Computational Structural Mechanics – Nonlinear Structural Dynamics

Research and Impact

Our group has developed advanced modeling and numerical techniques (that is widely used and cited) for nonlinear dynamic analysis of base isolated structures, stability of elastomeric bearings, and nonlinear dynamics of structures with passive nonlinear tuned mass dampers, smart base isolated benchmark problem, and vortex induced vibration of deepwater risers used in floating offshore platforms.

Such development has lead to the computer program 3D-BASIS has been used for analysis and design of numerous base isolated structures within the United States and in many countries around the world. Landmark structures where 3D-BASIS was used are the New San Francisco International Airport and the San Francisco General Services Building, both of which are supported on friction pendulum bearings.

3D BASIS Origins, Novel Developments and Its Impact in Real Projects around the World: Key computational challenges addressed

3D-BASIS suite of programs

3D-BASIS suite of programs and its impact

Google search on Nonlinear Dynamic Analysis of Three Dimensional Structures

Google search on Nonlinear Dynamic Analysis of Three Dimensional Base Isolated Structures

Origins and development of 3D-BASIS (3-Dimensional BASe Isolated Structures) was initially envisioned by the need for an efficient tool for nonlinear dynamic analysis of three-dimensional base isolated structures, particularly in solving the the highly nonlinear bidirectional stick-slip hysteretic response of a collection of sliding isolation bearings and the resulting response of the superstructure, as this was not available at that time. The primary challenge was to solve the stick-slip behavior of friction bearings—modeled using a differential equation (Bouc-Wen Model) due to its efficiency in representing constant Coulomb friction or variable velocity dependent friction by using a very small yield displacement during the stick phase resulting in very high tangential stiffness followed by a very small tangential stiffness during the sliding phase—and the resulting stiff differential equations. A challenge that is compounded when biaxial-friction is modeled, wherein even the traditional method of using Gear’s method to solve stiff differential equations breaks down—a problem that was vexing the research team at University at Buffalo trying to solve the problem at that time. The answer was the development of the novel pseudo-force solution algorithm along with a semi-implicit Runge-Kutta method to solve the difficult problem. The efficient solution procedure is needed primarily for the nonlinear isolation system consisting of (1) sliding and/or elastomeric bearings, (2) fluid dampers, (3) other energy dissipation devices, while the superstructure is represented by three dimensional superstructure model appropriately condensed (where only master nodes at the center of mass of the floor are retained).

3D-BASIS for Nonlinear Dynamic Analysis of Base Isolated Structures has been cited in several important code related documents [FEMA 273/274 [39], ATC 33, NEHRP, NIST]. “The most widely used computer program for analyzing base isolated structures today is the 3D-BASIS suite of programs…” is a direct quote from the book on “Earthquake Resistant Design with Rubber” by Professor James M. Kelly, 1997 [2]—see page 234. (NIST – NEHRP Nonlinear Structural Analysis for Seimsic Design NIST GCR 10-917-5-15wux56).

 

3D-BASIS has been used for analysis and design of numerous projects around the world; the most important of which are listed below.

  • U. S. Court of Appeals, San Francisco, CA, 1990-1991
  • LNG Tanks, Greece, 1994
  • San Francisco International Airport, CA, 1996
  • ATATURK International Airport in Istanbul, Turkey, 2000
  • Statue of Hermes, Museum at Olympia, Greece, 2004
  • Mills Peninsula Hospital, Burlingame, CA, 2005
  • Washington Hospital, Fremont, CA, 2005
  • Stanford University Hospital, CA, 2008
  • Lunskoye and Piltun Offshore Oil Platforms, Sakhalin, Russia, 2008
  • San Francisco General Hospital, CA, 2011
  • Arkundagi Offshore Oil Platform, Sakhalin, Russia, 2013
  • Apple headquarters, CA 2018

Book

Cimellaro, G. P., Nagarajaiah, S., and Kunnath, S. “Computational Methods in Seismic Protection, Hybrid Testing and Resilience in Earthquake Engineering,” Springer Publisher, Geotechnical, Geological and Earthquake Engineering Book Series, 2015.

