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Stiffness variations and wave propagation in railway catenaries are the main sources of contact loss between the pantograph and the railway catenary. The pre-sag of a contact wire is sometimes introduced to compensate for the stiffness variation. To include the pre-sag’s influence on the dynamic interaction of the pantograph–catenary, we present a modified single-degree-of-freedom (SDOF) dynamic system with a time-varying stiffness that is based on a simplified model from a previous study. The pantograph–catenary parameters that are related to the optimal pre-sag to minimise variations in the contact force are obtained by solving the equations of the SDOF dynamic system. The amount of optimal pre-sag is determined from parameters such as speed, span length, uplift, and the stiffness variation coefficient. Because wave propagation is not allowed in the SDOF model, we investigate the influence of pre-sag on the dynamic interaction between the pantograph and the catenary by using both SDOF and finite element method (FEM) models. These models show that, by using the optimal pre-sag, we can significantly reduce the variation in the contact force in the medium-speed range, which is near the 1/2 sub-resonance speed. The influence of pre-sag is confirmed by a field test that was performed on a Korean conventional catenary. However, the FEM model shows that in the high-speed range near 300 km h −1 , the introduction of the pre-sag can reduce the variation in the contact force slightly only if uplift force subject to the pantograph is large enough to cause slackening in the droppers next to the supports. Otherwise, it does not reduce the variation in the contact force. The FEM also shows that the optimal pre-sag (less than 1/2000 of span length) in the high-speed range is much smaller than that (about 1/1000 of span length) in the medium-speed range.

An energy-based method is developed in the present paper to evaluate the damping property of a stay cable when transversely attached to a viscous damper. The overall increase of the cable damping offered by the external damper is determined by examining the time history of the kinetic energy in the damped cable. The concept of kinetic energy decay ratio is introduced as a key index to evaluate the effectiveness of a damper design in suppressing cable vibration. Compared to earlier studies, the proposed energy-based approach has no restrictions on the damper location. In addition, the flexural rigidity and sag extensibility of the cable are included in the formulation. Numerical simulation of free vibration of a damped stay cable is conducted using ABAQUS. To assist the design process, a set of damping estimation curves, which directly relate a damper design with the corresponding equivalent structural damping in a damped cable are developed for the practical parameter ranges of bridge stay cables. A number of numerical examples are presented. The validity and accuracy of the proposed method and damping estimation curves are verified by comparing with other studies. Results show that the energy-based approach developed in the present study is effective and efficient in determining the overall damping property of a cable-damper system, particularly in the preliminary stage of a damper design. In addition, the flexible applications of the developed damping estimation curves to damper design are demonstrated through these examples.

This paper addresses the Jacobian analysis of a long-span cable-driven manipulator. The Jacobian matrix that maps the infinitesimal change of the cable length coordinate to that of the end-effector coordinate is deduced and then employed to numerically achieve the forward solution of cable-driven manipulators in the static state or moving slowly enough to neglect their dynamics. The catenary curve is utilized to account for the cable sag effects. Therefore, determining the Jacobian matrix involves not only the geometrical constraints but also the equilibrium equations of the manipulator. The incremental relationship between the displacement of the end-effector and the cable length variation is derived according to the static equilibrium equations. Numerical examples of the feed supporting system of a large radio telescope show that the method proposed can successfully find the forward solution with a very high precision.

This paper presents results of a study on the stability capacity and lateral bracing force of wood beam-columns subjected to biaxial eccentric compression loading. A numerical analysis model based on the column deflection curve method was developed. The model considers nonlinear parallel-to-wood-grain stress-strain relationship, size and stress distribution effects of wood strength, shear deformation, and the P-Delta effect of compression load. Material property tests and biaxial eccentric compression tests of wood beam-columns were conducted to provide input parameters and verification for the model. Good agreement was achieved. The adequacy of the 2% rule of thumb was also studied.

