Truss-like Structures Research Articles

Structural-Acoustic Optimization of Sandwich Panels

Sandwich panels comprising face sheets enclosing a core are increasingly common structural elements in a variety of applications, including aircraft fuselages, flight surfaces, vehicle panels, lightweight enclosures, and bulkheads. This paper presents the optimization of various innovative sandwich configurations for minimization of their structural-acoustic response. Laminated face sheets and core geometries comprising honeycomb and trusslike structures are considered. The design flexibility associated with the class of considered composite structures and with truss-core configurations provides the opportunity of tailoring the structure to the load and dynamic response requirements of a particular application. The results demonstrate how the proper selection of selected key parameters can achieve effective reduction of the radiated sound power and how the identified optimal configurations can achieve noise reduction over different frequency ranges and for various source configurations.

Optimal shakedown design of metal structures under stiffness and stability constraints

Optimal shakedown design of metal frame and truss-like structures is considered in this paper. Strength, stiffness and stability (only for trusses) constraints are included in non-linear mathematical models of volume minimization problems of structures. Stiffness conditions are realized by the restriction of structure deflections or nodal displacements, which can vary non-monotonically during the adaptation process. Determination of displacements is especially complicated if the variable repeated load is defined by variation bounds, which are not related to time. For trusses, stability constraints are related to recommendations of Eurocode 3 (EC3). Numerical examples concerning the calculation of frame and truss structures are presented. The results are valid for the small displacement assumptions.

Determination of strut-and-tie models using evolutionary structural optimization

This paper introduces a method to determine strut-and-tie models in reinforced concrete (RC) structures using evolutionary structural optimization (ESO). Even though strut-and-tie models are broadly adapted in the design of reinforced concrete members subjected to shear and torsion, conventional methods can hardly offer useful models of RC members subjected to complex loadings and geometry conditions. In this paper, the basic idea of the ESO method is used to determine more rational strut-and-tie models. Since an optimum topology of structures, finally obtained by the ESO method, usually represents a truss-like structure, the ESO method using truss elements can effectively be used in finding the best strut-and-tie models in RC structures. To prevent the structural instability that may occur during the evolutionary optimization process, a brick element composed of six truss elements is designed as a basic element unit. Systematic removal of each brick element that has the least virtual strain energy follows, and the optimal load transfer mechanism of an RC structure, which is equivalent to the optimal topology of the strut-and-tie model, is finally characterized on the basis of an optimization criterion of minimizing the total elastic strain energy of the structure. Several RC structures are used as examples to demonstrate the capability of the proposed method in finding the best strut-and-tie model of each RC structure and to verify its efficiency in application to real design problems.

Numerical calculations of effective elastic properties of two cellular structures

Young's moduli of regular two-dimensional truss-like and eye-shaped structures are simulated using the finite element method. The structures are idealizations of soft polymeric materials used in ferro-electret applications. In the simulations, the length scales of the smallest representative units are varied, which changes the dimensions of the cell walls in the structures. A power-law expression with a quadratic as the exponent term is proposed for the effective Young's moduli of the systems as a function of the solid volume fraction. The data are divided into three regions with respect to the volume fraction: low, intermediate and high. The parameters of the proposed power-law expression in each region are later represented as a function of the structural parameters, the unit-cell dimensions. The expression presented can be used to predict a structure/property relationship in materials with similar cellular structures. The contribution of the cell-wall thickness to the elastic properties becomes significant at concentrations >0.15. The cell-wall thickness is the most significant factor in predicting the effective Young's modulus of regular cellular structures at high volume fractions of solid. At lower concentrations of solid, the eye-shaped structure yields a lower Young's modulus than a truss-like structure with similar anisotropy. Comparison of the numerical results with those of experimental data for poly(propylene) show good aggreement regarding the influence of cell-wall thickness on elastic properties of thin cellular films.

