Transient Analysis for MBD

Transient analysis is used to calculate the response of a multi-body system to time-dependent loads and motions.

Forces and motions are time-dependent. Body initial conditions define the initial body velocities, while joint initial conditions define the initial displacement of a particular joint.

The results of a transient analysis are displacements, velocities, accelerations, forces, as well as modal contributions to stresses and strains in flexible bodies. The responses are usually time-dependent.

The equation of motion is given in the following form:

The matrix M is the mass matrix, the vector f is the vector of external forces, and the vector u represents the generalized coordinates. Stiffness, damping, constraint forces, external loads, and gravity are all included in the external force vector f. An initial and maximum integration time step, an end time, and integrator tolerance need to be defined.

Two analyses, kinematic and dynamic, are defined depending on the degree of freedom of the system analysis.

A kinematic simulation is performed if all degrees of freedom are constrained through appropriate joints and/or motions, making it a zero degree of freedom model. A kinematics simulation finds a system configuration that satisfies all kinematic constraints and motion equations at any given time. The configuration is obtained by solving a system of nonlinear algebraic equations representing constraints.

During a kinematic simulation, there is no need to integrate the differential equations of motion because the system configuration is fully determined by solving the constraint and motion equations alone. Even though forces are not used to compute the kinematics solution, joint reaction forces can be computed at any given time. The mass and inertia properties of bodies involved, and external forces acting on them, do not affect the resultant system configuration, but they do affect the joint reaction forces requested as outputs.

A dynamic simulation is employed whenever the model has one or more degrees of freedom. A dynamic simulation involves integrating the differential equations of motion subject to nonlinear algebraic equations representing kinematics constraints. In other words, the solution is obtained by solving a mixed system of differential-algebraic equations.

The resultant solution takes into account various dynamic effects and is dependent upon mass and inertia properties of bodies, damping within the system, and applied forces and motions. Additional simulation parameters, such as the integration scheme, integration time step, convergence tolerance, etc. could also affect the solution and; therefore, need to be specified appropriately.

If a simulation type of transient is requested, the solver automatically determines whether to run a kinematic or dynamic solution from the degree of freedom.

The equation of motion is solved using one of the three different integrators that are available. The choice is based on the stiffness of the problem. A problem is stiff if the numerical solution has its step size limited more severely by the stability of the numerical technique than by the accuracy of the technique. These are systems with high damping and low transience.

•	VSTIFF (Default) – Implicit integrator that utilizes the Variable Coefficient Differential Equation Solver (VODE). It is suited for stiff and non-stiff problems.

•	MSTIFF – Implicit integrator that utilizes the Modified Extended Backward Differentiation Formula (MEBDF) to solve the nonlinear equations of motion. It is suited for stiff problems.

•	ABAM (Adams-Bashforth-Adams-Moulton) – Explicit integrator that uses a finite differences scheme to solve the nonlinear equations of motion. This integrator is suitable for systems that are non-stiff.

A multi-body subcase needs to be defined in the input deck. Only one such subcase can be used in a model. The simulation type "transient" is defined on an MBSIM bulk data entry which must be referenced through a subcase statement MBSIM. The MBSIM bulk data entity also defines the integrator, end time, and time step. A sequence of several simulations of different types can be defined by referring to an MBSEQ bulk data statement instead. Loads and motions are referenced on MLOAD and MOTION subcase entries, respectively. Initial velocity is referenced through INVEL. SPC type constraints in Multi-body Dynamics analysis are allowed only for MBD-ESL optimization of a flexible body if displacements are used as constraints. Further information on loads and boundary conditions can be obtained from the sections Applied Forces and Motions and Initial Velocity.

The unit system for the simulation can be defined using a DTI, UNITS bulk data entry.