Stiffeners which are used to strengthen a plate can be constructed of piezoceramic materials and subsequently used as piezo actuators to improve the load carrying capacity of the plate. In the present study, a fibre composite plate with initial imperfections and under in-plane compressive loads is studied with a view towards minimizing its deflection using the piezo actuators and the fibre orientations. Piezoceramic stiffeners are bonded symmetrically on the top and bottom of the plate and deployed as actuators. Two cases of electric fields, namely, the in-phase and out-of-phase voltages are applied to the actuators. The presence of initial deflections leads to deformation under the in-plane compressive loads which should be less than the critical buckling load. Two cases of initial imperfections are considered, and the first one is the deterministic initial deflections which are known a priori and as such they are given as input parameters for the problem. In the second case the initial deflections are uncertain and they have to be obtained according to a given criterion. In the present study they are determined to produce the least favourable initial deflection (largest deflection) at a given point and the solution is obtained by convex modelling. The effect of the actuators, the ply angles and the voltage are studied and their effects on the transverse deflection are investigated. A performance index involving the L2 norm of the deflections is minimized using the piezo effect and as well as the ply angles the optimal values of which are determined for various problem parameters.

In the analysis and design of steel–concrete composite girders of a bridge, deflections, stresses, and strengths are typically obtained from elementary beam bending theory by utilizing the effective flange width concept. Shear lag effects are accounted for indirectly, by replacing the actual slab width by an appropriate reduced “effective” width. Besides the exact numerical values that can be given by numerical analysis of a bridge, it is necessary that code provisions should provide simplified practical method of evaluation of effective flange width without significant loss of accuracy. So each code implements different ideas and approaches for specifying effective flange width. Comparing them highlights distinct philosophies underlying the various effective width code formulations, which is the main objective of this paper. In this paper, the effective flange width provisions in the US, Britain, Canada, Japan, and European Committee are presented and compared. Characteristics of each provision are briefly described and summarized. Numerical comparisons for simply-supported spans and negative moment regions of continuous spans follow. The paper concludes with a summary outlining the commonalities and main differences among all these provisions.

In this paper, an experimental investigation is carried out to determine the important factors in causing cracks and the rupture of steel members and their elements under large imposed and repeated deformations, and the quantitative relationships between the important physical factors leading to failure. Nine thin-plates and 28 angles served as specimens, and were subjected to repeated axial loading after undergoing inelastic buckling. Particular attention was paid to the effects of loading patterns, failure modes, and the cross-sectional shape of the very-low-cycle fatigue behavior under repetitious loading in the order of a few to 20 cycles. The experimental results show that energy dissipation capacity depends on the entire history of loading, the failure mode, the slenderness ratio, and the width-to-thickness ratio. No simple quantitative relations were observed between the initiation of the visible cracks or rupture and the energy dissipation capacity. The maximum values of residual “net” strains are found to range from 25% to 40%, independent of the test parameters.

A series of elastoplastic large deflection FEM analyses has been performed on hatch covers of bulk carriers subjected to lateral load. Two types of hatch covers are considered which are the folding type and the side-sliding type. For the folding-type cover, one size is considered which is for Handy size bulk carrier, whilst for the side-sliding-type cover, two sizes are considered which are for Panamax and Cape size bulk carriers. For each type, two hatch covers are selected which are designed in accordance with the old ICLL rule and new IACS rule, respectively. Calculated collapse strengths are compared with individual design loads, and a strength assessment is performed. On the basis of collapse behaviour observed in FEM analyses, a simple method is proposed to evaluate the collapse strength of a hatch cover subjected to lateral load. It is confirmed that the collapse strength is accurately predicted by the proposed method.

This paper proposes engineering estimation equations for the maximum deflection of a cylinder subject to bending under elastic–plastic and elastic–creep conditions. Being based on the reference stress approach, the proposed equations are simple to use and can accommodate general tensile and creep behaviors. Validation against detailed 3D finite element (FE) results using actual stress–strain data and realistic creep-deformation data shows excellent agreement, which provides confidence in the use of the proposed equation. Based on the proposed equations, together with information on in-service inspection data, discussion is given how to estimate future time-dependent and time-independent deflection of the CANDU pressure tube. Thus, the present result would be valuable information for integrity assessment of the CANDU pressure tube.

