...
For well-behaved problems, we recommend using the Newmark method with
Wiki Markup |
---|
{math}beta{math} |
β = 1/4, which yields the constant average acceleration method, and for poorly converging nonlinear time-history cases, the Hilber-Hughes-Taylor (HHT) method with 0 <
Wiki Markup |
---|
{math}alpha{math} |
α ≤ -1/3. During HHT application, when
Wiki Markup |
---|
{math}alpha{math} |
α = 0, formulation is identical to the average acceleration method, so HHT will actually suffice for all problems. Note that all nodes should have mass, and rotational inertia may be added to improve dynamic response.
The Newmark method is unconditionally stable only when 2
Wiki Markup |
---|
{math}beta{math} |
...
Wiki Markup |
---|
{math}gamma{math} |
β ≥ γ ≥ 1/2, which is why we recommend using
Wiki Markup |
---|
{math}beta{math} |
β = 1/4. When
Wiki Markup |
---|
{math}beta{math} |
β = 1/6, which yields the linear acceleration method, formulation is only conditionally stable, and can become unstable when dt/T > 2√ 3/(
...
Wiki Markup |
---|
{math}pi{math} |
2π), where dt is the time step and T is the shortest structural period which is excited by loading. The shortest period may be obtained during modal analysis such that time step may be coordinated to ensure convergence.
Show if | ||
---|---|---|
| ||
Related Incidents:
|
See Also
- Mass and stiffness-proportional damping – Damping of stiff elements with inelastic softening
...