Showing papers on "Deflection (engineering) published in 1968"
TL;DR: In this paper, the elastic buckling and initial postbuckling behavior of clamped shallow spherical shells under concentrated load is considered and it is found that bifurcation into an asymmetric deflection pattern will occur before axisymmetric snap-buckling unless the ratio of the shell rise to the thickness lies within a narrow range corresponding to relatively thick shells.
129 citations
TL;DR: In this article, the mathematical theory of thin elastic plates loaded by transverse forces leads to biharmonic boundary value problems, which can be solved numerically to a tolerable accuracy for any shape of boundary by digital computer programs.
Abstract: The mathematical theory of thin elastic plates loaded by transverse forces leads to biharmonic boundary value problems. These may be formulated in terms of singular integral equations, which can be solved numerically to a tolerable accuracy for any shape of boundary by digital computer programs. Particular attention is devoted to clamped and simply-supported rectangular plates. Our results indicate support for the generally accepted treatment of such plates and for the intuitive picture of deflection behaviour at a corner.
115 citations
TL;DR: In this paper, the calculated performance of electrostatic analyzers of the cylindrical and spherical deflection type are compared. And it is shown that considering geometrical terms through the third order the cylinrical device is significantly superior.
Abstract: The calculated performance of electrostatic analyzers of the cylindrical and spherical deflection type are compared. It is shown that considering geometrical terms through the third order the cylindrical device is significantly superior.
114 citations
104 citations
Journal Article•
TL;DR: In this paper, the authors present an application of the Finite ELEment technology to the analysis of a DIGITAL COMPUTER program, which is made of a two-layered PROTOTolerant system.
Abstract: AN APPLICATION IS DESCRIBED OF THE FINITE ELEMENT TECHNIQUE TO THE ANALYSIS OF SYSTEMS REPRESENTATIVE OF PAVEMENT STRUCTURES USE IS MADE OF A DIGITAL COMPUTER PROGRAM WHICH GENERATES SUITABLE FINITE ELEMENT CONFIGURATIONS FOR AXISYMMETRIC STRUCTURES AND ACCOMMODATES APPROXIMATIONS OF NONLINEARITY WHICH APPEAR APPROPRIATE TO REPRESENT THE BEHAVIOR OF GRANULAR BASE AND COHESIVE SUBGRADE MATERIALS UNDER CONDITIONS CORRESPONDING TO MOVING TRAFFIC EXAMPLES ARE PRESENTED FOR SYSTEMS WITH LINEAR MATERIAL PROPERTIES SHOWING COMPARISONS BETWEEN DISPLACEMENTS AND STRESSES COMPUTED USING THE FINITE ELEMENT TECHNIQUE AND THOSE COMPUTED USING ELASTIC HALF-SPACE AND LAYERED SYSTEM ANALYSES TO ESTABLISH CRITERIA FOR BOUNDARY CONDITIONS IN THE FINITE ELEMENT PROCEDURE FOR THE ELASTIC HALF-SPACE SUBJECTED TO A UNIFORM CIRCULAR LOAD, DISPLACEMENTS AND STRESSES COMPUTED BY THE FINITE ELEMENT TECHNIQUE COMPARE FAVORABLY WITH THOSE DETERMINED FROM THE BOUSSINESQ SOLUTION WHERE THE NODAL POINTS IN THE FINITE ELEMENT PROCEDURE ARE FIXED AT A DEPTH OF 18 RADII FOR THE BOTTOM BOUNDARY AND CONSTRAINED FROM MOVING RADIALLY ON THE VERTICAL BOUNDARY AT A DISTANCE OF ABOUT 12 RADII FROM THE CENTER TWO ANALYSES ARE PRESENTED FOR DEFLECTION DETERMINATIONS FOR AN INSERVICE PAVEMENT NEAR GONZALES, CALIF, ONE FOR A CONDITION WHERE THE ASPHALT CONCRETE WAS AT A COMPARATIVELY HIGH TEMPERATURE (STIFFNESS MODULUS IN THE RANGE 120,000 TO 280,000 PSI), AND THE OTHER WITH THE MATERIAL AT A LOW TEMPERATURE (STIFFNESS MODULUS APPROXIMATELY 1,500,000 PSI) NONLINEAR MATERIAL PROPERTIES, DETERMINED FROM THE RESULT OF REPEATED LOAD TRIAXIAL COMPRESSION TESTS, WERE USED TO REPRESENT THE BEHAVIOR OF THE UNTREATED GRANULAR BASE AND SUBBASE AND THE FINE-GRAINED SUBGRADE SOIL DEFLECTIONS PREDICTED BY THE FINITE ELEMENT PROCEDURE ARE IN THE SAME RANGE AS THOSE MEASURED WITH THE CALIFORNIA TRAVELING DEFLECTOMETER INDICATING THAT THE METHOD HAS POTENTIAL TO SIMULATE ACTUAL