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Newmark Method for Initial Value Problems
Mohammad Tawfik
#WikiCourses
http://WikiCourses.WikiSpaces.com
Newmark Method for Initial
Value Problems
Mohammad Tawfik
Newmark Method for Initial Value Problems
Mohammad Tawfik
#WikiCourses
http://WikiCourses.WikiSpaces.com
Newmark method
• In many cases, the reduction of the second
order differential equation into a set of first order
systems results in ill-conditioned system
matrix!
• In such cases, the Runge-Kutta method fails to
converge.
• Many other methods were proposed, in this
lecture we will introduce the Nemark Method
Newmark Method for Initial Value Problems
Mohammad Tawfik
#WikiCourses
http://WikiCourses.WikiSpaces.com
Newmark method
• The Newmark method handles problems
in the form of:
• Where [M] is the mass matrix, [C] is the
damping matrix, [K] is the stiffness matrix,
and {f(t)} is the generalized excitation
(force) term.
           tfxKxCxM  
Newmark Method for Initial Value Problems
Mohammad Tawfik
#WikiCourses
http://WikiCourses.WikiSpaces.com
Algorithm
1. Evaluate the acceleration of the system
using
Newmark Method for Initial Value Problems
Mohammad Tawfik
#WikiCourses
http://WikiCourses.WikiSpaces.com
2. Then the velocity and displacement may
be evaluated using
Newmark Method for Initial Value Problems
Mohammad Tawfik
#WikiCourses
http://WikiCourses.WikiSpaces.com
• In the above algorithm, δ and μ are
parameters that have to obey the
constraints

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Newmark Time Integration

  • 1. Newmark Method for Initial Value Problems Mohammad Tawfik #WikiCourses http://WikiCourses.WikiSpaces.com Newmark Method for Initial Value Problems Mohammad Tawfik
  • 2. Newmark Method for Initial Value Problems Mohammad Tawfik #WikiCourses http://WikiCourses.WikiSpaces.com Newmark method • In many cases, the reduction of the second order differential equation into a set of first order systems results in ill-conditioned system matrix! • In such cases, the Runge-Kutta method fails to converge. • Many other methods were proposed, in this lecture we will introduce the Nemark Method
  • 3. Newmark Method for Initial Value Problems Mohammad Tawfik #WikiCourses http://WikiCourses.WikiSpaces.com Newmark method • The Newmark method handles problems in the form of: • Where [M] is the mass matrix, [C] is the damping matrix, [K] is the stiffness matrix, and {f(t)} is the generalized excitation (force) term.            tfxKxCxM  
  • 4. Newmark Method for Initial Value Problems Mohammad Tawfik #WikiCourses http://WikiCourses.WikiSpaces.com Algorithm 1. Evaluate the acceleration of the system using
  • 5. Newmark Method for Initial Value Problems Mohammad Tawfik #WikiCourses http://WikiCourses.WikiSpaces.com 2. Then the velocity and displacement may be evaluated using
  • 6. Newmark Method for Initial Value Problems Mohammad Tawfik #WikiCourses http://WikiCourses.WikiSpaces.com • In the above algorithm, δ and μ are parameters that have to obey the constraints