Contact dynamics of elasto-plastic thin beams simulated via absolute nodal coordinate formulation

Under the frame of multibody dynamics, the contact dynamics of elasto-plastic spatial thin beams is numerically studied by using the spatial thin beam elements of absolute nodal coordinate formulation（ANCF）. The internal force of the elasto-plastic spatial thin beam element is derived under the assumption that the plastic strain of the beam element depends only on its longitudinal deformation.A new body-fixed local coordinate system is introduced into the spatial thin beam element of ANCF for efficient contact detection in the contact dynamics simulation. The linear isotropic hardening constitutive law is used to describe the elasto-plastic deformation of beam material, and the classical return mapping algorithm is adopted to evaluate the plastic strains. A multi-zone contact approach of thin beams previously proposed by the authors is also introduced to detect the multiple contact zones of beams accurately, and the penalty method is used to compute the normal contact force of thin beams in contact. Four numerical examples are given to demonstrate the applicability and effectiveness of the proposed elasto-plastic spatial thin beam element of ANCF for flexible multibody system dynamics.

A NEW DETERMINISTIC FORMULATION FOR DYNAMIC STOCHASTIC PROGRAMMING PROBLEMS AND ITS NUMERICAL COMPARISON WITH OTHERS

A new deterministic formulation,called the conditional expectation formulation,is proposed for dynamic stochastic programming problems in order to overcome some disadvantages of existing deterministic formulations.We then check the impact of the new deterministic formulation and other two deterministic formulations on the corresponding problem size,nonzero elements and solution time by solving some typical dynamic stochastic programming problems with different interior point algorithms.Numerical results show the advantage and application of the new deterministic formulation.

Dynamic Phase Field Description on Ductile Fracture Process

In comparison to discrete descriptions of fracture process,the recently proposed phase field methodology averts the numerical tracking strategy of discontinuities in solids,which enables the numerical implement simplification.An implicit finite element formulation based on the diffuse phase field is extended for stable and efficient analysis of complex dynamic fracture process in ductile solids.This exhibited formulation is shown to capture entire range of the characteristics of ductile material presenting J2-plasticity,embracing plasticization,cracks initiation,propagation,branching and merging while fulfilling the basic principle of thermodynamics.Herein,we implement a staggered time integration scheme of the dynamic elasto-plastic phase field method into the commercial finite element code.The numerical performance of the present advanced phase field model has been examined through several classic dynamic fracture benchmarks,and in all cases simulation results are in good agreement with the associated experimental data and other numerical results in previous literature.

Computational dynamics of soft machines

Soft machine refers to a kind of mechanical system made of soft materials to complete sophisticated missions, such as handling a fragile object and crawling along a narrow tunnel corner, under low cost control and actuation. Hence, soft machines have raised great challenges to computational dynamics. In this review article, recent studies of the authors on the dynamic modeling, numerical simulation, and experimental validation of soft machines are summarized in the framework of multibody system dynamics. The dynamic modeling approaches are presented first for the geometric nonlinearities of coupled overall motions and large deformations of a soft component, the physical nonlinearities of a soft component made of hyperelastic or elastoplastic materials, and the frictional contacts/impacts of soft components, respectively. Then the computation approach is outlined for the dynamic simulation of soft machines governed by a set of differential-algebraic equations of very high dimensions, with an emphasis on the efficient computations of the nonlinear elastic force vector of finite elements. The validations of the proposed approaches are given via three case studies, including the locomotion of a soft quadrupedal robot, the spinning deployment of a solar sail of a spacecraft, and the deployment of a mesh reflector of a satellite antenna, as well as the corresponding experimental studies. Finally, some remarks are made for future studies.

A New Flexible Multibody Dynamics Analysis Methodology of Deployable Structures with Scissor-Like Elements

There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equations,a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements(SLEs)is presented.Firstly,a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation(ANCF),and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations.Secondly,according to features of deployable structures,the specification matrix method(SMM)is proposed to eliminate the constraint equations among SLEs in the frame of ANCF.With this method,the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently,especially on condition that there are vast nodal coordinates.So the element characteristic matrices can be added end to end circularly.Thus,the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation.Next,a new iteration procedure for the generalized-a algorithm is presented to solve the ordinary differential equations(ODEs)of deployable structure.Finally,the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements.The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure.The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.

