3D-Dynamics of Elastic-Plastic Robots

Multi-body dynamic systems (MBD-systems) consist of an ensemble of material bodies and connecting elements, like hinges and viscoelastic springs and dampers. MBD dynamic systems find a wide range of practical applications in engineering, from robotics to earthquake excited historical monuments. Originally, the single bodies have been assumed to be rigid in the literature. In order to consider flexible members, an increasing amount of work has been devoted to the development of computational tools for elastic MBD systems, with the single bodies assumed to be elastic. As a next step, in a previous project performed within the framework of the FWF-SFB 013 (Subproject F1311: Dynamics of Elasto-Plastic Multi-Body Systems), our group has developed computational methods for simulating the motion of elastic-plastic MBD systems. In this preliminary work, special emphasis has been laid upon plastic and damaged zones produced in the members of the MBD system by a severe loading. The formulations developed in this previous project however have been restricted to beam type members and to plane motions. It is the scope of the present project to extend these preliminary studies to more complex geometrical shapes of the elastic-plastic members, and to three-dimensional (3D) motions of the system. Special emphasis will be given to the modeling and simulation of advanced systems of robotics under critical operating conditions, such as impacts, collisions or weakening of strength due to environmental circumstances. In the case of a three-dimensional motion, the dynamic equations of the robot are intended to be formulated in their most efficient form, in order to give place for the time-consuming computation of plastic strain and damage. Here, the experience of the second project leader Professor Bremer concerning the equations of motion of multi-body systems shall be brought together with the experience of Professor Irschik concerning elastic-plastic vibrations. For the sake of including more complex shapes of the system members, our previous formulation will be extended from a one-dimensional beam type approximation towards the 3D theory of dynamic plasticity, where advanced inelastic constitutive relations shall be introduced. In that respect, the system members will be modeled by means of the finite element method. The necessary polynomial order of the elastic-plastic finite elements will be derived, and previous experience of the proposed project co-worker J. Gerstmayr concerning mesh generation and solving 3D-field problems by finite elements will be utilized. Application in practice furthermore requires to implement a catalogue of more complicated types of links and interconnecting hinges. This quite naturally leads to the requirement of including a second type of constitutive non-linearity, namely friction in the hinges, which may be of considerable influence upon the motion. The 3D-MBD system including elastic-plastic finite elements will eventually be described by a differential-algebraic system of equations, the numerical solution of which will be performed on the basis and in extension of the experience gained in the previous work. As an important aim from the computational point of view, the solution will be derived in the framework of an adaptive formulation, where the spatial distributions of the plastic strains and damage will be adaptively controlled by the local error of the approximated plastic strains. Visualization of the three-dimensional motion of realistic robotic systems, and especially of the plastic and damaged zones developing in the system members, will be a further topic of the project.

The present project was concerned with the modelling and simulation of advanced multibody dynamic systems under critical operating conditions, produced e.g. by impacts, collisions or weakening of strength due to possibly catastrophic environmental circumstances. Multibody dynamic systems - that are dynamic systems consisting of bodies which are linked with joints and driven by actuators - find a wide range of practical applications in engineering, particularly in industrial robotics, vehicle dynamics, aero- and astrospace, but also in various other fields, ranging from colliding automotive systems to earthquake excited historical monuments. It shall be emphasized that a possible application, which has even not been thought of at the beginning of the project, are very robust robots which can be used not only in industry but also for maintenance of civil infrastructure. Robotic systems also have already entered everyday life, at least since the development of cheap toy-robots, which are nowadays available at every department store. It was the scope of the project to formulate and solve the non-linear dynamic equations of motion of such multibody dynamic systems under critical operating conditions in a form that is efficient enough to give place for the time-consuming computation of plastic strain and damage in the 3D case. The computational methods developed in a previous project for simulating the motion of elasto-plastic multi-body systems were extended to more complex geometrical shapes of elasto-plastic members and to three-dimensional motions of the system. In a first step two-dimensional mechanisms have been studied and an optimised version of elasto-plastic multibody systems with adaptive discretization of plastic cells has been developed. In order to reach the main goals of the project, highly efficient time integration methods have been continuously investigated besides the direct study of multibody dynamics. The scientific results published in the project concern various successful solutions techniques. It is to be emphasized that their general topic, 3D elasto-plastic deformations of multibody systems, found an increasing international audience in the course of the project. Among other themes, the fundamental results obtained in the project dealt with the development of adaptive methods and plastic multiplier methods, improvements of the absolute nodal coordinate formulations using reduced strain formulations, inclusion of hydraulic actuators, studies on the influence of geometric stiffening, contact problems and more complicated types of interconnecting links, the successful implementation of higher order implicit Runge-Kutta Methods in the context of multibody dynamic systems suffering plasticity and damage, etc.