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Why Preload Parts for Explicit Dynamics Analysis, and How - Part 1

April 19, 2016 By: Steven Hale

There are many situations where you should preload parts to achieve a steady-state condition before running a transient dynamic analysis. Some examples include interference fits between parts, bolt preloads, spin loads for turbomachinery, internal pressures for pressure vessels, or gravity. Turbine engines, for example, are often analyzed with explicit dynamics solvers to determine damage to blades and other engine components caused by bird or ice strikes.  A sample model is shown in Figure 1. A preload analysis phase must be included to provide the initial conditions for the dynamic solution. The preload phase provides the steady-state stresses, strains, contact conditions, deformations, and velocities prior to impact (or other dynamic load). Without it, large oscillations in these critical values will occur because the initial conditions are suddenly applied at the beginning of the transient.

Several different methods can be used to run a preload phase for use with explicit dynamics analyses.  Unfortunately, preloading for explicit dynamics analyses is not as straightforward as preloading for implicit dynamics analyses, where a static analysis can be performed in one step followed by a simple switch to a transient analysis for subsequent steps.  There are three common preloading methods for explicit dynamics which I’ll describe below, along with their advantages and disadvantages.

1) Preload with an implicit solver:

• Use an implicit solver to solve the static preload phase.

• Stresses, strains, deformed geometry, contact status, and velocity are read as initial conditions for the explicit dynamics analysis.

• Advantages:  Typically yields the fastest solution when the preload analysis is not highly nonlinear.

• A preload solution that transfers only deformations to the explicit analysis will only be correct if the preload phase is linear and does not involve sliding contact.  In cases where the preload phase is nonlinear or contains sliding contact, the preload solution must transfer contact status, velocity, stress and strain. This is typically a problem when the implicit code is different from the explicit code. In such cases, deformations are usually the only results transferred to the explicit code. Some codes, such as LS-Dyna for example, contain implicit solvers which will transfer all required data and therefore can be used for nonlinear preload analyses.
• Consistent element formulations should be used. If not, dramatic stress spikes can occur at the beginning of the transient solution. This is typically a problem when the implicit code is different from the explicit code.  Because LS-Dyna includes an implicit solver, it can be used for the preload phase.
• The preload phase will likely have difficulty converging if the preload conditions are highly nonlinear. This is likely going to be a problem if you have complex contact conditions with significant sliding, contact with flexible bodies, or highly nonlinear material behavior.

• This method uses the explicit dynamics solver with damping to remove dynamic effects. This involves the same methodology described in my earlier blog, “How Can Explicit Solvers Help with Stubborn Nonlinear Statics Models?”. The user applies a damping value that removes dynamic effects during the preload phase which is included at the beginning of the explicit dynamics analysis.  The user then activates the initial velocities and transient loads to run the dynamic phase.

• This typically yields the fastest solution when the preload phase is highly nonlinear. This can be the best solution for preload conditions that involve complex contact with significant sliding, or highly nonlinear material models.

• It can be difficult to quickly dampen out the dynamic response. A number of runs with different damping values may be required to obtain the steady-state solution relatively quickly. An example of this is shown in Figure 2. In this case, a small block is resting on top of a larger flexible block and a gravity preload is applied. The graphs show the displacement history in the larger flexible block directly beneath the small block for different damping values. The final static solution is approximately -0.008 inches which is reached most rapidly with the ideally damped value.
• Methods for applying all dynamic loads and initial velocities after the preload phase must be available. Codes such as LS-Dyna allow for this.

3)  Preload with an explicit solver using dynamic relaxation:

• This is also a quasi-static method. However, unlike standard quasi-static methods, this uses an automated algorithm where a large amount of mass-proportional damping is applied automatically and adjusted during the solution to remove dynamic behavior. It periodically checks the kinetic energy of the system and the solution converges when this energy drops below a small percentage of the starting energy.

• Advantages:  It is typically easy to set up, requiring relatively few inputs.

• Disadvantages:  It can be very slow to converge when the solution is highly nonlinear.

Figure 2: Effect of Different Damping Values on the Displacement Directly Beneath the Small Block