Finite element based form-finding algorithm for tensegrity structures

This paper presents a novel form-finding algorithm for tensegrity structures that is based on the finite element method. The required data for the form-finding is the topology of the structure, undeformed bar lengths, total cable length, prestress of cables and stiffness of bars. The form-finding is done by modifying the single cable lengths such that the total cable length is preserved and the potential energy of the system is minimized. Two- and three-dimensional examples are presented that demonstrate the excellent performance of the proposed algorithm.     

Numerical form-finding of tensegrity structures

A novel and versatile numerical form-finding procedure that requires only a minimal knowledge of the structure is presented. The procedure only needs the type of each member, i.e. either compression or tension, and the connectivity of the nodes to be known. Both equilibrium geometry and force densities are iteratively calculated. A condition of a maximal rank of the force density matrix and minimal member length, were included in the form-finding procedure to guide the search of a state of self-stress with minimal elastic potential energy. It is indeed able to calculate novel configurations, with no assumptions on cable lengths or cable-to-strut ratios. Moreover, the proposed approach compares favourably with all the leading techniques in the field. This is clearly exemplified through a series of examples.     

张拉膜结构力密度法混合找形分析

论述了张拉膜结构力密度法混合找形的基本理论;所谓力密度法混合找形,即部分单元力密度控制,部分单元弹性控制;力密度控制采用线性求解,弹性控制采用非线性求解,通过迭代计算混合找形求出各结点的坐标值。据此编制了相应的计算软件;对工程实例进行了验算,结果表明,本文给出的计算结果与德国著名软件easy的计算结果相吻合。     

Adaptive force density method for form-finding problem of tensegrity structures

A numerical method is presented for form-finding of tensegrity structures. Eigenvalue analysis and spectral decomposition are carried out iteratively to find the feasible set of force densities that satisfies the requirement on rank deficiency of the equilibrium matrix with respect to the nodal coordinates. The equilibrium matrix is shown to correspond to the geometrical stiffness matrix in the conventional finite element formulation. A unique and non-degenerate configuration of the structure can then be obtained by specifying an independent set of nodal coordinates. A simple explanation is given for the required rank deficiency of the equilibrium matrix that leads to a non-degenerate structure. Several numerical examples are presented to illustrate the robustness as well as the strong ability of searching new configurations of the proposed method.     

A Monte Carlo form-finding method for large scale regular and irregular tensegrity structures

We propose a Monte Carlo form-finding method that employs a stochastic procedure to determine equilibrium configurations of a tensegrity structure. This method does not involve complicated matrix operations or symmetry analysis, works for arbitrary initial configurations, and can handle large scale regular or irregular tensegrity structures with or without material/geometrical constraints.     

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.     

Algebraic tensegrity form-finding

This paper concerns the form-finding problem for general and symmetric tensegrity structures with shape constraints. A number of different geometries are treated and several fundamental properties of tensegrity structures are identified that simplify the form-finding problem. The concept of a tensegrity invariance (similarity) transformation is defined and it is shown that tensegrity equilibrium is preserved under affine node position transformations. This result provides the basis for a new tensegrity form-finding tool. The generality of the problem formulation makes it suitable for the automated generation of the equations and their derivatives. State-of-the-art numerical algorithms are applied to solve several example problems. Examples are given for tensegrity plates, shell-class symmetric tensegrity structures and structures generated by applying similarity transformation.     

双向张弦梁找形的有限元法

根据双向张弦梁上弦压力和下弦拉力在节点产生的竖向分力与撑杆高度之间的关系推导了单元刚度矩阵,根据外荷载与上弦和下弦在节点产生的竖向分力相等的原则建立了以撑杆高度为未知数的双向张弦梁找形的线性有限元列式并编制了有限元程序,给出了张弦梁计算时下弦拉索初应变确定方法和张拉控制方法;通过对平屋顶和曲面屋顶双向张弦梁2个算例找形计算和受力分析验证了找形方法的正确性以及撑杆高度与屋面形状的无关性,本文给出的计算方法将撑杆高度作为未知量,考虑了上弦为曲面时拱的作用,计算方便、结果准确.     

