A computational framework for the form-finding and design of tensegrity structures

A new computational framework is proposed for the form-finding and design of tensegrity structures with or without super-stability. The form-finding of tensegrities is formulated as two unconstrained minimisation problems where their objective functions are defined based on eigenvalues of a modified force density matrix. The Nelder–Mead simplex method is then used to solve the minimisation problems. Furthermore, another efficient method is suggested for the interactive form-finding and design of tensegrities with geometrical and force constraints. Examples of the form-finding of tensegrities are presented and the results obtained are compared and contrasted with those analytical results documented in the literature, to verify the accuracy and efficiency of the developed methods.     

A time integral formulation and algorithm for structural dynamics with nonlinear stiffness

A newly-developed numerical algorithm, which is called the new Generalized-α (G-α) method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired overshoot properties as for a class of α-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zero-stable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.The English text was polished by Keren Wang.     

带约束多体系统动力学方程的隐式算法

研究了带约束多体系统隐式算法,用子矩阵的形式推导出了多体系统正则方程的Ｊａｃｏｂｉ矩阵,它适用于多种隐式算法并给出了隐式Ｒｕｎｇｅ－Ｋｕｔｔａ算法,最后用一算例表明了隐式算法的计算效率和精度明显优于算法。     

Impact dynamics of multibody systems with frictional contact using joint coordinates and canonical equations of motion

This paper presents a methodology in computational dynamics for the analysis of mechanical systems that undergo intermittent motion. A canonical form of the equations of motion is derived with a minimal set of coordinates. These equations are used in a procedure for balancing the momenta of the system over the period of impact, calculating the jump in the body momentum, velocity discontinuities and rebounds. The effect of dry friction is discussed and a contact law is proposed. The present formulation is extended to open and closed-loop mechanical systems where the jumps in the constraints' momenta are also solved. The application of this methodology is illustrated with the study of impact of open-loop and closed-loop examples.     

Stability of a numerical algorithm for gas bubble modelling

A free-surface-tracking algorithm based on the SOLA-VOF method is analysed for numerical stability when modelling gas bubble evolution in a fluid. It is shown that an instability can arise from the fact that the bubble pressure varies with its volume. A time step stability criterion is introduced which is a function of the natural oscillation period but does not depend on the mesh size. This dependence suggests that the instability is likely to arise in the case of a general motion of a bubble, especially if break-up occurs. The effect is shown using linear Fourier analysis of the discretized equation for radial bubble oscillation and demonstrated numerically using a CFD code FLOW-3D. One- and three-dimensional situations are considered: a bubble in a fluid bounded by two concentric surfaces and a bubble floating in a fluid chamber with and without gravity. In cases where no analytical solution is available, a numerical method for the stability time step limit calculation is suggested based on finding the natural oscillation frequency. The nature of the instability suggests that it can be a feature of any numerical algorithm which models transient fluid flow with a free surface.     

A two-step godunov-type scheme for the euler equations

A second-order Godunov-type scheme for the Euler equations in conservation form is derived. The method is based on the ENO formulation proposed by Harten et al. The fundamental difference lies in the use of a two-step scheme to compute the time evolution. The scheme is TVD in the linear scalar case, and gives oscillation-free solutions when dealing with nonlinear hyperbolic systems. The admissible time step is twice that of classical Godunovtype schemes. This feature makes it computationally cheaper than one-step schemes, while requiring the same computer storage.

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Sommario Viene data una nuova estensione al secondo ordine del metodo di Godunov per la soluzione delle equazioni di Eulero in forma conservativa. Il metodo é basato sulla formulazione ENO proposta da Harten et al. La differenza fondamentale consiste nel calcolo dell'evoluzione temporale, ottenuta mediante uno schema a due passi. Questo consente l'uso di un passo di integrazione nel tempo doppio rispetto agli altri schemi alla Godunov ad un solo passo. Il metodo proposto risulta quindi piú efficiente e puó inoltre essere implementato senza alcun aumento dell'occupazione di memoria. Viene dimostrato che lo schema é TVD nel caso lineare, e che fornisce soluzioni prive di oscillazioni spurie nel caso di sistemi non-lineari.