Review of Deployable structures: Analysis and design by C. J. Gantes

Conventional structures ~bridges, buildings, rockets, or satellites! are designed to be strong, stable, and able to perform their desired function. The ability of structures to be folded in a compact form and deployed ~unfolded! when needed opens up new possibilities. Although this is not a recent development, such deployable structures have been the subject of growing interest for both terrestrial and space-based applications. Recently, in January 2000, a 60 m truss-like structure was deployed from the space shuttle Endeavor to map 80% of the earth’s topography in a week. The ability to make structures light, compact, and mobile without sacrificing their other attributes is desirable for a variety of applications such as temporary shelters, retractable domes and large satellite solar panels. NASA is designing a 6 m deployable telescope to replace the Hubble Space Telescope by the end of this decade. Such large sensors requiring submicron levels of precision impose new challenges for the structural engineer. These challenges can only be met by combining advances in different engineering disciplines and through the creation of new educational and research programs. This is an excellent reference book, perhaps the only one on deployable structures. It is fairly extensive in its treatment of the history and development of deployable structures and leads up to the most recent developments in its applications to space-based sensor systems and temporary structures. The book describes both

Identification of the Special Configurations of the Octahedral Manipulator using the Pure Condition

This paper presents a technique, known as the Pure Condition, which has found use in analysing the rigidity of truss-like structures. The analysis is applied to the Stewart Platform where it can be used to identify special configurations. The conditions that produce special configurations in the octahedral manipulator are compared to previously known conditions and the associated geometry is seen to be more revealing with this method than was the case previously. The results lead to a simple and clear method for identifying special configurations in the octahedral manipulator and other specializations of the Stewart Platform.

Periodic unfolding and homogenization

A novel approach to periodic homogenization is proposed, based on an unfolding method, which leads to a fixed domain problem (without singularly oscillating coefficients). This method is elementary in nature and applies to cases of periodic multi-scale problems in domains with or without holes (including truss-like structures). To cite this article: D. Cioranescu et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 99–104.

Mechanical behavior of a three-dimensional truss material

A variety of novel manufacturing techniques can be used to make materials with a periodic, three-dimensional (3D) truss-like structure. The high stiffness per unit weight of such structures makes them attractive for use in sandwich panels. In this paper, we analyze the elastic moduli as well as the uniaxial and shear strengths of one particular geometry of 3D truss material as a function of the aspect ratio of the unit cell. The analysis gives a good description of the measured properties.

Nonholonomic elastoplastic analysis involving unilateral frictionless contact as a mixed complementarity problem

This paper deals with the elastoplastic analysis of suitably discretized elastoplastic structures under frictionless unilateral contact conditions. Whilst the mathematical programming formulation we adopt can cater equally for hardening as well as softening path-dependent (nonholonomic) plasticity, the state problem involving softening is by far the more difficult to solve in view of the inherent nonconvex nature of the underlying mathematical program. We propose a novel description of a fairly general class of piecewise linear softening laws and investigate use of an approximate stepwise holonomic (path-independent) approach for capturing the evolution of the structure with softening and/or hardening constitutive laws. This finite-step problem is formulated in a specific way to take advantage of the use of a robust and industry-standard complementarity solver named PATH from within the GAMS modeling environment. We illustrate its application on truss-like structures.

Optimum shakedown design under residual displacement constraints

We consider the minimum weight design of suitably discretized elastoplastic structures subjected to variable repeated loads and constraints on the amount of residual (or permanent) deflections. The optimization problem is formulated on the basis of the classical lower bound theorem of shakedown, supplemented by appropriate constraints on deflections obtained from existing bounding results. The primary purpose of the paper is to show that, even for large size structures, this important and challenging problem can be modeled and solved directly as a mathematical programming problem within the industry standard modeling framework GAMS. Examples concerning truss-like structures are presented for illustrative purposes.