An improved dynamic model for a silicone material beam with large deformation

Dynamic modeling for incompressible hyperelastic materials with large deformation is an important issue in biomimetic applications. The previously proposed lower-order fully parameterized absolute nodal coordinate formulation（ANCF） beam element employs cubic interpolation in the longitudinal direction and linear interpolation in the transverse direction, whereas it cannot accurately describe the large bending deformation. On this account, a novel modeling method for studying the dynamic behavior of nonlinear materials is proposed in this paper. In this formulation, a higher-order beam element characterized by quadratic interpolation in the transverse directions is used in this investigation. Based on the Yeoh model and volumetric energy penalty function, the nonlinear elastic force matrices are derived within the ANCF framework. The feasibility and availability of the Yeoh model are verified through static experiment of nonlinear incompressible materials. Furthermore,dynamic simulation of a silicone cantilever beam under the gravity force is implemented to validate the superiority of the higher-order beam element. The simulation results obtained based on the Yeoh model by employing three different ANCF beam elements are compared with the result achieved from a commercial finite element package as the reference result. It is found that the results acquired utilizing a higher-order beam element are in good agreement with the reference results,while the results obtained using a lower-order beam element are different from the reference results. In addition, the stiffening problem caused by volumetric locking can be resolved effectively by applying a higher-order beam element. It is concluded that the proposed higher-order beam element formulation has satisfying accuracy in simulating dynamic motion process of the silicone beam.

Axially variable-length solid element of absolute nodal coordinate formulation

An axially variable-length solid element with eight nodes is proposed by integrating the arbitrary Lagrangian-Eulerian (ALE) formulation and the absolute nodal coordinate formulation (ANCF). In addition to the nodal positions and slopes of eight nodes, two material coordinates in the axial direction are used as the generalized coordinates. As a consequence, the nodes in the ALE-ANCF are not associated with any specific material points and the axial length of the solid element can be varied over time. These two material coordinates give rise to a variable mass matrix and an additional inertial force vector. Computationally efficient formulae of the additional inertial forces and elastic forces, as well as their Jacobians, are also derived. The dynamic equation of a flexible multibody system (FMBS) with variable-length bodies is presented. The maximum and minimum lengths of the boundary elements of an FMBS have to be appropriately defined to ensure accuracy and non-singularity when solving the dynamic equation. Three numerical examples of static and dynamic problems are given to validate the variable-length solid elements of ALE-ANCF and show their capability.

Accurate real-time truck simulation via semirecursive formulation and Adams-Bashforth-Moulton algorithm

In this paper, a tailored four-step Adams-Bashforth-Moulton (ABM) algorithm is applied to a semirecursive formulation to perform a real-time simulation of a semitrailer truck. In the ABM algorithm, each integration step involves two function evaluations, namely predictor and corrector. This is fundamentally different when compared to the classic fourth-order Runge-Kutta (RK) integrator approach that contains four function evaluations. A semitrailer truck under investigation is modeled in term of a semirecursive method and simulated by using the presented ABM algorithm. The results show that the four-step ABM method can reduce CPU time almost 50% for solving the truck dynamics with very similar accuracy, in comparison to the fourth-order RK method. The presented ABM algorithm could be used in the semirecursive formulation to carry out accurate real-time simulation of medium-large vehicle systems.

Integrated computer-aided formulation design:A case study of andrographolide/cyclodextrin ternary formulation