     

A novel simulation model for ring type ultrasonic motor

In this paper, a novel mathematical model for a traveling wave ultrasonic motor, developed by Alenia Spazio, now Alcatel Alenia Space Italia S.p.A. (Roma, Italy), within an Italian Space Agency (ASI) program, is described. The dynamic equations for the stator and the rotors of the ultrasonic motor are assembled into a differential system, whose equations are coupled by terms which represent interface generalized forces. Neglecting transient conditions, the complete mathematic model of the system is solved and an iterative process is developed, in order to obtain the motor’s running curves for different operation parameters, geometric dimensions and physical features of the system. The algorithm is implemented in Matlab environment and a graphical user interface is constructed for user-friendly managing. The model, also validated by means of experimental tests, can be used for parametric analyses with respect to different parameters, in order to optimize motor’s configuration. It represents a simple but powerful aid to determine final motor design that can satisfy specifications or to predict motor’s behavior under different working conditions.     

二维柱坐标系中守恒的保球对称的中心型拉氏方法

提出了一种Godunov型中心型拉氏方法,用于求解二维柱坐标系中的可压缩多介质Euler方程组,该方法完全在体积控制体上离散,不仅保证质量、动量和总能量守恒,且该方法在二维柱坐标系中保一维球对称;并且对一维球对称问题在球对称网格划分下,精度测试表明该方法具有一阶精度,算例显示方法非常有效。     

多体系统动力学子系统求解算法

为了降低系统求解规模,提高复杂多体系统动力学求解效率,研究了多体动力学子系统求解算法.通过分析系统拓扑构型,基于雅克比矩阵分块特性,提出子系统综合算法.算法采用半递归法建立含开环、闭环的子系统运动方程,将子系统质量和外力等效作用在内接基体上,解耦系统运动方程组装和加速度求解.此外,针对松散耦合子系统,提出了予系统分治算法.算法针对子系统间的耦合特点,分解复杂多体系统模型,实现子系统的独立求解.最后以机构动力学数值求解实例,验证上述算法的正确性和求解效率.     

A numerical method for accelerating the rate of convergence of the SIMPLE-like algorithm for flow through a thin filter

The control volume, finite difference method and the k-? tubulence model are employed in a numerical simulation of the turbulent fluid flow both outside and inside a blunt cylindrical sampler which houses a paper filter in its chamber. The presence of a paper filter, which has a very large resistance, results in a large pressure drop across the filter and this causes difficulties in making the SIMPLE or the SIMPLEC scheme converge. In order to improve the rate of convergence of the SIMPLE-like algorithm when the resistance of the filter is very large, an average pressure correction formula is proposed. Based on global mass conservation, a line average pressure correction for the paper filter is derived using a modified Darcy law for a porous medium. A combination of this formula and the SIMPLE-like algorithm can rapidly build up the pressure drop across the filter and hence dramatically improve the rate of convergence of the iterative scheme. Comparisons of the convergence histories and the numerical results for the fluid flow when using SIMPLE and SIMPLEC with the average pressure correction method show that the average pressure correction method for dealing with the paper filter significantly accelerates the rate of convergence of the iterative scheme.     

A simple numerical technique for transient creep flows with free surfaces

A simple, but powerful iterative technique is presented for the numerical solution of the time-dependent flow of an incompressible viscous fluid with or without a free surface. The usual numerical stability restrictions related to the viscous acceleration terms are avoided using standard implicit differencing techniques. The properties and accuracy of the method are illustrated by several calculational examples.     

平面刚体系统的参数预调节保辛算法

保辛积分方法在约束哈密顿系统中有着重要的应用,是因为其在长时间仿真中表现出极好的稳定性。然而随着仿真时长增加,保辛格式通常具有较大的相位误差累积。本文提出了一种平面多刚体系统的参数预调节保辛积分方法。通过推导具有待定参数的改进的拉格朗日方程,并将其与已有保辛格式相结合并预先调节相关参数取值,可以大幅降低数值解的相位误差。理论分析与数值结果表明参数预调节保辛积分方法不仅保持了辛结构,而且具有很低的相位误差累积。因此,参数预调节保辛积分方法可应用于长时间仿真分析。     

A coupled zigzag theory for the dynamics of piezoelectric hybrid cross-ply plates