The paper deals with the non-linear dynamic analysis of cables with a pair of viscous dampers close to one support. Such cables are characterized by a sag-to-chord-length ratio below 0.02, for which natural frequencies for the vertical and the horizontal vibrations are pair-wise close. Under resonance the non-linear coupling of pairs of modes may cause whirling harmonic motions around the chord line. Whirling motion may occur after bifurcation from single-mode response for harmonic loads in either vertical or horizontal direction. The non-linear features are included in the two coupled modes, while all other modes are treated as linear. The motion is discretized by expansion in terms of the damped complex eigenfunctions. The applied base functions fulfil the transition condition at the damper, leading to fast convergence of the expansion. It is demonstrated that the behaviour of the whirling motion is controlled primarily by the damper acting in the direction of the unloaded mode, whereas the magnitude of the damper in the loaded mode is less important. If the dampers in the vertical and horizontal direction are close to the optimal value of the corresponding taut cable case, substantial reduction of the vibration level of the whirling mode as well as the frequency interval of its occurrence is attained.

For the purpose of developing a vibration-based tension force evaluation procedure for bridge cables using measured multimode frequencies, an investigation on accurate finite element modelling of large-diameter sagged cables taking into account flexural rigidity and sag extensibility is carried out in this paper. A three-node curved isoparametric finite element is formulated for dynamic analysis of bridge stay cables by regarding the cable as a combination of an “ideal cable element” and a fictitious curved beam element in the variational sense. With the developed finite element formulation, parametric studies are conducted to evaluate the relationship between the modal properties and cable parameters lying in a wide range covering most of the cables in existing cable-supported bridges, and the effect of cable bending stiffness and sag on the natural frequencies. A case study is eventually provided to compare the measured natural frequencies of main cables of the Tsing Ma Bridge and the computed frequencies with and without considering cable bending stiffness. The results show that ignoring bending stiffness gives rise to unacceptable errors in predicting higher order natural frequencies of the cables, and the proposed finite element formulation provides an accurate baseline model for cable tension identification from measured multimode frequencies.

In this paper a realistic estimation of the effective breadth of a stiffened plate is presented. For the estimation of the effective breadth the adopted model contrary to the models used previously takes into account the resulting inplane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists in isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The forces at the interface, which produce lateral deflection and inplane deformation to the plate and lateral deflection and axial deformation to the beam, are established using continuity conditions at the interface. The solution of the arising plate and beam problems, which are nonlinearly coupled, is achieved using the analog equation method. After the solution of the plate––beams system is achieved, the distribution of the axial stresses across the plate, resulting from both the bending and the inplane action of the plate, is obtained. Integrating this distribution across the plate the values of the effective breadth are obtained. The influence of these values from the beam stiffness and their variation along the longitudinal direction of the plate are shown as compared with those obtained from various codes through numerical examples with great practical interest.

WOS: 000172089100008 Two deflection functions due to both flexure and shear of an orthotropic cantilever beam subjected to both point and distributed loads have been obtained by the use of anisotropic elasticity theory. The deflections at the free end of the beam are calculated in order to see the effect of shear by using the obtained functions for different materials and fiber directions. In particular, when the cross-sectional height to beam-length ratio is equal to or greater than 0.25 or when the fiber directions are 0 and 90 degrees, the results show that ignoring shear effects causes significant error level in the deflections. (C) 2001 Elsevier Science Ltd. All rights reserved.

Stretch bending is a process of considerable importance for plastic forming purposes. Effective operations in the industry demand sufficient knowledge of how different parameters influence the process as well as the final shape of the product. Numerical simulations are an effective way of investigating these issues. However, the numerical model must be validated in order to obtain reliable results. This paper presents an analysis model in the code LS-DYNA which is shown to represent the behaviour in laboratory tests well. The model is subsequently used to check the influence of certain parameters on the response in a stretch bending process. Simple, analytical methods are also presented. It is shown that the local deformations of the cross-section during bending are primarily controlled by the geometry and tensile force level. The main parameters influencing the springback during unloading are the strain hardening properties of the material, and the tensile force.