Current formulation development strongly relies on trial-and-error experiments in the laboratory by pharmaceutical scientists,which is time-consuming,high cost and waste materials.This research aims to integrate various computational tools,including machine learning,molecular dynamic simulation and physiologically based absorption modeling(PBAM),to enhance andrographolide(AG)/cyclodextrins(CDs)formulation design.The light GBM prediction model we built before was utilized to predict AG/CDs inclusion's binding free energy.AG/γ-CD inclusion complexes showed the strongest binding affinity,which was experimentally validated by the phase solubility study.The molecular dynamic simulation was used to investigate the inclusion mechanism between AG andγ-CD,which was experimentally characterized by DSC,FTIR and NMR techniques.PBAM was applied to simulate the in vivo behavior of the formulations,which were validated by cell and animal experiments.Cell experiments revealed that the presence of D-α-Tocopherol polyethylene glycol succinate(TPGS)significantly increased the intracellular uptake of AG in MDCKMDR1 cells and the absorptive transport of AG in MDCK-MDR1 monolayers.The relative bioavailability of the AG-CD-TPGS ternary system in rats was increased to 2.6-fold and 1.59-fold compared with crude AG and commercial dropping pills,respectively.In conclusion,this is the first time to integrate various computational tools to develop a new AG-CD-TPGS ternary formulation with significant improvement of aqueous solubility,dissolution rate and bioavailability.The integrated computational tool is a novel and robust methodology to facilitate pharmaceutical formulation design.

New insight into the stability and dynamics of fluid-conveying supported pipes with small geometric imperfections

In several previous studies,it was reported that a supported pipe with small geometric imperfections would lose stability when the internal flow velocity became sufficiently high.Recently,however,it has become clear that this conclusion may be at best incomplete.A reevaluation of the problem is undertaken here by essentially considering the flow-induced static deformation of a pipe.With the aid of the absolute nodal coordinate formulation(ANCF)and the extended Lagrange equations for dynamical systems containing non-material volumes,the nonlinear governing equations of a pipe with three different geometric imperfections are introduced and formulated.Based on extensive numerical calculations,the static equilibrium configuration,the stability,and the nonlinear dynamics of the considered pipe system are determined and analyzed.The results show that for a supported pipe with the geometric imperfection of a half sinusoidal wave,the dynamical system could not lose stability even if the flow velocity reaches an extremely high value of 40.However,for a supported pipe with the geometric imperfection of one or one and a half sinusoidal waves,the first-mode buckling instability would take place at high flow velocity.Moreover,based on a further parametric analysis,the effects of the amplitude of the geometric imperfection and the aspect ratio of the pipe on the static deformation,the critical flow velocity for buckling instability,and the nonlinear responses of the supported pipes with geometric imperfections are analyzed.

A recursive formulation based on corotational frame for flexible planar beams with large displacement

A forward recursive formulation based on corotational frame is proposed for flexible planar beams with large displacement.The traditional recursive formulation has been successfully used for flexible mutibody dynamics to improve the computational efficiency based on floating frame,in which the assumption of small strain and deflection is adopted.The proposed recursive formulation could be used for large displacement problems based on the corotational frame.It means that the recursive scheme is used not only for adjacent bodies but also for adjacent beam elements.The nodal relative rotation coordinates of the planar beam are used to obtain equations with minimal generalized coordinates in present formulation.The proposed formulation is different from absolute nodal coordinate formulation and the geometrically exact beam formulation in which the absolute coordinates are used.The recursive scheme and minimal set of dynamic equations lead to a high computational efficiency in numerical integration.Numerical examples are carried out to demonstrate the accuracy and validity of this formulation.For all of the examples,the results of the present formulation are in good agreement with results obtained using commercial software and the published results.Moreover,it is shown that the present formulation is more efficient than the formulation in ANSYS based on GEBF.

QoS-Aware Dynamic Resource Management in Heterogeneous Mobile Cloud Computing Networks

In mobile cloud computing(MCC) systems,both the mobile access network and the cloud computing network are heterogeneous,implying the diverse configurations of hardware,software,architecture,resource,etc.In such heterogeneous mobile cloud(HMC) networks,both radio and cloud resources could become the system bottleneck,thus designing the schemes that separately and independently manage the resources may severely hinder the system performance.In this paper,we aim to design the network as the integration of the mobile access part and the cloud computing part,utilizing the inherent heterogeneity to meet the diverse quality of service(QoS)requirements of tenants.Furthermore,we propose a novel cross-network radio and cloud resource management scheme for HMC networks,which is QoS-aware,with the objective of maximizing the tenant revenue while satisfying the QoS requirements.The proposed scheme is formulated as a restless bandits problem,whose "indexability" feature guarantees the low complexity with scalable and distributed characteristics.Extensive simulation results are presented to demonstrate the significant performance improvement of the proposed scheme compared to the existing ones.

