Nonlinear Bending of Circular Sandwich Plates

In this paper,fundamental equations and boundary conditions of non-linear axisymmetrical bending theory for the circular sandwich plates with asoft core are derived by means of the method of calculus of variations.Especial-ly in the case of very thin faces,the preceding fundamental epuations andboundary conditions simplity considerably.For example,a circular sandwichplate with edge clamped but free to slip under the action of uniform lateralload is considered.A more accurate solution of this problem has been ob-tained by means of the modified iteration method.     

Dynamic Synthesis of Substructures∗

ABSTRACT

A new approach is presented to synthesize dynamic properties of a system that is composed of multiple degree of freedom subsystems attached to a multiple degree of freedom primary system at several points. Natural frequencies and mode shapes of the combined system are obtained in terms of modal properties of the primary system, subsystems, and their interaction parameters. The present solution is compared to the exact solution as well as approximate solutions obtained by earlier investigators. Derived properties can be used in conjunction with any response spectrum or random vibration formulation, to obtain the deterministic or probabilistic dynamic response of subsystems to any arbitrary excitation.     

Dynamic Behavior of Rigid–Plastic Sector Plates

The paper studies the dynamic behavior of perfect rigid-plastic plates in the form of a sector with hinged or clamped sides under short-term intensive loads. Two dynamic deformation mechanisms are demonstrated. The dynamic equation is derived for each of the mechanisms. The realization conditions for the mechanisms are analyzed. Analytical expressions are derived for the ultimate (high) loads and the maximum residual deflection. Numerical examples are given     

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.     

On an Eigenvalue Problem Related to the Buckling of Sandwich Beams

This paper gives various properties of eigenvalue problems related to the buckling of sandwichbeams.The applications of eigenfunctions are also indicated.     

On The Reissner Theory of Bending of Flastic Plates

The Reissner equations of elastic plates are rederived on the bases of the incomplete generalizedvariational principle of Complementary energy.The Stress function to is naturally obtained from thevariational Calculation in the form of Lagrange multiplier.The stucture of solutions of the Reissnerequations is thus defined.On the bases of these discussions,a simplified theory has been put forward,in which the equations of equilibrium involving the shearing influence can be reduced into a fourthorder differential equation similar to those of the Classical theory of plates.     

Analysis of Stability on Elastic Plates with Initial Imperfections

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Constrained Optimal Design of Circular Plates Against Buckling∗

Several problems are investigated in which the buckling loads of structures are maximized, subject to the restriction that the volume of structural material is specified. In addition, a constraint is placed upon either the maximum allowable prebuckling stress, or the minimum allowable thickness. The structures analyzed are flat, axisymmetric circular plates, loaded by uniform radial thrust, and assumed to buckle axisymmetrically. The plates are investigated for both sandwich and solid cross-sectional geometries.     

Stability of Lofty Air-Supported Cylindrical Membranes∗

The use of air-supported membranes has attracted considerable attention in recent years. There are, however, a number of problems in the behavior of these structures that have not been fully investigated. For example, the problem of lateral stability of such membranes has not been discussed heretofore. The present paper presents an analysis of the sidesway instability of a cylindrical air-supported membrane with vertical longitudinal axis, subjected to concentrated loads applied nonsymmetrically. A critical value of the load is established at which the configuration of these structures changes dramatically. During such change the lower portion of the membrane comes into contact with the support surface. For the problem treated, safe load limits, critical lengths, and critical weight densities for the membrane are derived. The Lagrangian variational method is used throughout the paper in obtaining solutions.     

Elastic Critical Buckling of Welded Thin Steel Rectangular Plates∗

A theoretical approach for the study of the effect of residual stresses due to welding on the elastic critical buckling behavior of thin steel rectangular plates is described. A finite difference technique is utilized for the determination of in-plane residual stresses due to a weld, and the Rayleight-Ritz method is used for the critical buckling problem, with stresses due to external loads being superimposed on the residual stresses. A number of illustrative examples are included, showing the possible detrimental effect of residual stresses due to welding. An approximately linear relationship is shown to exist between the square of the natural frequency of lateral vibration and the drop in buckling strength, for certain loading conditions     

On the Influence of the Kinetic Energy¶on the Stability of Equilibria¶of Natural Lagrangian Systems

Natural Lagrangian systems (T,Π) on R ² described by the equation are considered, where is a positive definite quadratic form in and Π(q) has a critical point at 0. It is constructively proved that there exist a C ^∞ potential energy Π and two C ^∞ kinetic energies T and such that the equilibrium q(t)≡ 0 is stable for the system (T,Π) and unstable for the system . Equivalently, it is established that for C ^∞ natural systems the kinetic energy can influence the stability. In the analytic category this is not true. Accepted: October 20, 1999     

Optimization of Internal Line Support Positions for Plates Against Vibration∗

ABSTRACT

This paper presents a simple numerical method for determining optimal positions of internal line supports for an arbitrarily shaped plate, so as to maximize the fundamental frequency of its transverse vibration. The vibration analysis is performed using the pb-2 Rayleigh-Ritz method. Because this method does not require discretization, since it treats the entire plate with its boundary conditions as a kind of superelement, the optimization problem becomes relatively easy to solve. To illustrate the method, trapezoidal, elliptical, and semi-circular plates with at most two internal line supports are considered. The optimization exercise, for optimal locations of internal line supports, demonstrates significant improvement in the value of fundamental frequency when compared to that of plates with specified positions of internal supports.     

On the Stability in Weak Topology of the Set of Global Solutions to the Navier–Stokes Equations

Let X be a suitable function space and let ${\mathcal{G} \subset X}$ be the set of divergence free vector fields generating a global, smooth solution to the incompressible, homogeneous three-dimensional Navier–Stokes equations. We prove that a sequence of divergence free vector fields converging in the sense of distributions to an element of ${\mathcal{G}}$ belongs to ${\mathcal{G}}$ if n is large enough, provided the convergence holds “anisotropically” in frequency space. Typically, this excludes self-similar type convergence. Anisotropy appears as an important qualitative feature in the analysis of the Navier–Stokes equations; it is also shown that initial data which do not belong to ${\mathcal{G}}$ (hence which produce a solution blowing up in finite time) cannot have a strong anisotropy in their frequency support.     

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.     

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.     

Rigid Plastic Plates under a Concentrated Moving Load∗

A rigid-plastic rectangular plate subjected to a moving transverse load is analyzed. The load is too large for the plate to be supported under static conditions. The present study indicates that there is a critical value for the moving load, above which the crossing cannot be made, irrespective of its speed. The relation between the moving load and its speed is given for values less than ciritical, as well as the distribution of displacement for a simply supported rectangular plate.     

Dynamic Elastic Buckling of Complete Spherical Shells with Initial Imperfections∗

The dynamic elastic buckling behavior of a geometrically imperfect complete spherical shell that is subjected to a uniform external step pressure is examined using Sander's equilibrium and kinematic equations, appropriately modified to include the influence of inertia forces and initial stress-free imperfections in the radius. A finite-difference procedure with either the Houbolt or Park methods of time integration is used to predict the axisym-metric dynamic elastic buckling pressures and associated critical mode numbers. The dynamic buckling pressure is significantly smaller than the corresponding static value for small initial imperfections, but is less imperfection