Three-dimensional Truss Structure Research Articles

518 セルラ・オートマトンを用いた構造物設計法

This paper describes the design method of the three-dimensional truss structure using cellular automaton. The cross-sectional areas of the truss members are taken as the design variables, which are updated according to the local rule. The local rule is derived from stationalizing the penalty function of the optimization problem. The derived rule is applied to the simple example in order to confirm the validity.

Optimal design of elastic-plastic structures with post-critical behaviour

This work deals with the optimal design of nonlinear structures where both geometric and path-dependent material nonlinearities are considered. Postcritical behaviour is allowed. Critical and postcritical constraints are considered. Constraints on local and global stability have been introduced. The classical critical load constraint against global instability is given with numerical advantage by a new method using a displacement constraint. The total Lagrangian description and a continuum variational formulation are used for the response and design sensitivity analysis. A continuation algorithm is used to implement the postcritical path. The path-dependent sensitivity problem is addressed by an incremental strategy. A direct differentiation approach is used to derive the response sensitivities with respect to both cross-section and configuration design. A finite element technique models the structure. A mathematical programming approach is used for the optimization process. Numerical examples are performed on three-dimensional truss 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.

Experimental measurements of vibrational energy and acoustic radiation for a 3-D truss

The MIT Structural Acoustics Group is making experimental measurements to determine the structural loss and radiation efficiency of an undamped, three-dimensional truss structure, constructed of 0.5-in. aluminum tubing connected by massive aluminum joints. The truss was excited with a shaker driven by wideband white noise out to 20 kHz. The total vibrational energy in the truss was calculated by spatially integrating the energy estimated from acceleration measurements made over the entire truss. This value and the total input power, as measured with an impedance head, allow estimation of the total loss factor for the truss as a function of frequency. Total radiated sound power was calculated by spatially integrating a set of average acoustic intensity measurements made over a grid surrounding the truss. Since the total radiated sound power is known, the total loss factor can easily be broken down into a structural loss factor and a radiation loss factor. These measurements show that the radiation loss is smaller than structural loss, but larger than radiation from an equivalent length single strut would predict. The additional radiation is accounted for by a factor due to multipath in the truss. This factor is frequency dependent and can be estimated from the data by comparing to theory. [Research supported by ARPA and ONR.]

Nonlinear dynamic analysis of lattice structures

A computational procedure for predicting the geometric and material nonlinear dynamic response of space trusses is presented. An updated Lagrangian method, based on the incremental formulation of the equation of motion, is employed. The constitutive law is cast into the Ramberg-Osgood polynomial model. Numerical studies of two- and three-dimensional truss structures under various dynamic loading are made. The structure dynamic response including different types of nonlinearity is compared with the linear response and with the results obtained from static analysis.

Consideration of plant uncertainties in the optimum structural-control design

An integrated design approach for the optimum design of a controlled structure is presented. The control design method takes into consideration both structured and unstructured uncertainties by improving a bound on the H∞ norm of the closed-loop system and satisfying a constraint on the linear quadratic Gaussian performance index. The controller is designed by solving three Riccati equations. The weight of the structure is specified as an objective function with constraints on the structural frequencies, the closed-loop damping, and the performance index. The numerical results are presented for a three-dimensional truss structure to illustrate the application of the integrated approach

Optimum Design of Truss Structure Considering Vibration Control.

An optimization problem for designing a three-dimensional truss structure is considered under the constraint of volume constancy. The objective function is a quantity with quadratic form of state and control variables, which represents a cost for vibration control. The direct velocity and displacement feedback is adopted with collocated sensors and actuators, which is known as an optimal control for quadratic performance. The optimization is carried out by means of the energy-ratio method. The present problem is one of the multicriteria problems for the control cost and volume, and Pareto optimum solutions are derived by the constraint method.

Detecting and Traversing Bifurcation Points in Nonlinear Structural Analysis

We investigate procedures for detecting and traversing bifurcation points that occur in the geometrically nonlinear analysis of elastic structures. In particular, we study a family of test functions for sharp detection and identification of bifurcation points. To accomplish branch switching without recourse to artifical imperfections, the selection of appropriate predictors and correctors which exclude the known branch from the converged solution is considered. These techniques are tried and assesed on several three-dimensional truss structures that exhibit bifurcation behavior.

A language for defining spatial trusses

This paper describes a computer language enabling its users to define three-dimensional truss structures. The language can be used either as a design tool in specifying the geometrical characteristics of these structures or as an input language to a program that actually performs their structural analysis. The main characteristic of the language is that it is procedural; programs defining a nucleus of a structure can be made into procedures (subroutines) which can be called within programs and other procedures in order to define more complex structures composed of that nucleus or its variants. This characteristic is particularly useful in defining repetitive geometrical patterns which themselves appear within repetitive patterns. The paper also describes a syntax-directed compiler whose input is a sentence in the language and whose output is interpretable code which, when executed, produces drawings and provides listings of the coordinates of the points and the linkages defined by the user in his source program. Several examples of structures defined using this language are included in the paper.