This investigation deals with deformations of individual cross-sectional members as flanges and webs in bending of rectangular hollow sections. Part I describes the experimental work, while analytical models developed to predict pre- and post-buckling deformations are presented in a paper to follow (Part II). The experimental program involved rectangular single- and double-chamber aluminium alloy AA6060 extrusions with three different wall thicknesses. The profiles were given two distinct heat treatments to obtain different hardening characteristics. Multiaxial tests were performed to determine the mechanical properties of the materials. The profiles were then bent into a number of different bend radii. Measurements of strains, curvatures, deflections and bending forces were taken. The results show that cross-sectional distortions take place from the very beginning of bending; at first in the form of a uniform sagging-like deformation along the entire length of both sides of the bend until the inner (compressive) flange buckles into several half-waves, superimposing the pre-deformation modes. The instant at which buckling occurs is found to be mainly associated with the width-to-thickness ratio of the flange and the strain hardening characteristic of the material. The magnitude of pre- and post-deformations, however, appears to be more directly related to the actual width of the flange than to its slenderness. The material stress–strain curve is shown to have an increasingly effect on the distortions of members directly sustained to buckling as bending proceeds beyond the onset of buckling, leading to severely concentrated deformations for sections made of low hardening materials. The material has less impact on sagging of the outer (tensile) flange.

This paper proposes a simplified, but effective, algorithm to obtain critical design moments for clamped and/or elastically supported parking garage girders, beams and slabs. Maintaining the uniformly distributed load concept, the equivalent vehicle load factors which can simulate vehicle load effects without conducting additional sophisticated numerical analyses for the concentrated loads are introduced. After determining a standard design vehicle of 2.4 tons through an investigation of small to medium-sized vehicles made in Korea, finite element analyses for concentrated wheel loads were carried out by referring to the influence lines for the girders and beams and influence surfaces for the slabs. Based on the obtained member forces, we determined the equivalent vehicle load factors for the girders, beams and slabs which represent the ratios of member forces under vehicle loads to those under uniformly distributed loads. In addition, the relationships between the equivalent vehicle load factors and sectional dimensions were established by regression and used to obtain the design moments by vehicle loads. The member forces calculated by the proposed method are compared with the results of different approaches mentioned in current design codes with the objective of establishing the relative efficiencies of the proposed method.

Deflection compensation of flexible boom structures in robot positioning is usually done using tables with inverse kinematics solutions. The number of table values increases greatly if the working area of the boom is large and the required accuracy is high. On the other hand, inverse kinematics problems are very nonlinear, and if the structure is redundant, in some cases it cannot be solved in closed form. If the flexibility of the structure is taken into account, the problem is almost impossible to solve using analytical methods. Neural networks offer a possibility to approximate any linear or nonlinear function. Four different methods of using neural networks in the static deflection compensation of a flexible hydraulically driven manipulator are presented. Training information required for training neural networks is obtained by employing a simulation model that includes elasticity characteristics. The functionality of the presented methods is tested based on simulated results of positioning accuracy. The positioning accuracy is tested in 25 separate coordinate points. For each point, positioning is tested with five different mass loads. The mean positioning error of a manipulator decreases from 48 to 5.8 mm in the test points. This accuracy enables the use of flexible manipulators in the positioning of larger objects.

Treated herein is a class of large deflection beam problems where one end of the beam is being held while the other end portion is allowed to slide freely over a frictionless support fixed at a distance from this end. The elastic beam is subjected to a point load. This highly non-linear problem is solved using both the elliptic integral method and the shooting-optimization technique, thus providing independent checks on the solutions. This kind of problem features: (1) the possibility of two possible equilibrium solutions for a given load magnitude; and (2) a maximum (or critical) load and a maximum deformed arc-length for equilibrium.

