Two-dimensional Loading Research Articles

A Combined Approach to the Pallet Loading Problem

Abstract In this paper the two-dimensional pallet loading problem is considered: that is, the problem of loading a rectangular pallet of size L by W, drawing from a set of n rectangular boxes. The objective is to maximize the area covered on the pallet by the boxes loaded. The problem is approached using a combination of dynamic programming and heuristics. The structured solutions resulting from the application of the dynamic program have two serendipitous characteristics: any item may be placed on the periphery of the pallet for easy access, and some control may be retained over the center of gravity of the pallet. Computational results are given.

Equivalence of the energy and force approaches in the theory of cracks in the general case of two-dimensional loading

Equivalence of the energy and force approaches in the theory of cracks in the general case of two-dimensional loading

High-speed two-dimensional electron-gas FET logic

Ring oscillators using planar enhancement-mode two-dimensional electron-gas FETs (TEGFETs) and ungated transistor loads are described. A propagation delay time of 19.1 ps has been measured at room temperature, the lowest yet reported for this temperature. Improvements on materials and circuit design should lead to a delay time of 10 ps at 300 K.

Bilinear Model for Coated Square Fabrics

An idealized composite model of a square biaxially loaded coated fabric is proposed. The model consists of straight linearly elastic yarns embedded in a thin layer of a linearly elastic isotropic coating material with the system loaded in the plane of the membrane. Governed by the assumptions of small strains, equations describing the material behavior are derived for a general state of two-dimensional loading. The resulting system of nonlinear simultaneous equations are then solved numerically for a range of coating and yarn properties. For relatively low stresses, the response is governed by the mechanism of crimp interchange and coating deformation, and at higher stresses the response is governed by yarn and coating properties. The general nonlinear result is further approximated by a set of bilinear equations and a procedure for evaluating definitive model parameters from data obtained from uniaxial tests is presented.

A pseudo three-dimensional finite element formulation for elastostatic problems and its geophysical applications

A special class of three-dimensional elastostatic problems sometimes encountered in geology, geophysics, and engineering involves structures which can be reasonably represented by two-dimensional bodies but for which two-dimensional load functions are not suitable approximations, for example, ocean tidal loading of continental margins and localized loading of linear geological features such as faults and dipping strata. A pseudo three-dimensional finite element formulation capable of treating these problems has been developed which involves a system of two-dimensional finite element equations with sinusoidally distributed loads along the third direction. Solutions to the system of equations yield three components of displacement at each nodal point. By means of Fourier synthesis a variety of arbitrarily shaped load functions can be constructed. The present technique does not require the exceedingly large computer storage capacity usually necessary for solving general three-dimensional elastostatic problems. The present finite element formulation has been applied to the problem of tidal gravity response due to ocean tidal loading on continental margin structures. Two different continental margin models were adopted, one having a uniform mantle and the other having a layered laterally heterogeneous mantle. Applied sinusoidally distributed loads include spatial wavelengths between 50 and 1000 km. The results indicate that for the surface vertical displacement and the load-induced gravity variation the influence of the transition between oceanic and continental crustal and upper mantle structures is most pronounced for loads located over the transition zone and is significant only within a limited region surrounding the transition zone. For any given location and load wavelength the values of the vertical surface displacement resulting from loads acting on the transition region, as expected, lie between the corresponding values resulting from loads acting on a purely oceanic crustal and upper mantle structure and on a purely continental crustal and upper mantle structure.

Closure to “Cable Movements Under Two-Dimensional Loads”

Closure to “Cable Movements Under Two-Dimensional Loads”

Cable Movements Under Two-Dimensional Loads

A numerical method is presented for the determination of the deflected shape of a suspended cable subjected to a general two-dimensional system of gradually applied, concentrated loads. Cable sag is treated. The equations of static equilibrium for the various load points and cable segments between load points are solved in terms of geometrical compatibility requirements by systematic, successive approximations. Other effects, such as temperature change, yielding of the supports, slipping of the cable at the supports, and uniformly distributed loads along parts of the span, are included. Two classes of suspended cable problems are considered: Loads attached at specified points along the cable, and the vertical and horizontal movements of the cable under these loads are determined; and the horizontal location of the final positions of the load points is specified, and the deflections of the load points and the location of their points of attachment in the unstressed condition of the cable are directly determined. The use of the method is demonstrated in three examples.

A Note on the Supersonic Panel Flutter of Oblique Clamped Plates

Summary and IntroductionRecently, the effect of sweepback on the boundaries of supersonic panel flutter was studied in Ref. (1), (2) and (3), all of them dealing with rectangular plates.The present note considers the problem of panel flutter boundary of plates in the shape of a parallelogram with all edges clamped.It is assumed that Ackeret's theory of linearised two-dimensional supersonic aerodynamic loading gives an adequate approximation to the air forces for high Mach numbers.The criterion of instability is the coalescence of frequencies.A four-mode solution was obtained by means of Galerkin's method using first two streamwise and spanwise deflection modes. The results are represented in the form of diagrams for different aspect ratios(a/b)and sweep angles(ϕ).

A Method for Investigating Certain Eigenvalue Problems of the Buckling and Vibration of Plates

In a recent investigation, a method was given for the approximate solution of certain boundary-value problems. This method lends itself well to the use of the electronic digital computer and is extended here to investigate the eigenvalue problems of the buckling under two-dimensional hydrostatic loading and the vibration of thin plates. The two-dimensional hydrostatic buckling loads of clamped square and equilateral-triangular plates are found by this method, the values agreeing well with the results obtainable by other methods where these results are known.

Stress-Strain Response of Fabrics Under Two-Dimensional Loading

The general philosophy of biaxial testing is discussed and several criteria estab lished for the performance of such tests. Existing testers have been evaluated in the light of these criteria and shortcomings pointed out. A tester developed in 1952 and embodying the more important principles is described, and some selected results are presented to indicate the possible scope of operation. Subsequent publications will be concerned with analysis of data on mechanical fabrics.