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- Newmark-beta_method abstract "The Newmark-beta method is a method of numerical integration used to solve differential equations. It is widely used in numerical evaluation of the dynamic response of structures and solids such as in finite element analysis to model dynamic systems. The method is named after Nathan M. Newmark, former Professor of Civil Engineering at the University of Illinois, who developed it in 1959 for use in Structural dynamics.Using the extended mean value theorem, the Newmark-β method states that the first time derivative (velocity in the equation of motion) can be solved as,wherethereforeBecause acceleration also varies with time, however, the extended mean value theorem must also be extended to the second time derivative to obtain the correct displacement. Thus,where againNewmark showed that a reasonable value of is 0.5, therefore the update rules are,Setting β to various values between 0 and 1 can give a wide range of results. Typically β = 1/4, which yields the constant average acceleration method, is used.".
- Newmark-beta_method wikiPageID "1013588".
- Newmark-beta_method wikiPageRevisionID "602561190".
- Newmark-beta_method hasPhotoCollection Newmark-beta_method.
- Newmark-beta_method subject Category:Numerical_differential_equations.
- Newmark-beta_method type Abstraction100002137.
- Newmark-beta_method type Communication100033020.
- Newmark-beta_method type DifferentialEquation106670521.
- Newmark-beta_method type Equation106669864.
- Newmark-beta_method type MathematicalStatement106732169.
- Newmark-beta_method type Message106598915.
- Newmark-beta_method type NumericalDifferentialEquations.
- Newmark-beta_method type Statement106722453.
- Newmark-beta_method comment "The Newmark-beta method is a method of numerical integration used to solve differential equations. It is widely used in numerical evaluation of the dynamic response of structures and solids such as in finite element analysis to model dynamic systems. The method is named after Nathan M.".
- Newmark-beta_method label "Méthode de Newmark".
- Newmark-beta_method label "Newmark-beta method".
- Newmark-beta_method label "Newmark-beta-Verfahren".
- Newmark-beta_method sameAs Newmark-beta-Verfahren.
- Newmark-beta_method sameAs Méthode_de_Newmark.
- Newmark-beta_method sameAs m.03z6_f.
- Newmark-beta_method sameAs Q766405.
- Newmark-beta_method sameAs Q766405.
- Newmark-beta_method sameAs Newmark-beta_method.
- Newmark-beta_method wasDerivedFrom Newmark-beta_method?oldid=602561190.
- Newmark-beta_method isPrimaryTopicOf Newmark-beta_method.