Bellows are an integral part of the containment pressure boundary in nuclear power plants. They are used at piping penetrations to allow relative movement between piping and the containment wall. In a severe accident they may be subjected to high pressure and temperature and a combination of axial and lateral deflections. A test program to determine the leak-tight capacity of containment penetration bellows is being conducted at Sandia National Laboratories, Albuquerque, NM. Several different bellows geometries representative of actual containment bellows are being subjected to extreme deflections along with pressure and temperature loads. The bellows geometries and loading conditions are described along with the testing apparatus and procedures. A total of 13 tests have been conducted. The tests showed that bellows are capable of withstanding relatively large deformations up to or near the point of full compression before developing leakage. The test data are presented and discussed.

Although today's engineering computer technology allows for precise analysis of the structural response of a building, it does not readily provide insight for economical design. Due to the complex nature of a modern tall building consisting of thousands of structural members, the traditional design method is generally highly iterative and time consuming. This paper describes an efficient computer-based technique for least-weight design of three-dimensional (3D) tall steel building frameworks under multiple lateral loading conditions. Stiffness constraints in terms of interstorey drifts are considered and optimum discrete member sizes are automatically selected from databases of commercial standard steel sections. The technique is remarkably efficient and the optimum design generally converges in a few cycles. The designs of two 3D lateral-load resisting building frameworks are presented as illustrations. The effectiveness and suitability of the technique for the design of large-scale tall steel building frameworks are discussed.

The governing equations for large deflections of heated non-homogeneous elastic circular plates with radially varying rigidity are derived by the Berger approach. Assuming the non-homogeneous Young's modulus and the temperature distribution as seen in aerodynamic heating, they are solved with the boundary condition of the edge clamped by the Galerkin method. Numerical results are shown in the graphs.

A finite element analysis of the large deflection behaviour of stiffened plates using the isoparametric quadratic stiffened plate bending element is presented. The evaluation of fundamental equations of the stiffened plates is based on Mindlin's hypothesis. The large deflection equations are based on von Karman's theory. The solution algmrithm for the assembled nonlinear equilibrium equations is based on the Newton-Raphson iteration technique. Numerical solutions are presented for rectangular plates and skew stiffened plates.

Centrally loaded, rigid-linear strain hardening rectangular beams with variable axial restraints are investigated. Load-deflection solutions are presented for beams with four common types of end conditions. It is found that the effect of strain hardening cannot be neglected, especially for beams of larger depth to length ratios. By considering strain hardening, the influence of such beam depth to length ratio on the load-deflection curve can be quantified and the length of the plastic zone estimated. Compared with the available experimental data for simply supported and fully clamped beams of various depth to length ratios, the results give realistically closer agreement than those given by a rigid-perfectly plastic analysis.

It is shown that the fundamental natural frequency of a wide variety of discrete and continuous systems is inversely proportional to the gravitational acceleration divided by the maximum static deflection, raised to the 1/2 power. The value of the constant of proportionality is determined for multi-degree-of-freedom discrete systems, axially vibrating prismatic and tapered rods, prismatic and tapered slender beams, membranes, and thin plates of many planforms. Particular attention is paid to the effects of taper, axial preload, geometry and boundary conditions. The results of this investigation should be useful in predicting the approximate fundamental natural frequency from the static deflection, either calculated or determined experimentally.

This paper presents a finite element beam formulation with application to the dynamic characterization of flexible slider-crank mechanisms made of laminated composites. The laminae are in the plane of motion as opposed to previous works. This configuration is selected to enhance the load capacity of the system. A new formalism is used to derive system dynamic equations. The formalism is based on an implicit algorithm to eliminate generalized dependent coordinates in Lagrange equation. The method eliminates the need for transformation from local coordinates to the global coordinate system. The procedure is implemented in a compact computer program and is used to characterize the dynamics of flexible slider-crank mechanism. Several simulations are presented to quantify the contribution of coriolis terms at various speeds.

