Assessment of explicit and semi-explicit classes of model-based algorithms for direct integration in structural dynamics
Summary The ‘model‐based’ algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid simulation in earthquake engineering, an experimental method where the system response is simulated by dividing it into a physical and an analytic...
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| Veröffentlicht in: | International journal for numerical methods in engineering Jg. 107; H. 1; S. 49 - 73 |
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Bognor Regis
Blackwell Publishing Ltd
06.07.2016
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| Abstract | Summary
The ‘model‐based’ algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid simulation in earthquake engineering, an experimental method where the system response is simulated by dividing it into a physical and an analytical domain. The term ‘model‐based’ indicates that the algorithmic parameters are functions of the complete model of the system to enable unconditional stability to be achieved within the framework of an explicit formulation. These two features make the model‐based algorithms also potential candidates for computations in structural dynamics. Based on the algorithmic difference equations, these algorithms can be classified as either explicit or semi‐explicit, where the former refers to the algorithms with explicit difference equations for both displacement and velocity, while the latter for displacement only. The algorithms pertaining to each class are reviewed, and a new family of second‐order unconditionally stable parametrically dissipative semi‐explicit algorithms is presented. Numerical characteristics of these two classes of algorithms are assessed under linear and nonlinear structural behavior. Representative numerical examples are presented to complement the analytical findings. The analysis and numerical examples demonstrate the advantages and limitations of these two classes of model‐based algorithms for applications in structural dynamics. Copyright © 2015 John Wiley & Sons, Ltd. |
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| AbstractList | Summary The 'model-based' algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid simulation in earthquake engineering, an experimental method where the system response is simulated by dividing it into a physical and an analytical domain. The term 'model-based' indicates that the algorithmic parameters are functions of the complete model of the system to enable unconditional stability to be achieved within the framework of an explicit formulation. These two features make the model-based algorithms also potential candidates for computations in structural dynamics. Based on the algorithmic difference equations, these algorithms can be classified as either explicit or semi-explicit, where the former refers to the algorithms with explicit difference equations for both displacement and velocity, while the latter for displacement only. The algorithms pertaining to each class are reviewed, and a new family of second-order unconditionally stable parametrically dissipative semi-explicit algorithms is presented. Numerical characteristics of these two classes of algorithms are assessed under linear and nonlinear structural behavior. Representative numerical examples are presented to complement the analytical findings. The analysis and numerical examples demonstrate the advantages and limitations of these two classes of model-based algorithms for applications in structural dynamics. Copyright © 2015 John Wiley & Sons, Ltd. The ‘model‐based’ algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid simulation in earthquake engineering, an experimental method where the system response is simulated by dividing it into a physical and an analytical domain. The term ‘model‐based’ indicates that the algorithmic parameters are functions of the complete model of the system to enable unconditional stability to be achieved within the framework of an explicit formulation. These two features make the model‐based algorithms also potential candidates for computations in structural dynamics. Based on the algorithmic difference equations, these algorithms can be classified as either explicit or semi‐explicit , where the former refers to the algorithms with explicit difference equations for both displacement and velocity, while the latter for displacement only. The algorithms pertaining to each class are reviewed, and a new family of second‐order unconditionally stable parametrically dissipative semi‐explicit algorithms is presented. Numerical characteristics of these two classes of algorithms are assessed under linear and nonlinear structural behavior. Representative numerical examples are presented to complement the analytical findings. The analysis and numerical examples demonstrate the advantages and limitations of these two classes of model‐based algorithms for applications in structural dynamics. Copyright © 2015 John Wiley & Sons, Ltd. Summary The ‘model‐based’ algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid simulation in earthquake engineering, an experimental method