Texture and strength changes of buried surface-hoar layers with implications for dry snow-slab avalanche release

AbstractBuried layers of surface hoar are the failure plane for many slab avalanches, including fatal human-triggered avalanches in various mountain regions. These layers may persist as weak layers in the snow cover for weeks or months. It is therefore essential for operational avalanche forecasters to monitor the evolution of persistent weak layers, such as buried surface hoar. Traditional grain-shape observations of isolated grains with a magnifier and crystal screen do not show bonding that is decisive for strength. In this study we used in situ microphotography and observations of texture to complement strength measurements from shear frame tests. Buried layers of surface hoar consist of crystals most of which extend from the layer below to the layer above, and may exhibit a columnar or truss-like structure. Observations and measurements show that texture and crystal size change little over periods of up to several months during which the snowpack remains dry. Under these conditions, layer thickness decreases while density and strength increase. Based on field measurements, we argue that the increase in strength is primarily due to penetration of the surface-hoar crystals into the adjacent layers, especially at the bottom of the buried surface-hoar layer, where bonding is critical. The weak bonding at the bottom implies that shear failure occurs at the lower interface rather than within the weak layer. On slopes, we find that surface-hoar crystals that were initially surface-normal are tilted downslope faster than predicted by published shear strain rates for settled snow, indicating that shear strain is concentrated in these layers. The characteristic texture of buried surface hoar (columnar or truss-like) permits collapsing at the time of fracture. The gravitational energy released by the displacement of the slab may contribute to the extensive fracture propagation associated with buried surface-hoar layers.

A smoothing scheme for a minimum weight problem in structural plasticity

We revisit an improtant and challenging class of minimum weight structural plasticity problems, the feature of which is the presence of complementarity constraints. Such relations mathematically express the perpendicularity of two sign-constrained vectors and mechanically describe an inherent property of plasticity. The optimization problem in point is referred to in the mathematical programming literature as a Mathematical Program with Equilibrium Constraints (MPEC). Due to its intrinsic complexity, MPECs are computationally very hard to solve. In this paper, we adopt recent ideas, proposed by mathematical programmers, on smoothing to develop a simple scheme for reformulating and solving our minimum weight problem as a standard nonlinear program. Simple examples concerning truss-like structures are also presented for illustrative purposes.

On the solution of a minimum weight elastoplastic problem involving displacement and complementarity constraints

This paper deals with a special class of minimum weight design problem involving discretized structures, holonomic (reversible) plasticity, and constraints on displacements. A key feature of the optimization problem is the presence of complementarity conditions, involving the orthogonality of two sign-constrained vectors. This problem falls within the important class of so-called Mathematical Programs with Equilibrium Constraints (MPECs). Two simple algorithms are proposed to solve our synthesis problem and application is illustrated by some examples concerning truss-like structures.

Velocity analysis of parallel manipulators by truss transformations

A method of velocity analysis of general parallel manipulators is presented. The method consists of transforming the parallel manipulator to an equivalent variable-geometry truss (VGT), and then generating the set of linear velocity equations that govern the transformed manipulator. VGTs are a special class of parallel manipulators. Their actuation is provided by extensible links terminating in spheric joints. A method for velocity analysis of VGT manipulators will be briefly reviewed. This method employs a connectivity chart to generate a system of linear algebraic equations for the manipulator velocity. In addition to the spheric joints and two-force member links that make up truss actuators, general parallel manipulators commonly contain revolute, prismatic, and cylindric joints and multi-force links, links that are more than two-force members. Further, a number of actuation schemes are possible. This work shows how such general parallel manipulators can be conceptually transformed into equivalent VGTs and thereby allow a straightforward velocity analysis approach. While this approach is applicable to general parallel manipulators, the method is most effective when applied to parallel manipulators with truss-like structures.

Vibration of truss structures

Recent trends in underwater vehicle design suggest the use of trusslike structures to support vibrating machinery. Experimental measurements are used to understand the dynamic behavior of a set of 1:15 model, three-dimensional truss structures over the full scale equivalent frequency range 10–1400 Hz. A cubic truss with all equal struts, a rectangular truss with two strut sizes, and a less practical truss composed of pyramid-shaped cells are considered. In conjunction with experiments, a direct global stiffness matrix numerical model is used to identify fundamental truss processes. The periodic nature of trusses causes them to act as mechanical comb filters in frequency with 3–5 dB per bay of attenuation at nonresonant frequencies. In trusses with long runs of axial struts, energy is carried down the truss axis primarily by compressional resonances. The spacing of the resonant peaks is controlled by strut length. A filtering strategy uses strut length to reduce the overall truss response via destructive interference of the frequency resonance structures of the individual struts. Multiple periodicities and impedance discontinuities at the truss joints cause the resonant peaks at low frequencies to widen. The consequence of this is that trusses with varied strut lengths tend to a low-pass frequency characteristic. This effect is compared to an equivalent applied damping and is shown to achieve up to 6 dB per bay of attenuation at the higher frequencies.