索网天线找形分析的参变量变分有限元法

针对柔性空间索网天线的非线性特点,建立了基于参变量变分描述索网拉压非线性和共旋列式描述几何非线性的有限元控制方程,应用Lernke与改进牛顿法进行求解.通过对索网预张力平衡计算,证明改进牛顿法比Newton-Raphson法具有更强的收敛能力.进一步将力密度法迭代原理与有限元法结合应用于索网天线的非线性找形分析中,获得了理想的索网构型.本文的索网找形方法可广泛应用于空间索网天线结构的设计.     

张力索杆结构最小势能分析方法与结构特性研究

张力索杆结构为柔性多态体系,计算方法复杂。本文基于势能最小化迭代建立平衡态的最小势能方法,推导了体系势能、下降向量及步长列式,建立势能最小化共轭梯度法迭代格式,并用VC++编程实现了算法。通过正交四边形网格索网数值分析算例验证了程序正确性,并分析了新型六边形网格马鞍形双曲索网和索杆张拉整体结构的非线性荷载特性。研究表明最小势能迭代分析是一种有效的柔性张力结构非线性分析方法。     

Transient-velocity gage for structures

A compact gage has been developed to measure transient velocities up to about 600 cm/sec. The design is based on the principle of a highly overdamped seismic oscillator. Frequency response of the gage is flat from 1 to 500 cps. The gage can be used at any inclination and measures the velocity component along one axis only unaffected by crosswise motion.     

折叠结构几何非线性分析

本文提出了一种推导折叠结构宏单元刚度矩阵的新方法,即在所假设普通单元位移模式的基础上直接引入位移约束条件,得到宏单元的形函数矩阵,进而给出宏单元的力与位移间关系。利用该思路,文中简捷地推导出剪式单元三节点梁大位移小变形的几何非线性切线刚度矩阵,并给出了线性刚度矩阵的显式。算例表明,分析折叠结构承载能力和自稳定结构的展开或收纳过程,考虑几何非线性的影响是必要的。     

Kagome plate structures for actuation

A class of planar, pin-jointed truss structures based on the ancient Kagome basket weave pattern with exceptional characteristics for actuation has been identified. Its in-plane stiffness is isotropic and has optimal weight among planar trusses for specified stiffness or strength. The version with welded joints resists plastic yielding and buckling, while storing minimal energy upon truss bending during actuation. Two plate structures are considered which employ the planar Kagome truss as the actuation plane. It is shown that these plates can be actuated with minimal internal resistance to achieve a wide range of shapes, while also sustaining large loads through their isotropic bending/stretching stiffness, and their excellent resistance to yielding/buckling.     

Stability conditions for tensegrity structures

Stability conditions for tensegrity structures are derived based on positive definiteness of the tangent stiffness matrix, which is the sum of the linear and geometrical stiffness matrices. A necessary stability condition is presented by considering the affine motions that lie in the null-space of the geometrical stiffness matrix. The condition is demonstrated to be equivalent to that derived from the mathematical rigidity theory so as to resolve the discrepancy between the stability theories in the fields of engineering and mathematics. Furthermore, it is shown that the structure is guaranteed to be stable, if the structure satisfies the necessary stability condition and the geometrical stiffness matrix is positive semidefinite with the minimum rank deficiency for non-degeneracy.     

Advanced pneumatic method for gradient flow analysis

Pneumatic 5-hole probes are widely known reliable sensors for the analysis of three-dimensional flow fields. Since the accuracy of such measurements depends strongly on the volume of the probe and the gradients in the flow, a miniature spherical five-hole-probe with an improved analysis method was developed. With the new method, the complete physically reasonable angle measurement range can be used now by introducing modified calibration functions. A dimensionless examination of the flow around spheres shows the independence of the calibration functions within a wide range of flow velocities. Misrepresentations in flows with high gradients caused by the volume of the probe are estimated by a geometry based correction method. The quality of the method is analysed by an extensive error calculation. Results of measurements in a three-dimensional model combustor are discussed.     

