s 800mm*600mm, supposng that the mddle dark regon wth dmenson 200mm*150mm s the local crtcal structure. Accordng to the symmetry of the structure, the dynamc responses of the four partcular stes (.e. Pont I, Pont II, Pont III and Pont IV) was utlzed to evaluate the precson of the local refne model. III II IV I B A D C Fgure 2. Smulatve model. (a) four edges fxed alumnum rectangular plate, (b) local structure and ts boundary condtons smulated by short plates Consderng the boundary effect, t s mpossble to obtan the precse results n the boundary ponts (.e., Pont II, Pont III and Pont IV) f only the dark regon wth dmenson 200mm*150mm s selected as the local structure. Thus, the local structure s selected a lttle wder than the dark regon, 186

4 .e., all the four selected responses calculaton ponts wll be the nternal ponts of the local structure. Then, the mddle regon wth dmenson 320mm*240mm was selected as the local model, and four short plates wth wdth 80mm were adopted to smulate the boundary condtons, as shown n Fg. 2 (b). In order to ncrease the calculaton precson wth the smulatve boundary, each short plate was dvded by two parts from the mddle, and the thcknesses of each plate was selected as the desgn parameters. Fnally, four desgn parameters (.e., the thckness of Regon A, Regon B, Regon C and Regon D n Fg. 2 (b) were obtaned by consderng the symmetry of the structure. As the natural frequency and mode shape are the basc dynamc characterstcs, these two characterstcs were adopted to form the objectve functon n the current example,.e. N N loc, ( t) glo, 1 MAC ( ) 1 f ( t) t 1 (1) where, t s the thckness vector whch ndcates the thcknesses of each short plates, s the natural T 2 loc, ( t) glo, frequency, MAC ( t) s the modal assurance crteron (MAC), s the T T ( ( t) ( t))( ) loc, loc, glo, glo, mode shape, the subscrpt loc ndcate the parameter related wth the local refned model, the subscrpt glo ndcate the parameter related wth the global model, the subscrpt ndcate the parameter related wth the th momal, N s the modal order consdered n the optmzaton procedure. Usng the objectve functon formed by the frst fve natural frequences and mode shapes, the optmzed thcknesses of Regon A, B, C and D are updated as 49.1mm, 0.759mm, 1.6mm and 34.7mm, and the optmzed modal parameters are lsted n Table 1. As shown n Table 1, the maxmum error n the natural frequences s 5.69%, and the MAC values are very close to 1,.e., the local refned model bult by the proposed method can be utlzed to obtan the precse results. Table 1. Optmzaton results usng the frst fve modes natural frequency modal global local order relatve errors model (Hz) model (Hz) MAC value % % % % % locaton Table 2. Relatve errors of the ampltudes of the acceleraton and dynamc stran between the local model and global model. acceleraton ampltude global model (ms -2 ) (ms -2 ) local model relatve errors dynamc stran ampltude global model (με) (με) local model relatve errors Pont I % % Pont II % % Pont III % % Pont IV % % In order to verfy the feasblty of the method further, the acceleratons and dynamc strans of the four partcular stes (.e., Pont I, Pont II, Pont III and Pont IV) n the model were calculated usng the local refned model, and compared wth the results by the global model. The large mass method was utlzed to smulate the base acceleraton exctaton, the large mass s set as 7*10 6 kg, and the 187

5 exctaton force s set as 1.4*10 9 *sn(80πt) N. The relatve errors of the ampltudes of the acceleraton and dynamc stran between the local model and global model are lsted n Table 2. It can be seen n Table 2 that the acceleratons of the partcular ponts the local refned model are very close to the results by the global model, but the errors n the dynamc strans are relatvely bgger. It s shown that: 1) precse acceleraton responses can be obtaned usng the objectve functon formed by the natural frequences and mode shapes; 2) t cannot obtan the precse dynamc strans usng only natural frequences and mode shapes, and some other characterstcs should be consdered n the constructon of the objectve functon. Summary Accordng to the fact that the effect of the surroundng structure on the local structure mght be smulated usng the equvalent boundary modeled by some smply physcal models (such as short beams, short plates), a structural local refned modelng method usng Genetc Algorthm was proposed n ths paper and llustrated by smulatve example of a four edges fxed alumnum rectangular plate. As only the natural frequences and mode shapes were consdered n the modelng procedure, the obtaned structural local refned model can only be utlzed to calculate the acceleratons precsely, and cannot be utlzed to acheve the precse dynamc strans. As we known, the dynamc strans are not only related wth natural frequences and mode shapes, but also be related wth the dampng parameters and structural local features. Then, the future work should be obtan a better modelng procedure for calculatng the dynamc strans precsely wth the help of the parameters related wth dynamc strans. Acknowledgement Ths work was supported by the Innovaton Funds of CALT for Unverstes of Chna (Grant no. CALT201508) and the Key Laboratory Foundaton (Grant no. XX0C93010). References [1] M. Z. Tao, Structure desgn of modern arcraft, X an, Northwestern Polytechncal Unversty Press, [2] S. Tanaka, H. Okada, S. Ogawa, S. Okazawa, Analyss of Three-dmensonal Crack n Welded Jont Structure usng Shell-Sold Zoomng Method, Proc. 20th Int. Offshore and Polar Eng. Conf., Bejng, 4 (2010) [3] K. De Langhe, D. Vandeptte, P. Sas, A combned dynamc-statc fnte element model for the calculaton of dynamc stresses at crtcal locatons, Comput. Struct. 65 (1997) [4] Z. X. L, Z. H. Sun, L. Guo, Concurrent mult scale modelng of structures and damage analyses, J. Southeast Unv. 37 (2007) [5] X. H. Bao, M. R. Ch, Y. H. Lu and F. Yang, Research on vehcle system dynamcs model of rgd-flexble mxture based on substructure method, Ralway Locomotve and Car 29 (2009) [6] K. S. Surana, Transton fnte elements for three-dmensonal stress analyss. Int. J. Numer. Meth. Eng. 15 (1980): [7] K. S. Surana, Geometrcally non-lner formulaton for the three dmensonal sold- shell transton fnte elements. Comput. Struct. 15 (1982) [8] K. S. Surana, Geometrcally nonlnear formulaton for the ax-symmetrc transton fnte elements. Comput. Struct. 17 (1983)

6 [9] Y. N. Gong, Local/global structural analyss by transton elements, Comput. Struct. 30 (1988) [10] R. W. McCune, C. G. Armstrong, Mxed dmensonal couplng n fnte element models, Int. J. Numer. Meth. Eng. 49 (2000) [11] K. W. Shm, D. J. Monaghan, C. G. Armstrong, Mxed dmensonal couplng n fnte element stress analyss, Eng. Comput. 18 (2002) [12] X. Ban, Study on Precse Dynamc Fnte Element Modelng of Local Structure, Master Thess, X an: Northwestern Polytechncal Unversty,