 

Ph.D. students who worked on research related to Computational Structural Mechanics and Nonlinear Structural Dynamics & related problems

2015, Dr. Keguan Zou, “Study of Adaptive Passive Stiffness Systems with Nonlinear Vibrations: New Analytical and Computational Techniques,” Ph.D. Dissertation, CEVE, Rice University, Dec. 2014, M.S., Southeast Univ., China, B.S., Tsinghua Univ., China

2014, Dr. Srivishnu Venkata Mohan Vemuru, “Dynamic Stability of elastomeric seismic isolation bearings and seismic protection using enhanced adaptive negative stiffness system.” Ph.D. Dissertation, CEVE, Rice University, M.S. Rice, B.S. NIT- Surtkal, India

2014, Dr. Chao Sun, “Structural Vibration Control of Nonlinear Systems Using the Smart Tuned Mass Damper (STMD) and the Nonlinear Tuned Mass Damper (NTMD).” Ph.D. Dissertation, CEVE, Rice University, M.S. Tongji University, China, B.S. Shanghai Jaio Tong University, China

2013, Dr. Chaojun Huang, “Structural Health Monitoring System for Deepwater Risers with Vortex-induced Vibration: Nonlinear Modeling, Blind Identification, Fatigue/Damage Estimation & Vibration Control” Ph. D. Dissertation, CEVE, Rice University, M.S. Tsinghua
University, China, B.S. Tsinghua University, China.

2004, Dr. Sriram Narasimhan, “Control of smart base isolated buildings with new semiactive devices and novel H2/LQG, H, and time frequency controllers” Ph.D. Dissertation, CEVE, Rice University., M.S. Rice, M.S. Louisiana State University, B.S. Osmania University, India.

 

Smart Base Isolated Benchmark Problem Based on MATLAB adaptation of 3D-BASIS and Enhancements suited for Structural Control

 

Narasimhan, S., Nagarajaiah, S. and Johnson, E. ” Smart Base Isolated Benchmark Building Part IV: Phase II Sample Controllers for Nonlinear Isolation Systems “Structural Control & Health Monitoring, DOI: 10.1002/stc.267, 15 (5), 657-672 (2008).

Nagarajaiah, S., Narasimhan, S. and Johnson, E., ” Structural Control Benchmark Problem: Phase II Nonlinear Smart Base Isolated Building subjected to Near Fault Earthquakes ” Structural Control & Health Monitoring, DOI: 10.1002/stc.280, 15 (5), 653-656 (2008).

Nagarajaiah, S. “Structural Control Benchmark Problem: Smart Base Isolated Building Subjected to Near Fault Earthquakes,” Structural Control & Health Monitoring, DOI: 10.1002/stc.98, 13(2-3), 571–572 (2006).

Nagarajaiah, S., and Narasimhan, S. “Smart base isolated benchmark building Part II:  Phase I Sample controllers for linear isolation system,” Structural Control & Health Monitoring, DOI: 10.1002/stc.100, 13(2-3), 589-604 (2006).

Narasimhan, S., Nagarajaiah, S., Gavin, H., Johnson, E. A. “Smart Base Isolated Benchmark Building Part I: Problem definition,” Structural Control & Health Monitoring, DOI: 10.1002/stc.99, 13(2-3), 573-588 (2006).

 

Papers resulting from research involving Computational Structural Mechanics – Nonlinear Structural Dynamics

Zou, K.G., and Nagarajaiah, S., (2016). “Closed-form criterion for convergence and stability of pseudo-force method for nonlinear dynamic analysis”, Nonlinear Dynamics, 86(2), 1035-1046, DOI: 10.1007/s11071-016-2944-5.

Vemuru, V.S.M., Nagarajaiah, S., and Mosqueda, G., (2016). “Coupled horizontal-vertical stability of bearings under dynamic loading”, Earthquake Engineering and Structural Dynamics, 45(6), 913-934, DOI: 10.1002/eqe.2691.

Zou, K., and Nagarajaiah, S., (2015) “An analytical method for analyzing symmetry breaking bifurcation and period doubling bifurcation”, Communications in Nonlinear Science and Numerical Simulation, 22(1-3), 780-792, DOI: 10.1016/j.cnsns.2014.08.015.

Zou, K., Nagarajaiah, S., and Dick, A.J. (2015). “Asymmetric Solutions of SDOF System with Wire Rope Vibration Isolator Subjected to Harmonic Excitation”, International Journal of Structural Stability and Dynamics, 15(6), DOI: 10.1142/s0219455414500898.

Eason, R. P., Sun, C., Dick, A. J., and Nagarajaiah, S. (2015). “Steady-state response attenuation of a linear oscillator-nonlinear absorber system using an adjustable-length pendulum in series: Numerical and experimental results”, Source: Journal of Sound and Vibration, 344, 332-344, DOI: 10.1016/j.jsv.2015.01.030.

Zou, K. and Nagarajaiah S. (2015). “Study of a piecewise linear dynamic system with negative and positive stiffness” Communications in Nonlinear Science and Numerical Simulation, 22(1-3), 1084-1101, DOI: 10.1016/j.cnsns.2014.08.016.

Zou, K. and Nagarajaiah S. (2015).“The solution structure of the Duffing oscillator’s transient response and general solution” Nonlinear Dynamics, 81(1-2), 621-639, DOI: 10.1007/s11071-015-2015-3.