PAVEMENT BEHAVIOR TO A REASONABLE DEGREE THE ANALYSIS ALSO INDICATES THAT WHEN THE EXTENSIONAL STRAINS IN THE ASPHALT CONCRETE ARE LARGE FOR THIS PAVEMENT (IE, WHERE THE STIFFNESS OF THE ASPHALT BOUND MATERIAL IS LOW), THE GRANULAR MATERIAL EXHIBITS A VERY LOW MODULUS UNDER THE LOADED AREA AND A LARGE PROPORTION OF THE SURFACE DEFLECTION CAN BE ATTRIBUTED TO DEFORMATIONS WITHIN THIS MATERIAL ON THE OTHER HAND, WHEN THE ASPHALT LAYER IS STIFF, THE MAJORITY OF THE SURFACE DEFLECTION IS CONTRIBUTED BY THE SUBGRADE AN ANALYSIS IS ALSO PRESENTED FOR THE RESULTS OF PLATE LOAD TESTS ON A TWO- LAYER PROTOTYPE PAVEMENT CONSISTING OF GRANULAR BASE AND A COHESIVE SUBGRADE SOIL USING THE SAME NONLINEAR CHARACTERIZATION FOR MATERIAL PROPERTIES AS FOR THE IN- SERVICE PAVEMENT /AUTHOR/
86 citations
TL;DR: In this paper, it was shown that the Timoshenko equations may be much more accurate if the deflection and rotation of the centroidal element of a cross-section is defined in terms of average values over the cross-sectional area.
Abstract: The deflection and rotation which appear in Timoshenko's beam theory may be defined either (a) in terms of the deflection and rotation of the centroidal element of a cross-section or (b) in terms of average values over the cross-section. By consideration of an example for which a theoretically exact solution is available it is shown that the Timoshenko equations may be much more accurate if the latter definition is adopted. The example considered is the vibration of a simply-supported beam of narrow rectangular cross-section. The accuracy of the Timoshenko theory depends on the slenderness ratio of the beam, but even when the depth of the beam is equal to the length the Timoshenko theory differs from the exact solution by less than 3.5% provided definition (b) is adopted. Far larger errors occur if definition (a) is used, the most serious error being associated not with shear deformation but with the moment-curvature relation.
76 citations
01 Sep 1968
75 citations
TL;DR: In this paper, the analysis of large deflections of rectilinear frames subjected to arbitrary discrete loads and boundary conditions is presented, where the problem is formulated as a system of simultaneous nonlinear equations obtained by combining the general solution of the exact nonlinear differential equation of bending and the equilibrium equations obtained for each of the segments between load points and/or points of discontinuity in curvature.
Abstract: The analysis of large deflections of rectilinear frames subjected to arbitrary discrete loads and boundary conditions is presented. The problem is formulated as a system of simultaneous nonlinear equations obtained by combining the general solution of the exact nonlinear differential equation of bending and the equilibrium equations obtained for each of the segments between load points and/or points of discontinuity in curvature, along with the prescribed boundary conditions. The system of equations is solved by a modified Newton-Raphson procedure. A stability criterion dependent upon the properties of the load-deflection curve and the relationships between the displacements is used to study the stability of the frame. These curves are readily constructed for the entire loading history of the frame by the incremental load method, thus making it possible to study the pre-buckling as well as the post-buckling behavior of the frame. Examples are given to illustrate the method of analysis for a frame which remains stable throughout its entire loading history and for frames which exhibit either a bifurcation or a snap-through type of instability.
73 citations
TL;DR: In this paper, the authors used the extended kantorovich method to analyze a clamped rectangular plate subjected to a uniform lateral load and found that the generated one term solution approximates very closely, throughout the plate region, not only the deflections but also the bending moments and shearing forces.