Dynamic Response Solution of Multi-Layered Pavement Structure Under FWD Load Appling the Precise Integration Algorithm

The pavement layered structures are composed of surface layer,road base and multi-layered soil foundation.They can be undermined over time by repeated vehicle loads.In this study,a hybrid numerical method which can evaluate the displacement responses of pavement structures under dynamic falling weight deflectometer(FWD)loads.The proposed method consists of two parts:(a)the dynamic stiffness matrices of the points at the surface in the frequency domain which is based on the domain-transformation and dual vector form equation,and(b)interpolates the dynamic stiffness matrices by a continues rational function of frequency.The mixed variables formulation(MVF)can treat multiple degree of freedom systems with considering the coupling term between degree of freedoms.The accuracy of the developed method has been demonstrated by comparison between the proposed method and published results from the other method.Then the proposed method can be applied as a forward calculation technique to emulate the falling weight deflectometer test for multi-layered pavement structures.

Dynamic analysis and regulation of the flexible pipe conveying fluid with a hard-magnetic soft segment

The recently developed hard-magnetic soft(HMS)materials can play a significant role in the actuation and control of medical devices,soft robots,flexible electronics,etc.To regulate the mechanical behaviors of the cantilevered pipe conveying fluid,the present work introduces a segment made of the HMS material located somewhere along the pipe length.Based on the absolute node coordinate formulation(ANCF),the governing equations of the pipe conveying fluid with an HMS segment are derived by the generalized Lagrange equation.By solving the derived equations with numerical methods,the static deformation,linear vibration characteristic,and nonlinear dynamic response of the pipe are analyzed.The result of the static deformation of the pipe shows that when the HMS segment is located in the middle of the pipe,the downstream portion of the pipe centerline will keep a straight shape,providing that the pipe is stable with a relatively low flow velocity.Therefore,it is possible to precisely regulate the ejection direction of the fluid flow by changing the magnetic and fluid parameters.It is also found that the intensity and direction of the external magnetic field greatly affect the stability and dynamic response of the pipe with an HMS segment.In most cases,the magnetic actuation increases the critical flow velocity for the flutter instability of the pipe system and suppresses the vibration amplitude of the pipe.

THE COUPLING DYNAMICAL MODELING THEORY OF FLEXIBLE MULTIBODY SYSTEM

Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The 'coupling matrix library' and Jourdain's variation principle and single direction recursive formulation method are used to establish the general coupling dynamical equations of flexible multibody system. Two typical examples show the coupling effect between coupling displacements and large overall motion on the dynamics of flexible multibody system consisting of beams.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids

This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation theorem for thermoviscoelastic solids (TVES) matter without memory. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics. This mathematical model is thermodynamically and mathematically consistent and is ideally suited to study nonlinear dynamics of TVES and dynamic bifurcation and is used in the work presented in this paper. The finite element formulations are constructed for obtaining the solution of the initial value problems (IVPs) described by the mathematical models. Both space-time coupled as well as space-time decoupled finite element methods are considered for obtaining solutions of the IVPs. Space-time coupled finite element formulations based on space-time residual functional (STRF) that yield space-time variationally consistent space-time integral forms are considered. This approach ensures unconditional stability of the computations during the entire evolution. In the space-time decoupled finite element method based on Galerkin method with weak form for spatial discretization, the solutions of nonlinear ODEs in time resulting from the decoupling of space and time are obtained using Newmark linear acceleration method. Newton’s linear method is used to obtain converged solution for the nonlinear system of algebraic equations at each time step in the Newmark method. The different aspects of the deformation physics leading to the factors that influence nonlinear dynamic response and dynamic bifurcation are established using the proposed mathematical model, the solution method and their validity is demonstrated through model problem studies presented in this paper. Energy methods and superposition techniques in any form including those used in obtaining solutions are neither advocated nor used in the present work as these are not supported by calculus of variations and mathematical classification of differential operators appearing in nonlinear dynamics. The primary focus of the paper is to address various aspects of the deformation physics in nonlinear dynamics and their influence on dynamic bifurcation phenomenon using mathematical models strictly based on CBL of CCM using reliable unconditionally stable space-time coupled solution methods, which ensure solution accuracy or errors in the calculated solution are always identified. Many model problem studies are presented to further substantiate the concepts presented and discussed in the paper. Investigations presented in this paper are also compared with published works when appropriate.