The nonlinear theory of Hoff type sandwich plates underlying geometrically nonlinear dynamic response is derived from Hamilton's principle. It is shown how the fundamental equations and boundary conditions of dimensionless form can be simplified to the Reissner-Mindlin type theory of moderately thick plates, the Reissner's theory of sandwich plates, and the Kirchhoff theory of thin plates. Nonlinear bending of rectangular sandwich plates is investigated under lateral pressure with some symmetric boundary conditions. Exact solutions of series form are obtained by developing a new technique of mixed Fourier series in nonlinear analysis. The nonlinear partial differential equations are reduced to an infinite set of simultaneous nonlinear algebraic equations, which are truncated and solved by iteration in numerical computations. The present solutions are satisfactory in comparison with other available results.

The von Karman large deflection theory is used in the analysis of antisymmetrically laminated angle-ply plates in cylindrical bending. The formulation considers the effect of transverse shear governing the behavior of moderately thick plates. The system of non-linear equations are solved numerically to evaluate the effect of transverse shear deformation on the response of the plate for a wide range of lateral pressure and lay-up angle. Numerical solutions are presented for uniformly loaded, simply supported plates having immovable edges in the plane of the plate. Solutions based on classical plate and shear deformation theories are compared to assess the influence of shear-bending coupling on the plate behavior in the non-linear regime.

Nonlinear static analysis of a cylindrical shell on a Pasternak foundation is carried out using a new approach due to Sinharay and Banerjee. This approach involves the use of variational principles and Galerkin's techniques. The effect of geometric, material and foundation parameters on load-deflection characteristics in investigated for simply supported movable and immovable edge conditions.

The large deflection profiles of tapered cantilevers under arbitrarily distributed loads are obtained through a weighted residual solution of the governing Bernoulli-Euler equation. The effect of a finite depth on deflections is studied for the range of beam geometries over which Bernoulli-Euler equation is applicable. Results are given for a variety of load shapes and geometries.

The aim of this paper is the investigation of the mechanical behaviour of bolted steel column-to-column connections under moment and axial loads by means of a method that takes into account the possibility of the appearance of detachment phenomena between the splice plates. As is well known, regions of detachment (called nonactive contact regions below), due to the appearance of the prying-action phenomenon, do appear on the adjacent fronts of such steel splice plates, greatly affecting the mechanical response of steel connections of this type. The significance of the problem under investigation arises from the fact that column-to-column splices are extensively applied in any possible combination to the design and construction of steel structures. It is therefore obvious that, since local failure phenomena on such connections due to undesirable—and not a priori defined—detachment between the splice plates (as consequence of the development of the prying-action phenomenon) may cause a total destruction of the whole steel structure. For this reason, it is important for such a behaviour to be accurately predicted and the previously mentioned nonactive contact regions on the splice plates to be defined. In this sense, such an investigation leads to an amelioration of the design principles for bolted steel column-to-column splices and to a refinement of the respective steel construction standards.

The differential quadrature method is used to analyse the deflection, buckling and free vibration behavior of anisotropic rectangular plates under various boundary conditions. The roots of Chebyshev polynomials are used to obtain grid-point locations and a new approach is used to apply boundary conditions. Results compare very well with existing numerical data, and less computational effort is required for the problems considered.

The non-linear bending analysis of simply supported symmetrically laminated orthotropic plates subjected to uniformly distributed load, using an accurate displacement based higher-order theory is presented. The non-linear governing equations are solved by the Galerkin procedure with the use of the Newton-Raphson method. Numerical results given here, based on analytical investigation, will be useful for comparison in future.

Non-linear static behaviour of rhombic plates has been analysed following Banerjee's hypothesis (B. Banerjee, Large deflections of polygonal plates under non-stationary temperature. J. Thermal Stresses 7 , 285–292 (1984)). Calculations have been carried out for different skew angles. To test the accuracy of the theoretical results so obtained, experiments were carried out on copper and steel rhombic plates. The theoretical results were found to be in excellent agreement with those obtained from an analysis of the experimental data.

