Dynamic Optimization Of Flexible Multibody Systems

Flexible multibody system(FMBS)is a kind of mechanical system composed of many flexible components and kinematic pairs,such as flexible robot arms,helicopter rotors,deployable antennas of a satellite and solar sail spacecrafts.Recently,with the development of the space technology,more and more variable-length flexible components have been used in the deployable space structures,including variable-length cables,plates,shells,membranes as well as variable-length solid structures.New challenges,hence,arise to establish an accurate dynamic model of an FMBS with variable-length bodies,as well as for the dynamic design of such an FMBS.Traditionally,trial-and-error method is used for the design of the flexible components in an FMBS.The method,however,is very time-consuming and cannot guarantee the best design.The flexible component in an FMBS is usually optimized based on a component-based approach without considering the interactions between the optimized component and its environment of the system.The static loads for the static response optimization are usually defined by the experience of the designers.Such an optimization design process,only suitable for stiff multibody systems,cannot optimize the flexible components in an FMBS undergoing both large overall motion and large deformation.This is due to the fact that when the component gets more and more flexible,the interactions between the component and the FMBS cannot be disregarded when performing optimization.The component-based structural optimization,therefore,should be extended to the FMBS-based structural optimization for both the aerospace field and the mechanical field.This thesis focuses on the dynamic model of an FMBS with variable-length bodies and the dynamic response and dynamic characteristics optimization of an FMBS described via the absolute nodal coordinate formulation(ANCF).The main contributions of the thesis are summarized as follows:(1)A fully coupled optimization method and a weakly coupled optimization method for the dynamic response optimization of an FMBS are proposed.In the fully coupled optimization method,the dynamic equation of an FMBS is integrated into the optimization equation.The solution of the dynamic equation,the sensitivity analysis and the solution of the fully coupled optimization equation are also presented.In the weakly coupled optimization method,the equivalent static loads(ESL)vector of a flexible component in an FMBS described via the ANCF is defined and analyzed.By using the ESL,the dynamic response optimization of an FMBS can be transformed into the static response optimization of a flexible component.The whole optimization process performs the dynamic analysis of an FMBS and the static response optimization with the ESL repeatedly until the convergence criterion is satisfied.(2)A level set-based topology optimization method of the flexible components in a 2D FMBS and a moving morphable components(MMC)-based topology optimization method of the flexible components in a 3D FMBS are proposed.The objective is to minimize the dynamic compliance(or strain energy)of a flexible component with a given amount of material distributed in a prescribed design domain.For the topology optimization of a 2D FMBS,the level set function is used to implicitly describe the topology of a component.The Hamilton–Jacobi partial differential equation is solved via a semi-implicit additive operator splitting scheme.For the topology optimization of a 3D FMBS,to overcome the so-called “curse of dimensionality” associated with conventional density-based and level set-based topology optimization methods,MMC are used to explicitly describe the topology of a component.(3)The dynamic model of an FMBS with variable-length bodies is studied via the arbitrary Lagrangian–Eulerian(ALE)description and the ANCF.The variable-length reduced beam element and variable-length thin plate element of ALE–ANCF are derived.A new axially variable-length solid elelment of ALE–ANCF is proposed.The vectors of the elastic forces and the additional inertial forces,as well as their Jacobian formulations,of the three variable-length elements are also given.In order to avoid excessively long and excessively short lengths of the boundary elements,a method for appropriately inserting and deleting nodes is proposed.(4)The topology optimization of the variable-length components in an FMBS is studied via the ALE–ANCF modeling scheme.An MMC-based topology optimization method of the variable-length components in an FMBS is proposed.In this method,by introducing the concept of virtual design domain,the ESL vector of a variable-length component in an FMBS is defined and analyzed.For the topology optimization of a variable-length components in a 3D FMBS,a new simultaneous topology and size optimization method is proposed.By using this method,a3 D variable-length component can be explicitly and efficiently designed either as a nonperiodic structure or as a periodic structure,including a homogeneous periodic structure and a heterogeneous periodic structure.(5)For the dynamic characteristics optimization of an FMBS,a new explicit and efficient MMC-based topology optimization method for eigenfrequencies is proposed.Two objectives for optimizing a rotating rectangular thin plate are considered,i.e.,maximizing either the first eigenfrequency or the gap between two consecutive eigenfrequencies.During the optimization,in order to remove the localized modes in the low-density areas,the mass and stiffness matrices of the thin plate elements of ANCF are carefully penalized.The sensitivities of a simple eigenfrequency and multiply repeated eigenfrequencies with respect to a design variable are analytically derived.