An effective nonlinear dynamic formulation to analyze grasping capability of soft pneumatic robotic gripper

Soft pneumatic robotic grippers have found extensive applica-tions across various engineering domains,which prompts active research due to their splendid compliance,high flex-ibility,and safe human-robot interaction over conventional stiff counterparts.Previously simplified rod-based models prin-cipally focused on clarifying overall large deformation and bending postures of soft grippers from static or quasi-static perspectives,whereas it is challenging to elaborate grasping characteristics of soft grippers without considering contact interaction and nonlinear large deformation behaviors.To address this,based on absolute nodal coordinate formulation(ANCF),comprehensively allowing for structural complexity,geometric,material and boundary nonlinearities,and incorpor-ating Coulomb’friction law with a multiple-point contact method,we put forward an effective nonlinear dynamic mod-eling approach for exploring grasping capability of soft grip-per.Moreover,we solved the established dynamic equations using Generalized-αscheme,and conducted thorough numer-ical simulation analysis on a three-jaw soft pneumatic gripper(SPG)in terms of grasping configurations,displacements and contact forces.The proposed dynamic approach can accurately both describe complicated deformed configurations along with stress distribution and provide a feasible solution to simulate grasping targets,whose effectiveness and precision were analyzed theoretically and verified experimentally,which may shed new light on devising and optimizing other multi-functional SPGs.

Dynamic Analysis and Optimal Parameter Design of FlexibleComposite Structures via Absolute Nodal Coordinate Formulation

The composite structure with the dielectric elastomer and soft materials is the main form of theactuators in soft robots. However, the theoretical model is hard to obtain due to the nonlinear large deformationof materials. In this paper, a new composite element model is established based on the absolute nodal coordinateformulation. The consistent deformation conditions at the contact interface between two thin plates are deduced.The hyperelastic constitutive model and the dielectric elastomer constitutive model are introduced for the twothin plates. Then the dynamic model is established to study the dynamic behaviors of the composite flexiblestructure with various parameters. The results show that the nonlinear deformation appears obviously whenthe flexible composite plate structure is driven by various voltages, and the warping deformation becomes moreobvious with the increase of the voltage. The width and thickness of the driven thin plate influence the stabilityof the whole structure. With the decrease of the width or thickness, the deformation of the structure is moreconsistent with obvious periodicity, and the control performance is improved. Finally, the structural parametersof the composite structures are optimized to improve the control performance based on the dynamic performance.Additionally, smaller width and thickness parameters are preferred to obtain better performance in the design offlexible actuator of soft robot.

基于绝对节点坐标法的架空线断线工况动力学计算

为了计算架空线断线工况下的动力学变化特性,考虑架空线的绞制几何结构及其初始构型的布置特点,以绝对节点坐标法为基础,建立了架空线单元,推导了架空线单元的质量矩阵和弹性力矩阵,给出了架空线的系统动力学方程。针对钢芯铝绞线的绞制几何结构,给出了其对应的轴向、弯曲刚度计算公式。通过仿真计算得到线缆的运动图像,设计试验验证了算法模型的可靠性。结合实际架空线初始位形和初始应力特点,对不同初始应力下的架空线断线工况动力学问题进行仿真分析,绘制了悬挂点处的受力时程曲线并对曲线进行了频谱分析,研究了初始应力对断裂架空线运动过程以及悬挂点受力的影响规律。

分析化学教学中引入动态缓冲容量“去公式化”计算的新策略

缓冲容量是分析化学重要内容。目前教材中缓冲容量计算没有考虑缓冲溶液与样品溶液混合时体积的变化,这种不考虑体积变化的缓冲容量被称为“静态”缓冲容量。而在实际应用中,往往缓冲溶液与样品溶液混合后的体积远远大于缓冲溶液的原始体积,此时需要考虑“动态”缓冲溶液。这里提出了一种“动态”缓冲容量问题的“去公式化”解决方案,它完全基于学科思想的底层逻辑,不会增加学生学习的记忆负担。