13 th World Conference on Earthquake Engneerng Vancouver, B.C., Canada August 1-6, 2004 Paper No. 78 RECENT DEVELOPMENTS IN SNAPS3D A FINITE ELEMENT ANALYSIS PROGRAM FOR 3-DIMENSIONAL NONLINEAR TIME- HISTORY
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13 th World Conference on Earthquake Engneerng Vancouver, B.C., Canada August 1-6, 2004 Paper No. 78 RECENT DEVELOPMENTS IN SNAPS3D A FINITE ELEMENT ANALYSIS PROGRAM FOR 3-DIMENSIONAL NONLINEAR TIME- HISTORY ANALYSIS OF PRECAST CONCRETE STRUCTURES Serdar ASTARLIOGLU 1, Andrew SCANLON 2, Al M. MEMARI 3 SUMMARY Ths paper descrbes the enhancements made to the fnte element analyss program (SNAPS3D) developed to carry out materally nonlnear statc or dynamc analyss of three-dmensonal precast concrete buldng structures. The fnte element lbrary conssts of three-dmensonal sold elements, shell elements to model wall panels and horzontal daphragms, frame elements to model beams and columns, and connecton elements to model the nterface between daphragm and wall panels as well as the nterface between beams and columns. The materal lbrary conssts of lnear elastc, elastoplastc, unaxal concrete, and shear-slp materal models. INTRODUCTION The approach taken by most buldng codes towards the desgn of precast concrete structures n sesmc zones has been to emulate the desgn prncples used n monolthc structures as a result of uncertantes concernng the performance of precast concrete structures durng earthquakes. When dry connectons are used, the behavor of a precast concrete structure under sesmc load can dffer from a smlar renforced concrete structure to a great extend, snce hghly localzed nonlnear behavor n the form of rockng and sldng s observed at the connecton regons. Whle a two-dmensonal approach wth the assumpton of rgd floor daphragms may be suffcent for smple or coupled shear wall layouts, n case of flexble floor daphragms and unsymmetrcal lateral load resstng system arrangements, ths approach may not provde suffcent accuracy. Because of ths, prevous analytcal research nto the behavor of precast structures has been lmted to two-dmensonal cases, where the wall systems were solated from the rest of the structure wth the assumpton of rgd floor daphragms (Kanoush [1,2], Caccese [3], and Pekau [4]). SNAPS3D has been developed to perform nonlnear dynamc analyss of three-dmensonal precast concrete buldng structures and to determne the effect of daphragm flexblty, rockng and sldng mechansms on the overall response of the buldng. Ths paper summarzes the changes and enhancements made to SNAPS3D. 1 S. Astarloglu, The Pennsylvana State Unversty, USA, 2 A. Scanlon, The Pennsylvana State Unversty, USA, 3 A. M. Memar, The Pennsylvana State Unversty, USA, DESCRIPTION OF SNAPS3D SNAPS3D was ntally developed (Astarloglu [5]) to model the behavor of large panel precast structures. The fnte element lbrary conssted of three-dmensonal sold elements to model wall panels and horzontal daphragm components, beam elements to model regular beams and couplng beams, sprng elements to model the behavor of jonts between panels and daphragms, and truss elements to model vertcal post-tensonng. Whle sold, beam, and truss elements exhbted only lnear-elastc behavor, sprng elements had nonlnear materal behavor to model potental crushng of concrete, sldng of panels at horzontal and vertcal jonts, and jont openngs. The source code for SNAPS3D was wrtten n FORTRAN 90 usng a procedural programmng approach where dfferent tasks were performed by specalzed subroutnes. The program conssted of the followng subroutnes: nput, loadng, ncremental loadng, stffness matrx assembly, soluton of equatons, resdual force calculatons, convergence check, and output results, n addton to modules for storage of global arrays such as nodal coordnates, element connectvty, materal propertes, and boundary condtons. Fgure 1 shows the ntal program layout (Owen [6]). Input Module Loadng Module Increment Loadng Stffness Matrx Assembly Module Frontal Soluton Module Resdual Force Calculaton Module Convergence Check Iteraton Loop Increment Loop Output Module Fgure 1. Flow Chart for SNAPS3D The new verson of SNAPS3D, whch wll be descrbed n the followng sectons, s radcally dfferent from the ntal verson summarzed above n two aspects: Element / materal lbrary and programmng approach. Element Lbrary Sold Element In the orgnal program, 8-node sold elements shown n Fgure 2 were utlzed to model the wall panels and floor daphragms. Unfortunately, ths approach requres through the thckness meshng of these structural members, resultng n hgh number of elements. For ths reason, sold elements were replaced wth contnuum based shell elements as the prmary fnte element for modelng these members. However, sold elements are stll avalable n SNAPS3D for reasons, whch wll be dscussed n programmng approach secton. Fgure 2. 