Research On High Efficient Numerical Algorithm Of The Flexible Multibody Dynamics With Large Deformation

Flexible body with large deformation is a kind of a promising structure in the field of aerospace. With high nonlinearity, both geometrically and physically, there exists strong coupling between rigid motion and flexible deformation, which forms a series of very special dynamic equations of the flexible multi-body system. When the second order ordinary differential equations show some properties like ‘stiff’ or with high frequency, it is difficult to obtain stable numerical solutions, especially for larger step size. In addition, real multi-body systems always undergo very complex external forces, of which the contact impact and friction will stimulate the high frequency response. For the on-orbit service largely flexible spacecraft structures, it is impossible to simulate the real operating status by ground experiments. Therefore, the numerical simulation is required within long term computation. Traditional numerical integrators are companied with different error accumulation and lead to abnormal energy consumption. Results at the latter stage will be unreliable. Thus, this paper is aiming at finding a suitable numerical integrator to solve problems with large deformation flexible body as well as keep long term stability.In order to perform a certain movement, the restrictive relationship is inherent in the body of the multi-body systems. This relationship could be on position or velocity. Also, it might satisfy an equation or an inequality. This paper consider the position complete constraint to research the relevant algebra features. Constraint equations together with the motion of equation form the differential-algebraic equations of the multi-body dynamics. In the differential-algebraic systems, it is no doubt that the algebraic relationship has an effect on the computation accuracy. When designing the calculation structure, the solution should follow the constraint relationship, even the difference order of this relationship.Take the one dimension slender pendulum as the research object, the large deformation continuous beam is modeled with the absolute nodal coordinate formulation. Considering position constraints, the index-3 differential-algebraic equations are solved by classical numerical damping algorithms from the structure dynamics and the geometric integrators under the Hamilton mechanics. From the node displacement, deformation, system energy error, energy transformation and time consuming, the accuracy, stability and efficiency of these two type algorithms are analyzed.During the movement, the coupling between deformation and rigid motion is likely to stimulate the high oscillation. When it carries high energy, the numerical damping strategy will cause large error. Since, the geometric integration is a symplectic mapping transformation, not only the extra damping is not involved, but also keep the geometric structure invariance of the dynamic model under phase space.Based on above analysis, the most important aspect of this thesis is to research the position-momentum St?rmer-Verlet projection integrator and apply it to the large deformation and strong coupling problems. Meanwhile, the solving condition has been extended to the low frequency large rotation and high frequency small oscillation. After long term simulation, the energy preservation and control ability of constraint drift on two order kinematics has been studied. Compared with numerical damping algorithms, this computation structure perform high efficiency as long as the stability condition is satisfied. This method will be one of the most promising algorithms in solving the large deformation problems with the combination of the absolute nodal coordinates formulation and geometric numerical integration algorithm.