Interval model identification and robustness analysis for uncertain flexible structures

System identification and robustness verification techniques are implemented for vibration control of flexible structures. This control methodology allows engineers to develop models which account for parametric uncertainties in a system. The test bed is a 10-bay aluminum truss-like structure. A reaction mass actuator (RMA) is used as the force actuator device for controlling the structure. A local velocity feedback controller is utilized to suppress structural vibration. Added masses to structural nodes represent parametric uncertainties. Interval control system analysis was applied to show the limits of performance of the uncertain experimental system.

Effect of mass loading on the dynamic behavior of a three-dimensional truss

Recent trends in submarine design suggest the use of trusslike structures, connected to the hull by a limited number of attachment points, to support rotating machinery and decks with passive loads. The ratio of the supported mass to the truss mass is high, typically 5–10. This loading must affect the dynamic response of the truss. It is believed that resiliently mounted mass will have a ‘‘fuzzy’’ effect on the truss and result in damping of structural waves. The MIT Structural Acoustics Group is making experimental measurements on a 1:15 scale model of a nonpractical, 3D, submarine truss, constructed of 0.5-in. aluminum tubing, up to frequencies of 5 kHz. The dynamic response of two identical trusses, one unloaded and one mass-loaded at a ratio of 5:1, to octave-band noise are measured and compared. The results show the effects of passive and resiliently mounted mass loading on a truss structure. [Research supported by ONR.]

On Optimum Truss Layout by a Homogenization Method

A new approach to the truss layout optimization problem is possible by using homogenization theory. Unlike traditional methods for optimization of truss topology, the new method does not require that the set of admissible connecting points be defined a-priori. This represents a great advantage over other strategies, which may inadvertently exclude optimum solutions by prescribing a set of connecting points that is inconsistent with the optimum connectivity. The homogenization approach, however, is based on the solution of the equations of plane elasticity over a two dimensional domain and its solutions are only truss-like structures. The relationship between these solutions and optimum truss structures is examined.

Numerical results of simplified dynamic analyses on large imperfect space structures

Large space structures, with eigenfrequencies in the order of 10 −3–10 −4 Hz undergo dynamic excitations which can be periodic (e.g. at the orbiting frequency) or shock-like, as sudden load application (crossing the Earth's shadow), and e.g. control system thruster pulses. The calculated dynamic response can essentially deviate from that obtained by linear analyses. Indeed the overall eigenfrequency of a truss-like structure can decrease by some orders of magnitude due to the inevitable imperfection of the struts, and a strong non-linearity occurs for larger vibration amplitudes. Slenderness ratios < 50 are relatively insensitive to initial crookedness, they lead, however, to complicated and expensive structures due to the great number of nodal points. With increasing length and slenderness ratios, the imperfection sensitivity grows and the eigenfrequency of the struts themselves decreases. In this paper an attempt is made to evaluate the fundamental influences by simple analytical and numerical invesigations and to find some indications towards the design of an improved conception.

Eigenstructure assignment approach for structural damage detection

In this work, a methodology for incorporating measured modal data into an existing refined finite element model is examined with the objective of detecting and locating structural damage. The algorithm is based on the partial inverse problem, in that only partial spectral information is required. The technique utilizes a symmetric eigenstructure assignment algorithm to perform the partial spectral assignment. Algorithms to enhance mode shape assignability and to preserve sparsity in the damaged FEM are developed. The sparsity preservation is of particular importance when considering damage detection in trusslike structures. Several examples are presented to highlight the key points made within the paper.