Analysis and Optimization of Plane Cable Trusses∗

ABSTRACT

A method for the optimization of plane cable trusses with loads distributed along the cables according to any arbitrary law, as well as a suitable finite element model for the individual cable section, is presented. The optimization method is divided into two steps. In the first, the structure is optimized through the use of a simplified model in which the two main cables are considered continuously connected by an infinite number of vertical inex-tensible wires. In the second step the optimal solution obtained for the simplified model serves as the point of departure for the optimization of the real structure, using Powell's method of conjugate directions. Suitable external penalty functions guarantee that the solution is feasible. A numerical example is also given.     

Transverse Vibrations and Stability of Systems with Gyroscopic Forces∗

Abstract

Rotating shafts and pipes conveying fluid are examples of systems involving gyroscopic forces. The vibration and stability properties of such systems are often of practical interest to structural engineers. In this paper attention is focused on the characteristic curves of gyroscopic conservative systems in an appropriately chosen loading-frequency space. An upper bound to the fundamental frequency is obtained via the concept of a “corresponding nongyroscopic system.” The choice of the parameters and the resulting

characteristic curves shed light on the stabilizing effect of gyroscopic forces. Special emphasis is placed on flutter instability. Three well-defined types of systems are discussed and several examples are analyzed. It is shown that various sequences of stable, divergence, and flutter regions may be exhibited as the loading parameter is increased, and that flutter instability may take place in an otherwise stable region.     

Dynamic Analysis of a Flexible Vehicle Structure with Nonlinear Force Elements Using Substructure Technique∗

ABSTRACT

The substnicturing technique is used to analyze the motion of a flexible vehicle structure with nonlinear force elements. The number of effective degrees of freedom of the combined system model is greatly reduced by synthesizing the individually modeled substructures, using constraints of geometric compatibility at the interfaces. When combining the substructures, recursive-type nonlinear integral equations (NIE) are introduced instead of the conventional nonlinear differential equations (NDE). It is shown that the NIE formulation is computationally more efficient than the NDE formulation in simulating steady-state and transient responses of a flexible vehicle with nonlinear dampers. The NIE formulation is further applied to the nonlinear damping optimization problem, and it is found that this method is efficient for optimization.     

Nonlinear Response of Double Wall Sandwich Panels∗

An analytical study is presented to predict the nonlinear response of a double wall sandwich panel system that is subjected to random-type loading. Viscoelastic and nonlinear spring-dashpot models are chosen to characterize the behavior of the core. The nonlinear panel response is obtained by utilizing modal analyses and Monte Carlo simulation techniques. Numerical results include the response spectral densities, root-mean-square responses, and probability density function histograms. It is found that by proper selection of the dynamic parameters and damping characteristics, the structural response can be significantly reduced.     

The Forced Response of the Lamped Dynamic Systems

This paper deals with the forced harmonie responses of the discrete or continuous dampedsystems to harmonic excitation,where the viscous damping matrix cannot be diagonalized.Theexplicit expressions of the response solutions are given.Hence,with these expressions,some generaland analytical study of some phenomena in vibration is made.For example,the“fixed amplitudepoint”phenomena in the single damped systems have been demonstrated generally.The conditions,under which all forces that exert on the system and possess common phase,which will excite com-mon phase responses,are also discussed.The solutions deduced here only involve the inverse matrices of lower order.Thus,in thenumerical computation for digital computers,the method is more simple,economical,and accuratethan others.The method described here can be used in the analysis of unbalance responses of the rotorsystems.     

Upper Bounds on Deformations of Elastic-Workhardening Structures in the Presence of Dynamic and Second-Order Geometric Effects∗

Abstract

Discrete models of elastoplastic structures are considered, Piecewise linear yield conditions and hardening rules are assumed. On this basis, a deformation bounding method resting on the use of fictitious loads as proposed first by Ponter [6, 7], is developed for situations in which: (a) the geometry changes affect the equilibrium equations but their effects may be expressed by bilinear terms in the pre-existing stresses and additional displacements (“second-order geometric effects”); (b) inertia and viscous damping forces play a significant role. Comparisons are made with different bounding methods previously established by the author [3,4], for the same classes of structures and mechanical situations.     

Segregated and Synchronized Vector Solutions for Nonlinear Schrödinger Systems

We consider the following nonlinear Schrödinger system in ${\mathbb{R}^3}$ $$\left\{\begin{array}{ll}-\Delta u + P(|x|)u = \mu u^{2}u + \beta v^2u,\quad x \in \mathbb{R}^3,\\-\Delta v + Q(|x|)v = \nu v^{2}v + \beta u^2v,\quad x \in \mathbb{R}^3,\end{array}\right.$$ where P(r) and Q(r) are positive radial potentials, ${\mu > 0, \nu > 0}$ and ${\beta \in \mathbb{R}}$ is a coupling constant. This type of system arises, in particular, in models in Bose–Einstein condensates theory. We examine the effect of nonlinear coupling on the solution structure. In the repulsive case, we construct an unbounded sequence of non-radial positive vector solutions of segregated type, and in the attractive case we construct an unbounded sequence of non-radial positive vector solutions of synchronized type. Depending upon the system being repulsive or attractive, our results exhibit distinct characteristic features of vector solutions.     

