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#pragma once
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#include "drake/multibody/fem/discrete_time_integrator.h"
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namespace drake {
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namespace multibody {
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namespace fem {
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namespace internal {
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/* Implements the interface DiscreteTimeIntegrator with Newmark-beta time
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integration scheme. Given the value for the next time step acceleration `a`,
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the states are calculated from states from the previous time step according to
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the following equations:
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v = vₙ + dt ⋅ (γ ⋅ a + (1−γ) ⋅ aₙ)
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q = qₙ + dt ⋅ vₙ + dt² ⋅ [β ⋅ a + (0.5−β) ⋅ aₙ].
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Note that the scheme is unconditionally unstable for gamma < 0.5 and therefore
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we require gamma >= 0.5.
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See [Newmark, 1959] for the original reference for the method.
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[Newmark, 1959] Newmark, Nathan M. "A method of computation for structural
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dynamics." Journal of the engineering mechanics division 85.3 (1959): 67-94.
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@tparam_nonsymbolic_scalar */
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template <typename T>
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class NewmarkScheme : public DiscreteTimeIntegrator<T> {
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public:
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DRAKE_NO_COPY_NO_MOVE_NO_ASSIGN(NewmarkScheme);
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~NewmarkScheme() = default;
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protected:
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NewmarkScheme() = default;
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/* Constructs a Newmark scheme with the provided timestep, `gamma` and `beta`.
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@pre dt > 0.
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@pre 0.5 <= gamma <= 1.
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@pre 0 <= beta <= 0.5. */
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NewmarkScheme(double dt, double gamma, double beta)
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: DiscreteTimeIntegrator<T>(dt), gamma_(gamma), beta_(beta) {
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DRAKE_DEMAND(0.5 <= gamma && gamma <= 1);
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DRAKE_DEMAND(0 <= beta && beta <= 0.5);
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}
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double gamma() const { return gamma_; }
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double beta() const { return beta_; }
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double gamma_{};
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double beta_{};
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};
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} // namespace internal
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} // namespace fem
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} // namespace multibody
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} // namespace drake
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