Advanced near-wall modeling for engine heat transfer

Recent developments in the engine heat transfer modeling tend to improve existing wall heat transfer models (temperature wall functions) which mostly rely on the standard or low-Re variants of k-ε turbulence model. Presently applied mesh resolutions already allow for first near-wall computational cells reaching the buffer or locally even viscous/conductive sub-layer, thus increasing the importance of more sophisticated modeling approach. As temperature gradient-induced density and fluid property variations become significant, wall heat transfer is strongly influenced by property variations (viscous/conductive sub-layer) and predictive capability of the turbulence model (buffer region), standard wall laws being inadequate anymore, even for attached boundary layers. The present approach relies on the k-ζ-f turbulence model and formulates a compressible wall function of Han and Reitz in the framework of hybrid wall treatment. The model is validated against spark ignition (SI) engine heat transfer measurements. Predicted wall heat flux evolutions on the cylinder head exhibit very good agreement with the experimental data, being superior to similar numerical predictions available in the published literature.     

Embedded-strain-sensor development for composite smart structures

The winding or layup procedure for fiber-reinforced composites lends itself to convenient installation of embedded sensors during fabrication. These permanently installed and protected sensors could be used during the service lifetime of the structure to monitor real-time conditions and determine when loading or vibration is excessive, and when damage has occurred. Such ‘smart or intelligent’ structures could be used to provide continuous ‘health monitoring’ of the structure as well as provide input for active vibration control. In the present study, two sizes of constantan wire (0.15-mm and 0.025-mm diameter) with a very thin but tough polyimide insulation were embedded in graphite-epoxy bars and tubes. The 25-mm by 2.5-mm by approximately 300-mm long bars were fabricated from hand-laid-up panels and subjected to static four-point bending and cantilever bending. The tubes (42-mm diameter by 1.25-m long) were subjected to static cantilever bending. Output from the constantan wire was monitored with conventional strain-gage indicators. Results indicate accurate tensile and compressive measurements of the integrated strain along the length of the constantan wire when compared with beam formulas and surface mounted strain gages. The constantan strain wire shows promise as an embedded sensor for ‘smart structures’.     

Constitutive model for special granular structures

This work deals with novel “smart systems” that are based on granular materials. These systems consist of mechanical components, such as a beam or bar, enclosed in a tight flexible sleeve that is filled with a granular material. When air is pumped out of the sleeve, the resulting underpressure causes the compression of the granules making the system more rigid and changing its damping characteristics. This allows for quick, easy, and inexpensive control of the damping and stiffness of such a system. This paper presents the experimental results of uniaxial tensile tests of a sleeve filled with different granular materials. These results support the modeling of the mechanics of such a system with the Chaboche viscoplastic constitutive law. The experiments provide the quantitative and functional dependence of the model parameters on the underpressure, which acts as the control variable. The highly non-linear dependence of the system's fundamental mechanical properties on the underpressure is described and discussed. This basic work opens the way to applications in mechanical systems where effective control of vibrations or noise is important.     

Dynamic vortex structures for flow-control applications

It is well known that the application of active flow-control strategies has the potential to increase the efficiency of many devices when compared to static actuator concepts. However, many aspects of the flow-control process are not well understood. In the case of pneumatic vortex generators the importance of coherent structures and their interaction with turbulent boundary layers remains an open question. A flat plate experiment was performed to determine the dynamic evolution of the induced vortex structures using phase-locked stereoscopic Particle Image Velocimetry. The qualification of the actuator system was performed by means of the time-resolved Particle Image Velocimetry measurements of the jet flow. The results show that an initial overshooting of the jet velocity dominates the unsteady start-up process, which results in a vortex structure of larger size and impact. This effect differs essentially from the case of steady blowing. In addition, the ability to shift high-momentum fluid into the near-wall region is a result of strong mixing combined with a minimum distance between the vortex core and the model surface.