The fourth-order differential equation of a beam resting on elastic supports is highly dependent upon the modulus of subgrade reaction, k. In general, the value of k is random; consequently, a beam resting on random supports is represented by a random differential equation of random coefficient. This differential equation has no exact solution; accordingly, approximate solution is recommended. The statistical moments of the solution process are expanded in terms of the stochastic scale parameter ζ and evaluated by using successive approximations

The paper presents the closed form solutions of the elastic deflections of one-dimensional bending members having circular cross-section with linearly and (in the binomial form) parabolically varying radius along the member's length. The solutions are obtained by transforming the fourth-order differential equations with variable coefficients into fourth-order differential equations with constant coefficients. For each radius variability four load conditions are considered: concentrated; uniformly distributed; linearly varying distributed; and parabolically varying distributed. The solutions give the distribution of the deflections, the rotations, the curvatures, the moments and the shearing forces of statically determinate and statically indeterminate members. Closed form solutions of the axial displacements are also presented. Numerical examples of structures commonly utilized in civil and mechanical engineering are provided.

Large deflection analysis of three-dimensional space structures with rotational degrees of freedom is considerably more complex than its two-dimensional counterpart, because of the non-vectorial property of large rotations in three-dimensional space. This paper describes, refines and compares three commonly known and widely used large deflection but small strain formulations for the nonlinear kinematics of space frames. The characteristics and computational efficiencies of these formulations are detailed and numerical examples illustrating their applications and accuracy are given. The findings obtained and conclusions drawn are believed to provide the analyst for nonlinear behaviour of space structures an insight into the proficiencies of these formulations.

Summary By assuming a kinematically admissible, time-dependent velocity field and considering the global equilibrium of all the forces acting on each rigid segment during large deflection of a plate, a complete theoretical investigation is undertaken herein to trace the large deflection dynamic plastic response (including the transient phase) of simply-supported or fully-clamped rectangular plates. This procedure deduces two modifying factors ƒ1 and ƒ2 which reflect the effect of the membrane forces and are employed to formulate the governing equations in the case of large deflections. The present prediction of the final plate deflection coincides excellently with the corresponding experimental results for deflections up to 5–10 times the plate thickness. This theory greatly improves the estimates based on the bending-only theory and provides a new way to trace the transient phase of dynamically loaded plates when the effect of membrane forces is significant.

A new approach due to Sinharay and Banerjee is extended for large deflection analysis of a shallow spherical shell on a Pasternak foundation. First, load-deflection characteristics are obtained using various approximate methods such as the Alpha method, Berger's method, the modified Berger's method and Sinharay and Banerjee's approach. The Alpha method is the least accurate one, Berger's method is more accurate than the Alpha method, and Sinharay and Banerjee's Approach is found to be the most accurate of all. Hence this technique is used to carry out the parametric studies for non-linear analysis. The effect of the geometric parameter, Poisson's ratio, foundation modulus and shear modulus on load-deflection characteristics is investigated for movably and immovably clamped and simply supported edge conditions.

The performance of large thrust bearings depends on the film profile and the thrust pad distortion. A mathematical model to estimate elastic distortion of a thrust pad on an elastic support by solving Reynolds' and elasticity equations simultaneously is discussed. Unlike a thrust pad which is pivoted, a thrust pad on an elastic support will move under load, with no zero deflection point on the surface. Therefore, it is necessary to differentiate between deflection and distortion. The analysis of a sector pad for an isoviscous lubricant is given. A new approach is used for loading stepwise, to change film profile slowly, to reach the target load through the proposed modified algorithm. Results are compared for cases where film thickness varies only along the direction of flow and where film thickness varies along and across the direction of flow.

Within the restrictions of the classical small bending theory of thin plates, the complex variable method is used to obtain exact expressions in series form for the deflection at any point of a thin isotropic circular plate simply supported along two concentric circles and eccentrically loaded. Numerical results and graphs illustrating the variation of the deflection along radii of the plate for two different load positions are presented. Special and limiting cases reduce the solutions derived above to those obtained by other authors.

The aim of the present investigation is to study the ‘blending band’ in-between two non-conforming cylindrical surfaces imposed on a planar thin elastic metal sheet. Initially, an experimental investigation was made over all the sheet, in order to make a survey of the bending and membrane stress and strain fields, principal curvatures, bending and membrane strain energy densities. Secondly, a rational explanation was sought for the most important experimental results collected. In view of the obvious analytical difficulties involved in such an attempt, a simple geometrical approach was adopted. Under the limitations of a preliminary study, the expressions for some geometrical parameters and for the bending and membrane energies thus obtained, lead to results compatible with the experimental data.

