Design of Structure Optimization with APDL

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1 Desgn of Structure Optmzaton wth APDL Yanyun School of Cvl Engneerng and Archtecture, East Chna Jaotong Unversty Nanchang Chna Abstract In ths paper, the desgn process of structure optmzaton wth ANSYS software has been dscussed. The author had developed programs wth ANSYS parametrc desgn language, and put t to use of 12-bar plane truss and lght portal frame structure optmzaton. Comparsons between orgnal desgn and ANSYS optmum results show that the approach proposed n ths paper s effectve and feasble. Introducton In general, structure desgn ncludes functon desgn and optmum desgn. The functon desgn emphasze that structure wll not fal, but some aspect of structure can also mprove. The desgn optmzaton emphaszes that fndng best desgn set from many feasble desgn sets but materal behavor accorded wth stress, deformaton, stablzaton, geometrcal composton and sympathetc vbraton of the code. Changed the structure geometrcal dmenson, materal type etc, whch s desgn varable, can adjust the dstrbuton of desgn resource wthn project system then the materal can exert ts ablty. Ths s the desgn of structure optmzaton. Procedure A common procedure of ANSYS optmzaton s descrbed wth fgure 1. Fgure 1. The Procedure of Optmum Desgn

2 Analyss and Analyss Results Optmum Desgn of truss structure The descrbe of truss structure optmzaton The math model of the least mass of truss structure that meet wth geometrcal composton, stress, transmogrfcaton and stablzaton s: where: 1) W(A) s total structure mass,w(a) s defned as object functon. 2) ρ the densty of materal. 3) L s the length of bar. 4) A=[A 1,A 2,,A n ] T are vector of the secton area of bar. A are defned as desgn varables. 5) σ 1, [σ 1 ] are the tensle stress and allowable tensle stress, the tensle stress s defned as state varable. 6) σ 2,[σ cr ] are the press stress and crtcal bucklng stress. The press stress s defned as state varable. 7) δ j,[δ j ] are the node dsplacement and allowable node dsplacement. The node dsplacements are defned as state varable. 8) mn s.t. A mn A W ( A σ δ σ 1 j 2,A mn ) = = 1 [ σ ] [ δ ] [ σ ] A max j cr n ρ A L; ( 1 A = 1,2,3, L, (j = 1,2,3, L, m) ( 2 = 1,2,3, L, n 2 max n 1 ) ) are the maxmum secton area and the mnmum secton area of the bar. 9) n,n 1,n 2,m are the total number of the bar, the number of tensle bar, the number of press bar and the number of node. Analyss Results Fgure 2. A 12-bar Truss

3 Fgure 3. Structure Weght Varaton Fgure 4. Stress Varaton

4 Fgure 5. Secton Area Varaton Fgure 6. Node Maxmum Dsplacement Varaton Accordng to the procedure of optmum desgn, the programs were developed wth APDL. A 12-bar truss structure s regarded as example; see fgure 2,Accordng to the procedure above the total mass of the structure s defned as the objectve functon. The secton dmenson of the bar s defned as desgn varable. The press stress, the tensle stress and the maxmum dsplacement of node are defned as state varables. The programs used to the optmzaton of the truss structure have been developed wth APDL, whch has suppled frst order optmzaton method. The research results are: 1) The varaton of structure weght s as the Fgure 3. 2) The varaton of secton stress s as the Fgure 4. 3) The varaton of secton area s as the Fgure 5. 4) The varaton of node maxmum dsplacement s as Fgure 6.