Abstract: The extendedKantorovich method discussed recently, byA. D. Kerr, is used to analyze a clamped rectangular plate subjected to a uniform lateral load. It was found that the generated one term solution approximates very closely, throughout the plate region, not only the deflections but also the bending moments and shearing forces. It is shown that the final form of the solution is independent of the initial choice, and that the convergence of the iterative procedure is very rapid. Because of the lack of a closed form exact solution in the technical literature, the coefficients occurring in the obtained solution were evaluated for various plate side ratios and are presented in graphs in order to simplify the utilization of the obtained results in engineering practice.
71 citations
31 Dec 1968
TL;DR: In this article, a displacement-type finite element of triangular shape is developed and applied to the solution of several problems in the bending of plates The deflection is represented by a fifth degree polynomial in the Cartesian co-ordinates of the midplane Six deflection parameters are specified at each vertex, yielding a total of 18 degrees of freedom for the element.
Abstract: A fully conforming, displacement-type, finite element of triangular shape is developed and applied to the solution of several problems in the bending of plates The deflection is represented by a fifth degree polynomial in the Cartesian co-ordinates of the mid-plane Six deflection parameters, namely the displacement and its first and second derivatives, are specified at each vertex, yielding a total of 18 degrees of freedom for the element Examples treated include static and dynamic analyses of a square plate with edges simply supported or clamped; statics of a triangular, simply-supported plate; and vibrations of cantilevered triangular plates Rates of convergence of the finite element approximations are investigated both theoretically and numerically Excellent accuracy is achieved in all cases, and the rates of error convergence agree closely with predicted asymptotic values
Patent•
24 Jan 1968
TL;DR: In this paper, a construction member is defined as a member of a construction team that is equipped with a hardened resin, where the resin can be used in conjunction with other constructors.
Abstract: A CONSTRUCTION MEMBER FORMED OF GLASS FIBER ELEMENTS IMPREGNATED WITH A HARDENED RESIN WHEREIN THE MEMBER HAS SUFFICIENT STRENGTH CHARACTERISTICS TO BE USED IN CONJUNCTION WITH OTHER CONSTRUCTION MEMBERS, OR MAY BE USED SEPARATELY, SUCH AS TO FORM A POLE OR THE LIKE. SUPERIOR STRENGTH CHARACTERISTICS ARE OBTANED BY INTERPOSING GLASS FIBER ROD TYPE ELEMENTS BETWEEN GLASS FIBER FABRIC LAYERS IMPREGNATED WITH A HARDENED RESIN WHEREIN THE RESIN BONDS THE FABRIC LAYERS TO EACH OTHER AND TO THE RODS TO PRODUCE AN ALL GLASS FIBER AND RESIN MEMBER CAPABLE OF WITHSTANDING HIGH BENDING MOMENT, AND LATERAL FORCES, WITHOUT EXCESSIVE DEFLECTION.
Patent•
11 Jun 1968
TL;DR: In this article, the authors describe a scenario in which the non-rotative SHAFT of a CONTROLLED DEFLECTION ROLL ASSEMBLY, is formed by one or more PISTONS working in cycleliners, each of which has a HYDROSTATIC BEARING PAD on its pressure-applying end.
Abstract: THE RADIAL-ACTING PRESSURE-APPLYING MEANS REQUIRED BETWEEN THE NONROTATIVE SHAFT AND THE ROTATIVE SHELL ENCIRCLING THIS SHAFT OF A CONTROLLED DEFLECTION ROLL ASSEMBLY, IS FORMED BY ONE OR MORE PISTONS WORKING IN CYLINDERS MOUNTED BY THIS SHAFT THE ONE OR MORE PISTONS EACH HAS A HYDROSTATIC BEARING PAD ON ITS PRESSURE-APPLYING END WHICH WORKS AGAINST THE INSIDE OF THE SHELL ROLL SO THAT THIS INSIDE PROVIDES THE RUNNER OF A HYDROSTATIC BEARING ASSEMBLY
TL;DR: It appears from the general similarity of bending and torsional stiffness and from thegeneral improvement in maximum torsion deflection that the stainless steel instruments would be more advantageous for clinical use.
