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Central Differnce operator in abaqus 6.11

cmksiva's picture

Dear All,

Please explain me what is central differnce operator, what is the role of central differnce played in Abaqus/Explcit analysis

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I don't understand your question. central difference method is the foundation of explicit analysis, it's nothing to do with abaqus. i suggest you to read more about explicit analysis, you should know what is explicit well first.

cmksiva's picture

My question is what's the role played by central differnce operator in dynamic explicit analysis?

Regards,
Shiva

Dear Shiva,

The role is to use the expressions

df/dt = [f(t_n+1) - f(t_n)]/h or df/dt = [f(t_n) - f(t_n-1)]/h

d^2(f)/dt = [f(t_n+1) - 2f(t_n) + f(t_n-1)]/(h^2) with h being the step size

to approximate the derivatives of a function with its differences and thus
replace a given differential equation with its difference equation. In this
manner you can turn a system of differential equations into a system of
algebraic equations in the value of function at various time steps and
therefore obtain an approximate solution. This method or variations of it are
used in commercial softwares to solve the set of governing differential
equations.

Mohsen

cmksiva's picture

Dear All,

Could anyone explain what is stable time increment in explicit, why it is used?

Regards,
Shiva

cmksiva's picture

Dear All,

Could anyone explain what is stable time increment in explicit, why it is used?

Regards,
Shiva

A stable time increment is the one that leads to the convergence of algorithm. So if the algorithm does not converge you should consider a smaller time step. If the algorithm does not converge by consecutively cutting time steps then you should expect some sort of instability in your model.

Mohsen

regarding the stability of explicit algorithms, topic is well discussed in:

Analysis of transient algorithms with particular reference to stability behavior 
HUGHES, T J R
Computational methods for transient analysis (A84-29160 12-64). Amsterdam, North-Holland, 1983, p. 67-155 

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