Nonlinear transient response and its sensitivity using finite elements in time (Q1912033)
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scientific article; zbMATH DE number 873787
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlinear transient response and its sensitivity using finite elements in time |
scientific article; zbMATH DE number 873787 |
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Nonlinear transient response and its sensitivity using finite elements in time (English)
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10 June 1996
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The bilinear formulation proposed earlier by \textit{D. A. Peters} and \textit{A. P. Izadpanah} [ibid. 3, No. 2, 73-88 (1988; Zbl 0627.73081)] to develop finite elements in time to solve undamped linear systems, is extended (and found to be readily amenable) to develop time finite elements to obtain transient responses of both linear and nonlinear, and damped and undamped systems. The formulation is used in the \(h\)-, \(p\)- and \(hp\)-versions. The resulting linear and nonlinear algebraic equations are differentiated to obtain the sensitivity of the transient response with respect to various design parameters.
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Legendre polynomials
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basis functions
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integrated Legendre polynomials
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\(h\)-version
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\(p\)-version
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\(hp\)-version
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bilinear formulation
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design parameters
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0.89785886
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0.8902936
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0.88247204
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0.8799619
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0.86834246
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0.86733234
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0.8595115
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0.85817236
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