8-node sold element. Shell Element The shell elements mplemented n SNAPS3D are based on contnuum-based shell approach poneered by Ahmad [7] for analyss of curved shells. Snce these wall panels and floor daphragms are flat (not curved) structural members, the formulaton of the element was modfed to ncorporate drllng degrees of freedom (Cook [8]). The resultng element s a sub-parametrc fnte element n whch the geometry nterpolaton s based on the shape functons of an 8-node sold element, whle the dsplacement nterpolaton s based on a 12-node sold element (wth addtonal nodes at centers of sde faces). The element, shown n Fgure 3, has eght master nodes that have three translatonal degrees of freedom (dof) and four slave (nternal) nodes that have three translatonal and three rotatonal dof. Fgure 3. 8-node shell element wth 4 slave nodes. Frame Element Degenerated contnuum based approach used n development of shell element has also been used n the development of the frame element, shown n Fgure 4. Further detals on ths type of frame element are avalable n Belytscko [9]. In ths case, 4 master nodes at each end of the frame element are condensed nto a sngle slave node wth three translatonal and three rotatonal dof. Ths element can be used to model rectangular beams and columns. Fgure 4. 8-node frame element wth 2 slave nodes. Connecton Element The connecton element, shown n Fgure 5, s very smlar to the frame element n most aspects. The major dfference s that the connecton element does not use gauss ntegraton ponts for stffness matrx ntegraton. Instead, the ntegraton ponts have to be provded by the user. Ths element can also be used to model beams and columns that do not have a rectangular cross secton such as I and L beams. Alternatvely, usng the nonlnear materal models that are descrbed n the next secton, t s possble to use ths element to model column to beam and wall panel to horzontal floor connecton nterfaces. In ths mode, dfferent materals can be assgned to each ntegraton pont. Unlke the sprng element, whch requres a load-deflecton (lumped) relatonshp to defne nonlnear behavor, the connecton element requres stress-stran (dstrbuted) relatonshp. Fgure 5. Cross-secton of connecton element. The elements descrbed above allow the modelng of not only be used to model connectons n precast panel buldngs, whch was the orgnal objectve of SNAPS3D, but precast frames wth PRESSS type connectons (Prestley [10]) as well. Fgure 6 shows a typcal fnte element mesh at a platform type wall panel / floor daphragm connecton. Fgure 7 shows a typcal fnte element mesh at a frame connecton. Fgure 6. FE mesh for a wall to slab connecton. Fgure 7. FE mesh for a column-beam connecton. Materal Lbrary Asde from the lnear elastc materal model, SNAPS3D has unaxal concrete (Fgure 8), steel (Fgure 9), and shear-slp (Fgure 10) materal models to smulate the nonlnear behavor of connecton nterfaces under sesmc load. Of these models, concrete and steel models can be assgned to dfferent ntegraton ponts on the same element to represent the axal stress-stran relatonshp, whle shear-slp model has to be assgned to all the ntegraton ponts. Fgure 8. Unaxal concrete stress-stran curve. The nonlnear part of the concrete stress-stran relatonshp n Fgure 8 s n the followng form (Darwn [11]): E0ε σ = 2 E 0 ε ε (3) Es εc εc Where, ε : Unaxal stran n the prncpal stress drecton σc, ε c : Maxmum compressve stress and correspondng stran E : Intal tangent modulus 0 E : Secant modulus s The tensle strength of concrete s neglected, and the unloadng/reloadng s assumed to occur parallel to ntal tangent modulus. Fgure 9 shows the elastc-perfectly plastc stress stran relatonshp assumed for steel. The compresson and tenson branches of the stress-stran relatonshp are assumed to be dentcal, unloadng/reloadng s assumed to take place parallel to the ntal modulus, and stran hardenng s not consdered. Fgure 9. Steel stress-stran model. Fgure 10 shows the shear-slp relatonshp used n ths study. Ths relatonshp s only actvated when the ntegraton pont under consderaton s under compressve stresses (σ ). If the normal stresses become zero (gap opens), then the shear resstance s lost, tll the gap closes agan. The parameters defnng the relatonshp are: G : Tangent shear modulus of the connecton materal d G : Tangent shear modulus of the slp surface s µ : Coeffcent of frcton σ : Compressve stress actng on the pont The unloadng/reloadng s assumed to take place parallel to the ntal modulus. Fgure 10. Shear-slp relatonshp Programmng Approach The source code for SNAPS3D has been completely rewrtten n C#, an object-orented programmng language developed by Mcrosoft [12]. In ths approach, the program s organzed nto objects that store both