A recently developed coupled third-order zigzag theory for the statics of piezoelectric hybrid cross-ply plates is extended to dynamics. The theory combines a third-order zigzag approximation for the in-plane displacements and a sub-layerwise linear approximation for the electric potential, considering all components of the electric field. The nonuniform variation of the transverse displacement due to the piezoelectric field is accounted for. The conditions for the absence of shear traction at the top and bottom surfaces and continuity of transverse shear stresses in the presence of electromechanical loading are satisfied exactly, thereby reducing the number of displacement variables to five, which is the same as in a first- or third-order equivalent single-layer theory. The governing equations of motion are derived from the extended Hamilton's principle. The theory is assessed by comparing the Navier solutions for the free and forced harmonic vibration response of simply supported plates with the exact three-dimensional piezoelasticity solutions. Comparisons for hybrid test, composite and sandwich plates establish that the present theory is quite accurate for the dynamic response of moderately thick plates.     

A numerical approach for pressure transient analysis of a vertical well with complex fractures

A new well test model for a vertical fractured well is developed based on a discrete-fracture model in which the fractures are discretized as one dimensional (1-D) entities. The model overcomes the weakness of complex meshing, a large number of grids, and instability in conventional stripe-fracture models. Then, the discrete-fracture model is implemented using a hybrid element finite-element method. Triangular elements are used for matrix and line elements for the fractures. The finite element formulation is validated by comparing with the semi-analytical solution of a single ver-tical fractured well. The accuracy of the approach is shown through several examples with different fracture apertures, fracture conductivity, and fracture amount. Results from the discrete-fracture model agree reasonably well with the stripe-fracture model and the analytic solutions. The advantages of the discrete-fracture model are presented in mesh gen-eration, computational improvement, and abilities to handle complex fractures like wedge-shaped fractures and fractures with branches. Analytical results show that the number of grids in the discrete-fracture model is 10%less than stripe-fracture model, and computational efficiency increases by about 50%. The more fractures there are, the more the com-putational efficiency increases.     

A SYMPLECTIC ALGORITHM FOR DYNAMICS OF RIGID BODY

For the dynamics of a rigid body with a fixed point based on the quaternion and the corresponding generalized momenta,a displacement-based symplectic integration scheme for differential-algebraic equations is proposed and applied to the Lagrange’s equa- tions based on dependent generalized momenta.Numerical experiments show that the algorithm possesses such characters as high precision and preserving system invariants. More importantly,the generalized momenta based Lagrange’s equations show unique ad- vantages over the traditional Lagrange’s equations in symplectic integrations.     

A comparison of spatial grids for numerical modelling of flows in near-coastal seas

Three-dimensional algorithms for the numerical computation of flows caused by tides or meteorological forcing are developed for four of Arakawa's spatial grid types using a spectral method in the vertical dimension. Three of the grids, in which the velocity components are computed at the same grid points, offer potential advantages over the commonly used C-grid. The computed results from the four grids are compared for three test problems based on the linearized hydrodynamical equations. It is concluded that the B-grid provides a viable alternative to the C-grid, with significant advantages when a spectral method is used.     

A modified constraint force algorithm for flexible multibody dynamics with loop constraints

Nonlinear Dynamics - This paper presents a modified constraint force algorithm (m-CFA) for the dynamics of flexible multibody systems in arbitrary topologies. The m-CFA can efficiently calculate...     

A chassis-based kinematic formulation for flexible multi-body vehicle dynamics

This research proposed an efficient implicit integration method for the real-time simulation of flexible multi-body vehicle dynamics models. The equations of motion for the flexible bodies were formulated with respect to the moving chassis-body reference frame instead of the fixed inertial reference frame. The proposed approach does not require evaluation of system Jacobian and its LU-decomposition in time loof of simulation. This is one of the key aspects that enable high computational efficiency of the proposed method. The numerical simulation results of the proposed approach were matched up with those of the conventional approach but the computation time can be reduced by applying the proposed method. The joint constraint and generalized force equations are the same as the equations for rigid vehicle dynamics models because the joints and forces between flexible bodies are connected by the RBE (rigid body element). On the various driving conditions, the numerical simulation results show that the proposed approach yields almost exact solutions compared to the conventional approach. And the proposed approach spends only 22.9% of conventional approach on computation time under CPU 3.2 GHz personal computer.     

A NON－INCREMENTAL TIME－SPACE ALGORITHM FOR NUMERICAL SIMULATION OF FORMING PROCESS

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