where the system response is simulated by dividing it into a physical and an analytical domain. The term ‘model‐based’ indicates that the algorithmic parameters are functions of the complete model of the system to enable unconditional stability to be achieved within the framework of an explicit formulation. These two features make the model‐based algorithms also potential candidates for computations in structural dynamics. Based on the algorithmic difference equations, these algorithms can be classified as either explicit or semi‐explicit, where the former refers to the algorithms with explicit difference equations for both displacement and velocity, while the latter for displacement only. The algorithms pertaining to each class are reviewed, and a new family of second‐order unconditionally stable parametrically dissipative semi‐explicit algorithms is presented. Numerical characteristics of these two classes of algorithms are assessed under linear and nonlinear structural behavior. Representative numerical examples are presented to complement the analytical findings. The analysis and numerical examples demonstrate the advantages and limitations of these two classes of model‐based algorithms for applications in structural dynamics. Copyright © 2015 John Wiley & Sons, Ltd. The 'model-based' algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid simulation in earthquake engineering, an experimental method where the system response is simulated by dividing it into a physical and an analytical domain. The term 'model-based' indicates that the algorithmic parameters are functions of the complete model of the system to enable unconditional stability to be achieved within the framework of an explicit formulation. These two features make the model-based algorithms also potential candidates for computations in structural dynamics. Based on the algorithmic difference equations, these algorithms can be classified as either explicit or semi-explicit, where the former refers to the algorithms with explicit difference equations for both displacement and velocity, while the latter for displacement only. The algorithms pertaining to each class are reviewed, and a new family of second-order unconditionally stable parametrically dissipative semi-explicit algorithms is presented. Numerical characteristics of these two classes of algorithms are assessed under linear and nonlinear structural behavior. Representative numerical examples are presented to complement the analytical findings. The analysis and numerical examples demonstrate the advantages and limitations of these two classes of model-based algorithms for applications in structural dynamics. |
| Author | Ricles, James M. Kolay, Chinmoy |
| Author_xml | – sequence: 1 givenname: Chinmoy surname: Kolay fullname: Kolay, Chinmoy email: Correspondence to: Chinmoy Kolay, ATLSS Research Center, 117 ATLSS Drive, Bethlehem, PA 18015., chk311@lehigh.edu organization: Department of Civil and Environmental Engineering, Lehigh University, PA, 18015, Bethlehem, USA – sequence: 2 givenname: James M. surname: Ricles fullname: Ricles, James M. organization: Department of Civil and Environmental Engineering, Lehigh University, PA, 18015, Bethlehem, USA |
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| Cites_doi | 10.1016/j.engstruct.2012.08.009 10.1002/nme.4869 10.1061/JMCEA3.0000098 10.1061/(ASCE)0733-9445(2008)134:4(581) 10.1002/eqe.4290060111 10.1061/(ASCE)0733-9399(2002)128:9(935) 10.1002/eqe.4290050306 10.1002/nme.4720 10.1061/(ASCE)0733-9445(1994)120:2(441) 10.1016/S0045-7825(00)00262-0 10.1002/eqe.2484 10.1115/1.2900803 10.1007/BF01963532 10.1061/(ASCE)0733-9399(2008)134:8(676) 10.1002/eqe.838 10.1061/(ASCE)0733-9399(2007)133:5(541) 10.1002/eqe.2401 10.1002/nme.1620151011 |
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| References | Chen C, Ricles JM. Development of direct integration algorithms for structural dynamics using discrete control theory. Journal of Engineering Mechanics 2008; 134(8):676-683. Ricles J, Popov E. Inelastic link element for EBF seismic analysis. Journal of Structural Engineering-ASCE 1994; 120(2):441-463. Hilber HM, Hughes TJR, Taylor RL. Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Engineering and Structural Dynamics 1977; 5(3):283-292. Wood WL, Bossak M, Zienkiewicz OC. An alpha modification of Newmark's method. International Journal for Numerical Methods in Engineering 1980; 15(10):1562-1566. Newmark N. A method of computation for structural dynamics. Journal of the Engineering Mechanics Division-ASCE 1959; 85(3):67-94. Chung J, Hulbert GM. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. Journal of Applied Mechanics 1993; 60(2):371-375. Pegon P. Alternative characterization of time integration schemes. Computer Methods in Applied Mechanics and Engineering 2001; 190(20-21):2707-2727. Chang S. A family of noniterative integration methods with desired numerical dissipation. International Journal for Numerical Methods in Engineering 2014; 100(1):62-86. Chang SY. An explicit structure-dependent algorithm for pseudodynamic testing. Engineering Structures 2013; 46:511-525. Hilber HM, Hughes TJR. Collocation, dissipation and [overshoot] for time integration schemes in structural dynamics. Earthquake Engineering and Structural Dynamics 1978; 6(1):99-117. Dahlquist G. A special stability problem for linear multistep methods. BIT Numerical Mathematics 1963; 3(1):27-43. Großeholz G, Soares JD, Estorff O. A stabilized central difference scheme for dynamic analysis. International Journal for Numerical Methods in Engineering 2015; 102(11):1750-1760. Chopra AK. Dynamics of Structures (4edn.) Prentice Hall: Upper Saddle River, New Jersey 07458, 2011. Charney FA. Unintended consequences of modeling damping in structures. Journal of Structural Engineering 2008; 134(4):581-592. Richtmyer RD, Morton K. Difference Methods for Initial-value Problems (2edn.) Krieger Pub Co: Malabar, Florida, 1994. Franklin GF, Powell JD, Emami-Naeini A. Feedback Control of Dynamic Systems (6edn.) Prentice Hall: Upper Saddle River, New Jersey, 2009. Enhanced CSY, Stable U. Explicit pseudodynamic algorithm. Journal of Engineering Mechanics 2007; 133(5):541-554. Chang SY. Explicit pseudodynamic algorithm with unconditional stability. Journal of Engineering Mechanics 2002; 128(9):935-947. Chen C, Ricles JM, Marullo T, Mercan O. Real-time hybrid testing using the unconditionally stable explicit CR integration algorithm. Earthquake Engineering and Structural Dynamics 2009; 38(1):23-44. Kolay C, Ricles JM, Marullo TM, Mahvashmohammadi A, Sause R. Implementation and application of the unconditionally stable explicit parametrically dissipative KR-α method for real-time hybrid simulation. Earthquake Engineering and Structural Dynamics 2015; 44(5):735-755. Kolay C, Ricles JM. Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation. Earthquake Engineering and Structural Dynamics 2014; 43(9):1361-1380. 1959; 85 1980; 15 2011 2001; 190 1993; 60 2013; 46 2015; 102 2007; 133 1994; 120 2015; 44 1963; 3 2002; 128 1976 2009 1994 2008; 134 2014; 100 2009; 38 1968 1977; 5 2014; 43 1978; 6 e_1_2_11_10_1 e_1_2_11_21_1 e_1_2_11_14_1 e_1_2_11_13_1 Franklin GF (e_1_2_11_19_1) 2009 e_1_2_11_24_1 e_1_2_11_9_1 e_1_2_11_12_1 e_1_2_11_23_1 e_1_2_11_8_1 e_1_2_11_11_1 e_1_2_11_22_1 e_1_2_11_7_1 e_1_2_11_18_1 e_1_2_11_6_1 Newmark N (e_1_2_11_2_1) 1959; 85 e_1_2_11_5_1 e_1_2_11_16_1 e_1_2_11_4_1 e_1_2_11_15_1 e_1_2_11_3_1 Richtmyer RD (e_1_2_11_17_1) 1994 Chopra AK (e_1_2_11_20_1) 2011 |
| References_xml | – reference: Enhanced CSY, Stable U. Explicit pseudodynamic algorithm. Journal of Engineering Mechanics 2007; 133(5):541-554. – reference: Dahlquist G. A special stability problem for linear multistep methods. BIT Numerical Mathematics 1963; 3(1):27-43. – reference: Hilber HM, Hughes TJR. Collocation, dissipation and [overshoot] for time integration schemes in structural dynamics. Earthquake Engineering and Structural Dynamics 1978; 6(1):99-117. – reference: Charney FA. Unintended consequences of modeling damping in structures. Journal of Structural Engineering 2008; 134(4):581-592. – reference: Ricles J, Popov E. Inelastic link element for EBF seismic analysis. Journal of Structural Engineering-ASCE 1994; 120(2):441-463. – reference: Kolay C, Ricles JM. Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation. Earthquake Engineering and Structural Dynamics 2014; 43(9):1361-1380. – reference: Franklin GF, Powell JD, Emami-Naeini A. Feedback Control of Dynamic Systems (6edn.) Prentice Hall: Upper Saddle River, New Jersey, 2009. – reference: Chang S. A family of noniterative integration methods with desired numerical dissipation. International Journal for Numerical Methods in Engineering 2014; 100(1):62-86. – reference: Chen C, Ricles JM. Development of direct integration algorithms for structural dynamics using discrete control theory. Journal of Engineering Mechanics 2008; 134(8):676-683. – reference: Chang SY. An explicit structure-dependent algorithm for pseudodynamic testing. Engineering Structures 2013; 46:511-525. – reference: Pegon P. Alternative characterization of time integration schemes. Computer Methods in Applied Mechanics and Engineering 2001; 190(20-21):2707-2727. – reference: Newmark N. A method of computation for structural dynamics. Journal of the Engineering Mechanics Division-ASCE 1959; 85(3):67-94. – reference: Wood WL, Bossak M, Zienkiewicz OC. An alpha modification of Newmark's method. International Journal for Numerical Methods in Engineering 1980; 15(10):1562-1566. – reference: Richtmyer RD, Morton K. Difference Methods for Initial-value Problems (2edn.) Krieger Pub Co: Malabar, Florida, 1994. – reference: Chen C, Ricles JM, Marullo T, Mercan O. Real-time hybrid testing using the unconditionally stable explicit CR integration algorithm. Earthquake Engineering and Structural Dynamics 2009; 38(1):23-44. – reference: Großeholz G, Soares JD, Estorff O. A stabilized central difference scheme for dynamic analysis. International Journal for Numerical Methods in Engineering 2015; 102(11):1750-1760. – reference: Hilber HM, Hughes TJR, Taylor RL. Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Engineering and Structural Dynamics 1977; 5(3):283-292. – reference: Kolay C, Ricles JM, Marullo TM, Mahvashmohammadi A, Sause R. Implementation and application of the unconditionally stable explicit parametrically dissipative KR-α method for real-time hybrid simulation. Earthquake Engineering and Structural Dynamics 2015; 44(5):735-755. – reference: Chung J, Hulbert GM. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. Journal of Applied Mechanics 1993; 60(2):371-375. – reference: Chopra AK. Dynamics of Structures (4edn.) Prentice Hall: Upper Saddle River, New Jersey 07458, 2011. – reference: Chang SY. Explicit pseudodynamic algorithm with unconditional stability. Journal of Engineering Mechanics 2002; 128(9):935-947. – year: 2011 – year: 2009 – volume: 134 start-page: 581 issue: 4 year: 2008 end-page: 592 article-title: Unintended consequences of modeling damping in structures publication-title: Journal of Structural Engineering – volume: 38 start-page: 23 issue: 1 year: 2009 end-page: 44 article-title: Real‐time hybrid testing using the unconditionally stable explicit CR integration algorithm publication-title: Earthquake Engineering and Structural Dynamics – volume: 60 start-page: 371 issue: 2 year: 1993 end-page: 375 article-title: A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized‐ method publication-title: Journal of Applied Mechanics – volume: 190 start-page: 2707 issue: 20‐21 year: 2001 end-page: 2727 article-title: Alternative characterization of time integration schemes publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 134 start-page: 676 issue: 8 year: 2008 end-page: 683 article-title: Development of direct integration algorithms for structural dynamics using discrete control theory publication-title: Journal of Engineering Mechanics – volume: 102 start-page: 1750 issue: 11 year: 2015 end-page: 1760 article-title: A stabilized central difference scheme for dynamic analysis publication-title: International Journal for Numerical Methods in Engineering – volume: 5 start-page: 283 issue: 3 year: 1977 end-page: 292 article-title: Improved numerical dissipation for time integration algorithms in structural dynamics publication-title: Earthquake Engineering and Structural Dynamics – volume: 120 start-page: 441 issue: 2 year: 1994 end-page: 463 article-title: Inelastic link element for EBF seismic analysis publication-title: Journal of Structural Engineering‐ASCE – volume: 128 start-page: 935 issue: 9 year: 2002 end-page: 947 article-title: Explicit pseudodynamic algorithm with unconditional stability publication-title: Journal of Engineering Mechanics – year: 1968 – volume: 46 start-page: 511 year: 2013 end-page: 525 article-title: An explicit structure‐dependent algorithm for pseudodynamic testing publication-title: Engineering Structures – volume: 44 start-page: 735 issue: 5 year: 2015 end-page: 755 article-title: Implementation and application of the unconditionally stable explicit parametrically dissipative KR‐ method for real‐time hybrid simulation publication-title: Earthquake Engineering and Structural Dynamics – volume: 85 start-page: 67 issue: 3 year: 1959 end-page: 94 article-title: A method of computation for structural dynamics publication-title: Journal of the Engineering Mechanics Division‐ASCE – volume: 100 start-page: 62 issue: 1 year: 2014 end-page: 86 article-title: A family of noniterative integration methods with desired numerical dissipation publication-title: International Journal for Numerical Methods in Engineering – volume: 133 start-page: 541 issue: 5 year: 2007 end-page: 554 article-title: Explicit pseudodynamic algorithm publication-title: Journal of Engineering Mechanics – volume: 6 start-page: 99 issue: 1 year: 1978 end-page: 117 article-title: Collocation, dissipation and [overshoot] for time integration schemes in structural dynamics publication-title: Earthquake Engineering and Structural Dynamics – volume: 15 start-page: 1562 issue: 10 year: 1980 end-page: 1566 article-title: An alpha modification of Newmark's method publication-title: International Journal for Numerical Methods in Engineering – volume: 43 start-page: 1361 issue: 9 year: 2014 end-page: 1380 article-title: Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation publication-title: Earthquake Engineering and Structural Dynamics – volume: 3 start-page: 27 issue: 1 year: 1963 end-page: 43 article-title: A special stability problem for linear multistep methods publication-title: BIT Numerical Mathematics – 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The ‘model‐based’ algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid... The ‘model‐based’ algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid simulation in... Summary The 'model-based' algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid... The 'model-based' algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid simulation in... |
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| SubjectTerms | Algorithms Computer simulation Difference equations direct integration algorithm dynamic analysis Dynamic structural analysis Dynamical systems Dynamics explicit Mathematical analysis Mathematical models numerical damping unconditional stability |
| Title | Assessment of explicit and semi-explicit classes of model-based algorithms for direct integration in structural dynamics |
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