Details
| Original language | English |
|---|---|
| Pages (from-to) | 114-145 |
| Number of pages | 32 |
| Journal | Journal of engineering mechanics |
| Volume | 139 |
| Issue number | 2 |
| Publication status | Published - 17 Mar 2012 |
Abstract
Time integration is the most versatile tool for analyzing semidiscretized equations of motion. The responses are approximations, with deviations from the exact responses mainly depending on the integration method and the integration step sizes. When repeating the analyses with smaller steps, the responses generally converge to the exact responses. However, the convergence trends are different in linear and nonlinear analyses.Whereas in linear analyses, by decreasing the sizes of integration steps, the errors decrease with a rate, depending on the orders of accuracy, in nonlinear analyses, the change in errors might be unpredictable. The main reason is the inconsistency between the integration steps sizes and the residuals of nonlinearity iterations. In this paper, based on careful selection of nonlinearity tolerances, a methodology and a method to overcome this inconsistency for semidiscretized systems with piecewise linear behavior are introduced. When the responses converge, except for systems with very complex behaviors, the proposed method leads to proper convergence, with tolerable computational costs. In addition, by implementing the proposed method, more reliable error estimations can be expected from convergence-based accuracy controlling methods.
Keywords
- Accuracy-controlling methods, Nonlinearity residual, Nonlinearity tolerance, Order of accuracy, Piecewise linear, Proper convergence, Pseudoerror, Space of nonlinearity, Time integration, Time step
ASJC Scopus subject areas
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
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In: Journal of engineering mechanics, Vol. 139, No. 2, 17.03.2012, p. 114-145.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Practical Integration of Semidiscretized Nonlinear Equations of Motion
T2 - Proper Convergence for Systems with Piecewise Linear Behavior
AU - Soroushian, Aram
AU - Wriggers, Peter
AU - Farjoodi, Jamshid
PY - 2012/3/17
Y1 - 2012/3/17
N2 - Time integration is the most versatile tool for analyzing semidiscretized equations of motion. The responses are approximations, with deviations from the exact responses mainly depending on the integration method and the integration step sizes. When repeating the analyses with smaller steps, the responses generally converge to the exact responses. However, the convergence trends are different in linear and nonlinear analyses.Whereas in linear analyses, by decreasing the sizes of integration steps, the errors decrease with a rate, depending on the orders of accuracy, in nonlinear analyses, the change in errors might be unpredictable. The main reason is the inconsistency between the integration steps sizes and the residuals of nonlinearity iterations. In this paper, based on careful selection of nonlinearity tolerances, a methodology and a method to overcome this inconsistency for semidiscretized systems with piecewise linear behavior are introduced. When the responses converge, except for systems with very complex behaviors, the proposed method leads to proper convergence, with tolerable computational costs. In addition, by implementing the proposed method, more reliable error estimations can be expected from convergence-based accuracy controlling methods.
AB - Time integration is the most versatile tool for analyzing semidiscretized equations of motion. The responses are approximations, with deviations from the exact responses mainly depending on the integration method and the integration step sizes. When repeating the analyses with smaller steps, the responses generally converge to the exact responses. However, the convergence trends are different in linear and nonlinear analyses.Whereas in linear analyses, by decreasing the sizes of integration steps, the errors decrease with a rate, depending on the orders of accuracy, in nonlinear analyses, the change in errors might be unpredictable. The main reason is the inconsistency between the integration steps sizes and the residuals of nonlinearity iterations. In this paper, based on careful selection of nonlinearity tolerances, a methodology and a method to overcome this inconsistency for semidiscretized systems with piecewise linear behavior are introduced. When the responses converge, except for systems with very complex behaviors, the proposed method leads to proper convergence, with tolerable computational costs. In addition, by implementing the proposed method, more reliable error estimations can be expected from convergence-based accuracy controlling methods.
KW - Accuracy-controlling methods
KW - Nonlinearity residual
KW - Nonlinearity tolerance
KW - Order of accuracy
KW - Piecewise linear
KW - Proper convergence
KW - Pseudoerror
KW - Space of nonlinearity
KW - Time integration
KW - Time step
UR - http://www.scopus.com/inward/record.url?scp=84879533845&partnerID=8YFLogxK
U2 - 10.1061/(ASCE)EM.1943-7889.0000434
DO - 10.1061/(ASCE)EM.1943-7889.0000434
M3 - Article
AN - SCOPUS:84879533845
VL - 139
SP - 114
EP - 145
JO - Journal of engineering mechanics
JF - Journal of engineering mechanics
SN - 0733-9399
IS - 2
ER -