methods (equvalent to FORTRAN subroutne/functon) and data, and a group of objects that have common behavors, methods, and operators are called classes. Ths results n a source code, whch s easer to mantan and modfy (by addng new elements and/or materals) as reported by Forte [13]. SNAPS3D contans classes for nodes, elements, materals, solvers, wndows forms (for nput and output), and matrces. The concepts of nhertance and polymorphsm are also used throughout the program. Fgure 11 shows the mplementaton of nhertance for dervaton of element classes. Each element contans propertes that defne ts nodes, ntegraton ponts, and materal(s), as well as methods to calculate the shape functons, stran dsplacement matrx, consttutve matrx, stffness matrx, mass matrx, and nternal force vector. The element base class provdes abstract nformaton on these propertes and methods. Each subclass derved from element base class must mplement ts own verson of any of the methods mentoned above. The sold element and truss element classes, whch drectly nhert from element class, have to mplement ther own versons of the methods for evaluatng the shape functons and stran-dsplacement relatonshps, etc. Shell and frame element classes nhert from sold, and add new propertes as nternal (slave) nodes, whch do not exst n the sold element class. These subclasses overwrte some of the methods, such as the method for calculatng consttutve matrx, from the sold element class wth ther own versons. The method for calculatng the stffness matrx on the other hand s not overwrtten and both shell and truss element classes use the sold verson of the method for stffness matrx calculaton. The other mportant beneft of object-orented approach s polymorphsm. For example, n the case of statc analyss, the class for assemblng the global stffness matrx, all the elements are accessed by ther base class name (element). As a result, addton of a new element class does not requre the assembly class to be changed. Fgure 11. Elements namespace and element class herarchy. The way the matrces are handled s also qute dfferent from the orgnal verson of the program. In the object-orented verson, there are two matrx classes: submatrx and matrx. Submatrx s dentcal to a FORTRAN style matrx and s flled wth real numbers and when an nstance of ths class s created, enough memory to hold all the elements (n ths case real numbers) of the matrx has to be allocated. Matrx class on the other hand, s a matrx of submatrx objects. When an nstance of matrx class s created, memory to hold all the elements (n ths case submatrx objects) s not automatcally allocated. All stffness matrces n SNAPS3D (element or global) are of matrx type. RESULTS SNAPS3D s stll n development/verfcaton phase. Results wll be made avalable when program testng and verfcaton s completed. CONCLUDING REMARKS Prevous analytcal studes on behavor of precast structures have been lmted to two-dmensonal models. The computer program beng developed n ths study promses to provde useful nsghts nto the three-dmensonal behavor of precast concrete large panel structures and frames under sesmc load. REFERENCES 1. Kanoush MR, Scanlon A. Inelastc Sesmc Response of Precast Concrete Large Panel Coupled Shear Wall System. Unversty of Alberta, Kanoush MR, Elmors R, Scanlon A. Response of Large Panel Precast Wall Systems: Analyss and Desgn. PCI Journal 1996: Caccese V, Harrs HG. Sesmc Resstance of Precast Concrete Shear Walls. Earthquake Engneerng and Structural Dynamcs 1987; 15: Pekau OA, Hum D. Sesmc Response of Frcton Jonted Precast Panel Shear Walls. PCI Journal 1991; 36(2): Astarloglu S, Memar AM, Scanlon A. Modelng Strateges for Three Dmensonal Analyss of Precast Panel Buldngs Under Sesmc Load. Proceedngs of the 12th World Conference on Earthquake Engneerng, Auckland, New Zealand, Paper No. 1356, Owen DRJ, Hnton E. Fnte Elements n Plastcty: Theory and Practce. Swansea: Pnerdge Press, Ahmad S, Irons BB, Zenkewcz OC. Analyss of Thck and Thn Structures by Curved Fnte Elements. Internatonal Journal for Numercal Methods n Engneerng 1970; 2: Cook RD. Four-Node Flat Shell Element: Drllng Degrees of Freedom, Membrane-Bendng Couplng, Warped Geometry, and Behavor. Computers and Structures 1994; 50(4): Belytscko T, Lu WK, Moran B. Nonlnear Fnte Elements for Contnua and Structures. West Sussex: John Wley and Sons Ltd, Prestley MJN, Srtharan S, Conley JR, Pampann S. Prelmnary Results and Conclusons from the PRESSS Fve-Story Precast Concrete Test Buldng. PCI Journal 1999: Darwn D, Pecknold D. Inelastc Model for Cyclc Baxal Loadng of Renforced Concrete. Unversty of Illnos at Urbana-Champagn, Mcrosoft Corp Forte BWR, Fosch RO, Stemer SF. Object-Orented Fnte Element Analyss. Computers and Structures 1990; 34(3):
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