TL;DR: In this paper, two classes of EO prism configurations for light beam deflection are proposed and design curves for KD*P and LiNbO 3 deflectors using focused laser beams at room temperature are plotted.
Abstract: Two classes of special EO prism configurations for light beam deflection are proposed. Simple formulas expressing resolvable spots N R and deflection angle φ in terms of the induced optical path difference between the two boundary rays of a parallel beam traversing the prisms are derived and are used to compare the relative merits of the special prism configurations. Design formulas for prisms in tandem are laid down. As examples, design curves for KD*P and LiNbO 3 deflectors using focused laser beams at room temperature are plotted. Some problems related to two-dimensional deflection are discussed.
TL;DR: In this paper, an analysis capability for predicting the nonlinear behavior of elastic structural systems that can be adequately idealized with rectangular plate and cylindrical shell discrete elements is reported, where displacement patterns in each element are approximated in terms of products of one-dimensional al, first-order Hermite interpolation polynomials and undetermined nodal displacement parameters.
Abstract: An analysis capability for predicting the nonlinear behavior of elastic structural systems that can be adequately idealized with rectangular plate and cylindrical shell discrete elements is reported. The displacement patterns in each element are approximated in terms of products of one-dimension al, first-order Hermite interpolation polynomials and undetermined nodal displacement parameters. Geometric admissibility of the displacement state for an assembled set of these discrete elements can be readily assured. Incorporation of geometric nonlinearities in the strain-displacement relations permits the prediction of finite displacements. For example, elastic postbuckling behavior can be analyzed using this method. The option to impose a prescribed end-shortening and then determine the boundary-force distribution required to maintain the resulting displacement pattern is a valuable feature of this capability. Numerical solutions are obtained by direct minimization of the total potential energy. The elastic postbuckling behavior of a flat-plate panel and a cylindrical shell panel are presented as examples. The applicability of these discrete elements to predicting the elastic postbuckling behavior of integrally stiffened plate and cylindrical shell panels is provided by the assumed element displacement patterns.
TL;DR: In this article, a series of the characteristic functions representing the normal modes of vibration are taken as the approximating functions for the bending displacements in the directions of the co-ordinate axes, leading to a considerable reduction in the number of elements in the final matrix equation and also considerably reducing the computing time.
Abstract: The Rayleigh-Ritz method is used to determine the natural frequencies and mode shapes of vibration of pre-twisted rectangular cross-section beams. The method is dependent upon a good choice of approximating functions for the dynamic deflection curves. In the present analysis, series of the characteristic functions representing the normal modes of vibration are taken as the approximating functions for the bending displacements in the directions of the co-ordinate axes. The choice of this particular series leads to a considerable reduction in the number of elements in the final matrix equation and also considerably reduces the computing time.The natural frequencies of vibration are obtained for various width-to-thickness ratio beams with pre-twist angle in the range 0-90°, and the mode shapes of vibration are presented for one particular width to thickness ratio beam. The results are compared to results obtained by other methods and to experimental results, and good agreement is shown to exist.
01 Apr 1968
TL;DR: Performance evaluation of annular plug and expansion-deflection nozzles including external flow effects at transonic Mach numbers is presented in this article. But the evaluation is limited to transonic numbers.
Abstract: Performance evaluation of annular plug and expansion-deflection nozzles including external flow effects at transonic Mach numbers
TL;DR: In this paper, the behavior of several multistory, one-bay and two-bay planar frames is examined by means of computerized elastic-plastic analysis, where each frame is unbraced, fixed at its base, and loaded by static, proportional forces up to the maximum load carrying capacity.
Abstract: The behavior of several multistory, one-bay and two-bay planar frames is examined by means of computerized elastic-plastic analysis. Each frame is unbraced, fixed at its base, and loaded by static, proportional forces up to the maximum load carrying capacity. The results of first-order elastic-plastic analyses are used as a basis for classifying and explaining the behavior of second-order models. The magnitudes of second-order effects on both load carrying capacity and deformations are presented. The influence of axial deformation is included in the examination of frame behavior.
TL;DR: In this paper, the mild steel reinforcement has been successfully bonded to the wood by adhesives, and the reinforced beams have behaved as a true composite within the elastic range, and a substantial decrease of deflection and increase of load carrying capacity have been obtained.