If the front and back faces of a pair of flanges are conical, continuous contact of the joint faces is achieved on assembly. This does not occur in flat flanges. However, high stresses may occur in the flanges because sufficient bolt load must be applied before the joint closes, so that sealing can be maintained under operating loads. Bending of the bolts may also occur on assembly. Sixteen tests were carried out on 7 different flange pairs having internal diameters of 147, 457 and 688 mm and cone angles of 2–6°, tightened by 8–48 bolts. Stresses in a 457 mm diameter flange pair were also investigated using the finite element method; an axisymmetric model was used. Bolt strains were obtained experimentally and closure loads were determined by analysis and experiment. Comparison of the axisymmetric finite element analysis of the 457 mm diameter flanges with experimental data shows that the flange flexibilities are accurately predicted for flanges having more than 24 bolts. For practical cone angles, the flexibility is independent of the cone angle. Bolt bending only occurs during tightening. However, the bending is insignificant at the rated torque, at which it was found that the effective line of action of the bolt load was inside the pitch circle of the bolt holes.

Thermally-induced large-deflection behaviors of laminates, including flat plates and cylindrical and doubly-curved panels, are investigated. The finite element technique based on the first-order shear deformation theory is employed to predict the shell response. Post-critical equilibrium paths are traced using the arc-length and the Riks methods. Laminate strength is also predicted, based upon the Tsai-Wu criterion.

Large deflection bending analysis of antisymmetric rectangular cross-ply plates based on Von-Karman plate theory is investigated in this paper, with one-term approximation for the in-plane and transverse displacements, under sinusoidal loading. The presence of bending-stretching coupling in such plates results in an additional square nonlinear term which makes the solution (for example, displacements) load direction dependent, unlike isotropic, orthotropic, symmetric, square antisymmetric cross-ply and symmetric and antisymmetric angle-ply plates. The effect of this term on large deflection response, based on the Rayleigh-Ritz method is presented for various configurations and modular ratios of such plates. It is shown that the presence of this square term could alter the very nature of nonlinearity i.e. hardening or softening for certain values of the load parameter.

The influence of the elastic foundation configuration on the large deflection axisymmetric response of cylindrically orthotropic thin annular plates is examined for uniformly distributed loads. The solution of the dynamic form of the Von Karman type equations governing the behaviour of the system is obtained using a fourth order finite difference representation for the spatial domain with the Newmark-β scheme being used for the time domain. Results for the fixed edge and simply supported immovable edge boundary conditions for a plate on a Pasternak foundation with or without an annular cut-out are presented for both the static and step loading cases. The inner edge boundary conditions for these configurations of a Pasternak foundation are examined and the apparent anomaly of the annular foundation increasing the stiffness in the recent literature addressed. The significance of the foundation parameters on plate response as well as the geometric non-linearity is considered.

The method of equivalent linearization and the Markov-vector approach are applied to the problem of the single mode nonlinear response of a stretched or compressed simply supported plate subjected to random uniform pressure. Closed form results are obtained for the latter solution in terms of parabolic cylinder functions which are tabulated and whose asymptotic forms are known. RMS values of maximum deflection and stress calculated by the two methods are compared and are found to be in excellent agreement provided the plate has not buckled. For buckled plates the two methods yield values which differ significantly for low values of loading spectral density.

An elastic large deflection analysis of uniformly loaded sector plates is presented. Numerical solutions are obtained by means of the Dynamic Relaxation (DR) algorithm coupled with an interlacing central finite-difference discretization scheme. Comprehensive verification of the DR results is provided via comparison with exact small deflection solutions and approximate large deflection solutions—the latter being derived from the ANSYS finite element program. Some new large deflection results, in the form of centre deflection vs pressure response curves, are presented for simply supported and clamped plates for a range of sector angles.