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As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics (SPH) method is used to model the compressible fluid, the natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit (GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach. [ABSTRACT FROM AUTHOR]

A topology optimization methodology is proposed for the flexible multibody system undergoing both large overall motion and large deformation. The system of concern is modeled via the absolute nodal coordinate formulation. The equivalent static load method is employed to transform the topology optimization of the nonlinear dynamic response of the system into a static one, and evaluated to adapt to the absolute nodal coordinate formulation by splitting the elastic deformations of the flexible components from the overall motions of those components. During the static topology optimization, the material interface is implicitly described as the zero level set of a higher-dimensional scalar function. Then, the semi-implicit level set method with the additive operator splitting algorithm is employed to solve the corresponding Hamilton-Jacobi partial differential equation. In addition, the expert evaluation method of weights based on the grey theory is utilized to define the objective function, and a modified augmented Lagrange multiplier method is proposed to treat the inequality volume constraint so as to avoid the oscillation and drift of the volume. Finally, two numerical examples are provided to validate the proposed methodology. [ABSTRACT FROM AUTHOR]

• A new formulation of segment-to-segment frictionless contact dynamics is proposed. • The mortar method is used to discretize the contact constraint conditions. • A rescale and reconstruction strategy is proposed to recover the gap function. • The contact problem of rigid-flexible multibody systems can be handled accurately. A new formulation of segment-to-segment frictionless contact dynamics is proposed for the planar multibody systems subject to large deformations, based on the absolute nodal coordinate formulation, which is not only able to describe both large deformations and overall motions, but also to offer the C 1-continuous surface representation for contact problems. The mortar method is used to discretize the contact constraints, established in an integral form on the nonconforming contact surfaces. A rescale and reconstruction strategy is proposed to recover the gap function as following. The gap function is revised via a scale factor first, and then the slope of the gap function is reconstructed via weighted average method. To satisfy the frictionless contact condition, the magnitude of the normal contact force is discretized via the third-order Hermite interpolation, while the direction of the force is along the normal vector of the contact surface. The penalty method is used to enforce the contact constraints. The generalized forms and Jacobians of the contact forces are derived. The generalized-alpha method is adapted to solve the dynamic equations. Finally, four numerical examples are given to verify the accuracy, convergence, and robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The most popular way to study the dynamics of a multibody system with random parameters is the probabilistic method under the assumption that the mean values and variances of the random parameters are deterministic. For many engineering systems, however, the mean values and variances of those random parameters are inherently interval parameters. In this work, a new computation method is proposed to study the dynamics of flexible multibody systems with hybrid uncertain parameters, i.e., the random parameters with interval mean values and interval variances. The flexible multibody system of concern is described by using the Absolute Nodal Coordinate Formulation first. Then, the perturbation-based method is developed in order to incorporate hybrid uncertain parameters in the dynamic analysis of flexible multibody systems. Afterwards, the dynamics equations are expanded about the mean values of the uncertain input variables by means of the second-order Taylor series. The Chebyshev collocation method, together with the scanning method, is utilized to generate the interval bounds for the deduced surrogate model. Finally, the interval mean values and interval variances of the system dynamics are obtained by using the interval arithmetic. As a consequence, the proposed method can be degenerated into the pure interval method. [ABSTRACT FROM AUTHOR]

The paper presents how to optimize the flexible components in a flexible multibody system undergoing both large overall motion and large deformation by using the Absolute Nodal Coordinate Formulation (ANCF) and the equivalent static load (ESL) method. Before the structural optimization, the flexible multibody system is modeled via ANCF first so as to describe the coupled overall motion and large deformation accurately. During the structural optimization, the elastic deformation of the flexible component to be optimized is split from the overall motion of the flexible component, and then the equivalent static loads are determined by using the ESL method such that the structural optimization of nonlinear dynamic response can be transformed into a static one. In addition, the nonlinear interior point method is adopted to solve the corresponding structural optimization problem of nonlinear static response. The paper gives three numerical examples to validate the above optimization procedure. The final example of optimizing the arms in a rigid-flexible grasping robot shows that the proposed optimization procedure enables one to deal with realistic engineering systems. [ABSTRACT FROM AUTHOR]