Abstract: Preliminary results on the reinforcing of glue-laminated wood beams are presented and a new method of reinforcing such beams with mild steel strips is described. With this method the reinforcement can be effectively concealed and the beam will retain its natural appearance. The mild steel reinforcing has been successfully bonded to the wood by adhesives, and the reinforced beams have behaved as a true composite within the elastic range. Considerable decrease of deflections and increase of load carrying capacity have been obtained. The stiffness of the beams reinforced on the top and bottom surfaces, has been increased 100% and greater. Shear deflection varied between 14% and 19% of the total deflection and has been an important factor in deflection calculations.
01 Oct 1968
TL;DR: In this article, the authors present workable methods of analyses for thin, elastic shells of revolution, and provide computer programs for performing such analyses by means of these methods, the following problems for a thin elastic shell of revolution can be solved: (1) stresses and deflections can be determined when the shell is subjected to arbitrary mechanical and/or thermal loads; (2) natural frequencies and mode shapes can be found for free vibration for a shell subject to or free of prestress.
Abstract: : This project was undertaken to present workable methods of analyses for thin, elastic shells of revolution, and to provide computer programs for performing such analyses. By means of these methods, the following problems for a thin, elastic shell of revolution can be solved: (1) stresses and deflections can be determined when the shell is subjected to arbitrary mechanical and/or thermal loads; (2) natural frequencies and mode shapes can be found for free vibration when the shell is subjected to or is free of prestress; (3) buckling loads, according to the classical stability theory, can be found when the shell is subjected to axisymmetric or sinusoidal nonsymmetric prestress. (Author)
TL;DR: In this article, the duality between the basic equations and the dependent variables in problems of stretching and of bending of plates is applied to the finite element method, and a displacement method is a stress function method in the bending problem and vice versa.
Abstract: The duality between the basic equations and the dependent variables in problems of stretching and of bending of plates is applied to the finite element method. A displacement method in the stretching problem is a stress function method in the bending problem and vice versa. The stress function method has the same properties of accuracy and convergence as the well established dual displacement method for plate stretching, using only two equations per node. A computer program, originally written for the analysis of plane stress and plane strain problems by the displacement method, is used to solve plate bending problems. Results show that a high degree of accuracy may be achieved for the stress couples. The determination of the deflection and slopes is made from the curvatures and involves no loss of accuracy. Comparisons with results of the fully compatible displacement method are presented.
TL;DR: In this article, the expected deflection and expected bending moment of an infinitely long elastic beam subject to a moving concentrated force whose position is a stochastic function of time is analyzed.
Abstract: The problem considered is that of an infinitely long elastic beam subject to a moving concentrated force whose position is a stochastic function of time, X(t). The expected deflection and expected bending moment are analyzed, with special attention being given to the case of a stationary process X(t) and to the case in which X(t) is a Wiener process.
TL;DR: In this paper, the non-linear bending equation for a cantilever beam with a perpendicular load applied at the tip, undergoing large deflections, is solved by computer methods for both rectangular and round cross-sections, for varying degrees of taper and are compared with values obtained by laboratory tests.
TL;DR: In this article, the stiffness influence coefficients of a pile are derived from simple matrices defining elastic constants and position or from a list of equations, and the elastic constants dependent on bending may be derived in several ways including tests or physical models based on an assumed behavior of the system such as: a semi-infinite beam on an elastic foundation, a free cantilever fixed at an assumed depth, or as a free camber fixed to a semi infinite beam on a elastic foundation.
Abstract: Analysis of pile foundations is accomplished by calculation of the stiffness influence coefficients. Piling loads and deflections can be determined, as well as the principal frequencies. Axial and torsional elastic constants for a pile may be adjusted to the physical problem; the torsional constant has negligible effect and may usually be neglected. The elastic constants dependent on bending may be derived in several ways including tests or physical models based on an assumed behavior of the system such as: a semi-infinite beam on an elastic foundation, a free cantilever fixed at an assumed depth, or as a free cantilever fixed to a semi-infinite beam on an elastic foundation. The stiffness influence coefficients may be formed from simple matrices defining elastic constants and position or from a list of equations.
TL;DR: In this article, the postbuckling behavior of truncated conical shells under a temperature distribution was studied and thin shell theory and finite-deflection relations were used in the geometric compatibility equation as well as the boundary conditions.