Vemuru, V., Nagarajaiah, S., Masroor, A., and Mosqueda, G. (2014). “Dynamic Lateral Stability of Elastomeric Seismic Isolation Bearings.” Journal of Structural Engineering, DOI: 10.1061/(ASCE)ST.1943-541X.0000955, A4014014, 140(8) (2014).

Sun, C., Nagarajaiah, S. and Dick, A. J. “Family of smart tuned mass dampers with variable frequency under harmonic excitations and ground motions: closed-form evaluation” Smart Structures and Systems, DOI: 10.12989/sss.2014.13.2.319, 13(2), 319-341 (2014).

Sun, C., Eason, R.P., Nagarajaiah, S., Dick, A.J. “Hardening Düffing oscillator attenuation using a nonlinear TMD, a semi-active TMD and multiple TMD,” Journal of Sound and Vibration, DOI: 10.1016/j.jsv.2012.10.016, 332 (4), 674-686, (2013).

Eason, R.P., Sun, C., Dick, A.J., Nagarajaiah, S. “Attenuation of a linear oscillator using a nonlinear and a semi-active tuned mass damper in series,” Journal of Sound and Vibration, DOI: 10.1016/j.jsv.2012.07.048, 332 (1), 154-166, (2013).

Nagarajaiah, S., and Sun, X., “Base Isolated FCC building: Impact Response in Northridge Earthquake,” Journal of Structural Engineering, ASCE, DOI: 10.1061/(asce)0733-9445(2001)127:9(1063), Vol. 127, No. 9, 1063-1074 (2001).

Nagarajaiah, S., and Sun, X., “Response of base isolated USC hospital building in Northridge Earthquake,” Journal of Structural Engineering, ASCE, DOI: 10.1061/(asce)0733-9445(2000)126:10(1177), Vol. 126, No. 10, 1177-1186 (2000).

Nagarajaiah, S., and Ferrell, K. “Stability of elastomeric seismic isolation bearings,” Journal of Structural Engineering, ASCE, DOI: 10.1061/(asce)0733-9445(1999)125:9(946), Vol. 125, No. 9, 946-954 (1999).

Nagarajaiah, S., Reinhorn, A. M., and Constantinou, M. C., “Torsion in base isolated structures with elastomeric isolation systems,” Journal of Structural Engineering, ASCE, DOI: 10.1061/(asce)0733-9445(1993)119:10(2932), Vol. 119, No. 10, 2932-2951 (1993).

Nagarajaiah, S., Reinhorn, A. M., and Constantinou, M. C., “Torsional coupling in sliding base isolated structures,” Journal of Structural Engineering, ASCE, DOI: 10.1061/(asce)0733-9445(1993)119:1(130), Vol. 119, No. 1, 130-149 (1993).

Nagarajaiah, S., Reinhorn, A. M., and Constantinou, M. C., “Nonlinear dynamic analysis of 3D-base isolated structures,” Journal of Structural Engineering, ASCE, DOI: 10.1061/(asce)0733-9445(1991)117:7(2035), Vol. 117, No. 7, 2035-2054 (1991).

 

Technical Reports

Nagarajaiah, S, and Sun, X., “Response of base isolated buildings during the 1994 Northridge earthquake,” Rice Technical Report 51, to California Strong Motion
Instrumentation Program, (1999).

Reinhorn, A.M., Nagarajaiah, S., Constantinou, M.C., Tsopelas, P.C., and Renfen, L., “3DBASIS-TABS Version 2.0: A computer program for nonlinear dynamic analysis for three dimensional base isolated structures,” Report No. NCEER-94-0018, National Center for Earthquake Engineering Research, SUNY, Buffalo, New York (1994).

Nagarajaiah, S., Li, C., Reinhorn, A. M., and Constantinou, M. C., “3D-BASIS-TABS: A computer program for nonlinear dynamic analysis for three-dimensional base isolated structures,” Report No. NCEER-93-0011, National Center for Earthquake Engineering
Research, SUNY, Buffalo, New York (1993).

Tsopelas, P., Nagarajaiah, S., Constantinou, M. C., and Reinhorn, A. M., “3D-BASIS-M: Nonlinear dynamic analysis of multiple building base isolated structures,” Report No. NCEER-91-0014, National Center for Earthquake Engineering Research, SUNY, Buffalo, New York (1991).

Nagarajaiah, S., Reinhorn, A. M., and Constantinou, M. C., “3D-BASIS: Nonlinear dynamic analysis of three-dimensional base isolated structures – Part II,” Report No. NCEER-91- 0005, National Center for Earthquake Engineering Research, SUNY, Buffalo, New York (1991).

Nagarajaiah, S., Reinhorn, A. M., and Constantinou, M. C., “Nonlinear dynamic analysis of three dimensional base isolated structures (3D-BASIS),” Report No. NCEER-89-0019, National Center for Earthquake Engineering Research, SUNY, Buffalo, New York (1989).