5 Dscusson and comparson The No.5 document had dscussed a 12-bar truss that s same as ths paper wth genetc algorthms. The stress of the press bar, whch s defned as state varable, has been were led nto the process of optmzaton. Comparng wth the varables of the document, the value of the state varable s modfed accordng to the change of the desgn varables; the other parameter s the same. The optmum results n the artcle can save steel materal 29.6% comparng wth that of the document. The comparson s seen table 1. Table 1. Compare of results (unts: cm 2 ) Method W(kg) A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 Orgnal desgn Genetc algorthms [5] Ths paper Optmum Desgn of lght portal frame structure The descrbe of truss structure optmzaton The lght portal frame Accorded wth stress, transmogrfcaton, stablzaton and geometrcal composton of the code s regarded as another example of optmzaton. Accordng to the ANSYS procedure of optmum desgn, the three varables are defned. 1) The least structure weght of lght portal frame, whch web plate heght s changeable, s regarded as the objectve functon. 2) The changeable begnnng and end web plate heght of beam and column, the thckness of web plate, the wdth of beam s wng, the wdth of column s wng and thckness of wng are defned as desgn varables 3) The constrant of geometrcal composton whch have the rato of heght and thckness, the rato of wdth and thckness, the rato of web plate heght and wdth of wng, the rato of begnnng heght of secton and the end heght of secton and so on are defned as state varable. The constrant of response behavor of structure, whch have ntensty, stffness and stablty, are also defned as state varable, the maxmum and mnmum value of state varable are modfed accordng the results of fnte element analyss. The formulas of state varable don t provde. The detal can be provded n the document 6. Accordng to the formulas [6] programs have been developed wth APDL, whch put t to use of lght portal frame of automoble nternatonal marketplace buldng of Jangx provnce n Chna. Analyss Results The research results are: 1) The model of GJ-3# lght portal frame s as Fgure 7. 2) The varaton of structure weght s as the Fgure 8. 3) The varatons of beam s heght of web plate are as the Fgure 9. 4) The varatons of column s heght of web plate are as the Fgure 10.

6 Dscusson and comparson The optmum results n the artcle can save steel materal 24.4% comparng wth orgnal desgn, whch s desgned by Guangdong constructon and desgn offce n Chna. The comparson s seen Table 2. Table 2. Compare of results (unts: m) DVs W(kg) HWZE HWZS HWBE HWBS HWB0 BFC BFB TW TF Orgnal desgn Ths paper Where: 1) w: the weght of lght frame 2) HWZE: the end sde s heght of web plate of the column 3) HWZS: the begnnng sde s heght of web plate of the column 4) HWBE: the end sde s heght of web plate of the beam 5) HWBS: the begnnng sde s heght of web plate of the beam 6) HWB0: the heght of web plate of unchangeable secton beam 7) BFC: the wdth of column s wng 8) BFB: the wdth of beam s wng 9) TW: the thckness of web plate 10) TF: the thckness of wng Fgure 7. Lght Portal Frame

7 Fgure 8. Structure Weght Varaton Fgure 9. Secton Heght Varaton

8 Fgure 10. Column s Secton Heght Varaton Concluson The results of truss and lght portal frame ndcates: 1. APDL s a sold and useful desktop that can easly put t to use of structure optmzaton. The programs that develop wth APDL can use ANSYS software s fnte element analyss functon. If you can modfy the program provded from the paper, other structures can also use wdely. 2. The optmum method of truss and lght portal frame s effectve, the results are provded wth credblty. I use the program wth APDL to desgn the real constructon. References [1] ANSYS Advanced Analyss Technques, 3 rd Edton, SAS, IP, Inc. [2] ANSYS Commands Reference, Tenth Edton, SAS, IP, Inc. [3] APDL Programmer's Gude, Thrd Edton, SAS, IP, Inc. [4] Chen Jny, CAE ANSYS User Gude,Bejng, Ralway Press of Chna,2001 [5] Zhang Wenyuan Wu Zhfeng,Genetc Algorthm for the Desgn of structural Optmzaton,Journal of Harbn Unversty of C.E. & Archtecture Vol. 32 No.4 Aug.1999 [6] Lght Portal Frame Buldng Structure Technque Code ( CECS102:98),Bejng, Engneerng Project Constructon Standardzaton Unon of Chna, 1999 [7] Archtecture desgn nsttute of Guangdong Provnce,Shop Drawng of Automoble nternatonal marketplace n Jangx provnce, Guangdong,2002.9

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