Abstract: The dynamics and control of a rigid-flexible multibody system with multiple cylindrical clearance joints are studied via the Absolute Coordinate Based (ACB) method that combines the Natural Coordinate Formulation (NCF) describing rigid bodies and the Absolute Nodal Coordinate Formulation (ANCF) describing flexible bodies. The spatial cylindrical joints with clearances are modeled by two rigid bodies, that is, the journal and bearing, where the difference in radius and axial directions defines the radial clearance and axial clearance, respectively. A new four-point contact kinematic model of NCF is proposed for the rigid cylindrical clearance joint. A combined control scheme consisting of a feedforward torque and a PID feedback controller is adopted to track the joint trajectories. Based on the principle of virtual work, a new and simple method is proposed to evaluate the feedforward torque. To improve computational efficiency, an OpenMP based parallel computational strategy is used to solve the large scale equations of motion. Three examples are given to verify the effectiveness of the proposed formulations and demonstrate the complex dynamics of rigid-flexible multibody systems with multiple cylindrical clearance joints. [Copyright &y& Elsevier]

• A new formulation of segment-to-segment frictional contact dynamics is proposed. • The mortar method is used to discretize the contact constraint conditions. • The algorithm can capture the stick–slip phenomenon. • The rescale and reconstruction strategy is revised and used to recover the gap functions and the tangential friction force. • The contact problem of rigid-flexible multibody systems can be handled accurately. A new formulation is presented to simulate the segment-to-segment frictional contact dynamics of planar multibody systems that are subjected to large deformations and large motions. The contact bodies are meshed via planar elements of the absolute nodal coordinate formulation, which offers a C 1-continuous surface representation for contact regions. To maintain the optimal convergence, the mortar method is used to discretize the contact constraints, which are established in an integral form on the nonconforming contact surface. By using Coulomb's friction law, the switch between stick and slip status can be realized. The penalty approach and return mapping algorithm are adopted to enforce contact constraints. The rescale and reconstruction strategy proposed in the previous study of authors is improved to recover the gap functions and the tangential friction force. In the mortar space, the magnitudes of the normal contact force and tangential friction force are discretized via the third-order Hermite interpolation, while their directions are along the normal vector and tangential vector of the contact surface, respectively. Several numerical examples are presented to demonstrate the effectiveness of the formulation. [ABSTRACT FROM AUTHOR]

Abstract: A computational approach is proposed for the dynamic analysis of complicated membrane systems, such as parachutes and solar sails, which undergo overall motions, large deformations, as well as wrinkles owing to the small membrane resistance to the compressive stress therein. Based on previous studies, a thin shell element of gradient deficient Absolute Nodal Coordinate Formulation (ANCF) is proposed first. Then, the strain energy of the above shell element is derived by using the definition of the Green–Lagrange strain tensor in continuum mechanics. The computationally efficient formulations of elastic forces and their Jacobian for the above shell element are also derived via the skills of tensor analysis. Afterwards, a membrane element of ANCF is proposed by integrating the criterion of wrinkle/slack into the above shell element. To deal with the small compressive stiffness for the membrane element, the Stiffness Reduction Model (SRM) is introduced to the membrane elements. Finally, four case studies including both statics and dynamics of different membrane systems are given to validate the proposed approach. The final example of the spinning deployment of a solar sail shows the efficacy of the proposed approach in the dynamic analysis of complicated membrane system undergoing an overall motion, large deformations and wrinkles. [Copyright &y& Elsevier]

Abstract: A new methodology is proposed for the dynamic analysis of rigid-flexible multibody systems with ElastoHydroDynamic (EHD) lubricated cylindrical joints. The EHD lubricated cylindrical joint is formulated by the Natural Coordinate Formulation (NCF) and the 20-node hexahedral elements of Absolute Nodal Coordinate Formulation (ANCF), with the lubricant pressure determined through the resolution of the Reynolds’ equation employing the finite difference method. The main outcomes are validated with those obtained by using the commercial software ADINA. It is shown that the bearing flexibility plays a significant role in the system responses, extends the lubricant distribution space and, consequently, reduces the lubricant pressure. [Copyright &y& Elsevier]