Analysis of Motion Resisted by Friction. I. Constant Coulomb and Linear/Coulomb Friction∗

ABSTRACT

An exact method for analysis of the transient and steady-state response of harmonically excited frictional oscillators is presented. This method does not postulate antiperiodic type of motion. The method is used to analyze the motion of the constant Coulomb oscillator, under the following conditions: (a) transient conditions; (b) steady-state conditions in the region of multiple stops per cycle and in the presence of viscous damping, where it is shown that viscous damping tends to reduce the number of stops; and (c) at degenerate values of the ratio of driving frequency to natural frequency, where it is shown that unsymmetric motion with only one stop per cycle exists. Furtherfore, the method is applied in analysis of the motion of a linear/Coulomb oscillator, in the region of multiple stops per cycle.     

Optimization of a Thin-Walled,Anisotropic Curved Bar for Maximum Torsional Stiffness∗

ABSTRACT

ABSTRACT A curved bar in the form of a circular ring sector is under uniform torsion when acted upon by two equal and opposite forces directed alone the axis passing through the center of the ring and perpendicular to its plane, i.e., forces acting along the axis of rotation. The exact torsion theory can be extended to this case when the material of which the bar consists is cylindri-cally anisotropic, with the axis of anisotropy directed along the axis of rotation and having an elastic symmetry about any plane of the transverse cross section. In this paper, a thin-walled curved bar having the loading conditions and material properties described above is optimized so as to maximize its torsional stiffness. The optimization is carried out with respect to the cross-sectional shape of the bar subject to constraints on the transverse area (single-purpose design) and bending stiffness (multipurpose design). In the special case of an orthotropic material, the angle of inclination of the ortho-tropy axes with respect to the middle plane is optimally determined for a cross section with constant thickness. A perturbation method is used to obtain analytical solutions, and numerical results are presented indicating the efficiency of the designs and the optimal cross-sectional shapes.     

Crystal-Plasticity-Based Dynamic Constitutive Model of AZ31B Magnesium Alloy at Elevated Temperature and with Explicit Plastic-Strain-Rate Control

In this study,a series of experiments were carried out on the AZ31B magnesium alloy,including both a macro-experiment(mechanical experiment)and a micro-experiment(dislocation observation).Next,based on the consideration of the deformation mechanism of magnesium alloys(dislocation slip and twinning),a dynamic constitutive model of the magnesium alloy was established.In the developed model,the strain-rate-sensitivity control and the effect of temperature on the dynamic mechanical performance of the alloy were also investigated.The model parameters were determined by fitting the macroscopic experimental results.Next,the evolution of the micro-deformation mechanism was calculated by the developed model,and the trend of macro-mechanical behavior was also discussed.     

A Coordinate Reduction Technique for Dynamic Analysis of Spatial Substructures with Large Angular Rotations∗

A substructuring technique is presented for transient dynamic analysis of systems composed of interconnected rigid and elastic bodies that undergo large angular displacements. Displacement of elastic bodies is represented by superposition of local linear elastic deformation on large displacement of body reference coordinate systems. Elastic bodies are thus represented by combined sets of reference and local elastic generalized coordinates. Modal analysis and substructuring of individual elastic components allow for elimination of insignificant modes. Equations of motion and constraint are formulated in terms of mixed sets of modal and reference generalized coordinates. Planar and spatial linkages with flexible elements are presented to illustrate use of the method developed.     

A Structural Model of Ceramic Deformation and Fracture∗

ABSTRACT

A new structural model of deformation and fracture of ceramics is presented. The real material is simulated as a periodic grid of hexagonal elastic grains connected with elastic bondings. A method for deformation analysis of such a medium is introduced, and the effective modules of the material are calculated. The solution of the problem of wave propagation gives dispersion correlations. The deformation model introduced and the procedure of Fourier transforms yields a Green function for an infinite periodic grid of nondeformable hexagonal grains that are connected with elastic bondings. The fundamental solution is used to examine the strength of the medium with local defects and to compare it with the strength of a defectless material.     

Nonlinear modeling and dynamic analysis of the rotor-bearing system

To overcome the shortcomings of extreme time-consuming in solving the Reynolds equation, two efficient calculation methods, based on the free boundary theory and variational principles for the unsteady nonlinear Reynolds equation in the condition of Reynolds boundary, are presented in the paper. By employing the two mentioned methods, the nonlinear dynamic forces as well as their Jacobians of the journal bearing can be calculated saving time but with the same accuracy. Of these two methods, the one is called a Ritz model which manipulates the cavitation region by simply introducing a parameter to match the free boundary condition and, as a result, a very simple approximate formulae of oil-film pressure is being obtained. The other one is a one-dimensional FEM method which reduces the two-dimensional variational inequality to the one-dimensional algebraic complementary equations, and then a direct method is being used to solve these complementary equations, without the need of iterations, and the free boundary condition can be automatically satisfied. Meanwhile, a new order reduction method is contributed to reduce the degrees of freedom of a complex rotor-bearing system. Thus the nonlinear behavior analysis of the rotor-bearing system can be studied time-sparingly. The results in the paper show the high efficiency of the two methods as well as the abundant nonlinear phenomenon of the system, compared with the results obtained by the usual numerical solution of the Reynolds equation.     

Simulation of Initially Slackened and Stiffened Structures by Virtual Distortions∗

ABSTRACT

Variational principles and computational methods for analysis of initially slackened and stiffened structures are discussed. The simulation of clearances or internal dry fraction in structural elements by virtual (eigen) distortions is applied. Considerations presented are used in the problem of nonstandard design of structural settings, with clearances or friction in the structural joints, for load capacity maximization.     

Investigation of Continuously Differentiable Solutions Bounded on ℝ2 for Systems of Nonlinear Partial Integro-Differential Functional Equations with Linearly Transformed Arguments

For a system of partial integro-differential functional equations with linearly transformed arguments, we prove a theorem on the existence of a continuously differentiable solution bounded on ².