Narrow Results

In this paper, static and dynamic stabilities of a cantilever laminated composite beam, having a linear translation spring as elastic support whose position is changeable from the free end to midspan of the beam, subjected to periodic vertical end loading, are examined. The beam is assumed to be an Euler beam and the finite element model used can accommodate symmetric and antisymmetric lay-ups. Solutions referred to as combination resonance are investigated for the dynamic stability analysis. The effects of length-to-thickness ratio, the variation of cross-section in one direction, orientation angle, static and dynamic load parameters, stiffness and position of the elastic support on stability are examined.

By using Pontryagin's maximum principle, we determine the optimal shape of an elastic rod free at one and clamped at the other. The rod is loaded with a concentrated force at the free end and its own weight. The optimality criterion is the volume of the rod guaranteeing lateral stability.

Based on the energy principle, a theoretical study of the elastic lateral distortional buckling (LDB) and restrained distortional buckling (RDB) of I-beams is presented. First, because the existing potential energy expressions for LDB are not suitable for members under a transverse distributed load, a new general potential energy expression of I-beams for lateral buckling is derived by using the nonlinear elastic theory. The proposed expression is equivalent to the classical potential equation when web distortion is suppressed and caters for I-beams under transverse distributed load, transverse concentrated load, and end moments, and when the web is flexible. Then, an LDB equation for simply supported, doubly symmetric, I-beams under uniform distributed load is developed by invoking the Ritz method. In addition, an RDB equation for continuous composite beams is also deduced by using some simplifications. The corresponding simplifications and equations are verified by the finite element method. Suggestions for further study are also presented. The outcomes of the present paper have important theoretical and practical significance and provide a rational basis for practical design methods.

The struts in a beam string structure (BSS) may buckle laterally under compression. The lateral buckling of the struts is determined not only by the rotational stiffness of the beam–strut joints and the length and bending stiffness of the struts, but also by the rise and lateral stiffness of the beam, the number of struts, and the layout of strings. In this paper, the multi-strut BSS with several types of layout of strings is studied. An analytical method for estimating the lateral buckling load of the struts in BSS is proposed. Parametric studies are carried out to investigate the variation of the lateral buckling of the struts in the BSS for different string layouts. In the end, the validity of the proposed method is examined by means of numerical simulations using the geometrically nonlinear finite element method.

This paper presents the stability analyses of glulam arches subjected to distributed vertical loading. The present analysis employs a strain-based formulation of a nonlinear geometrically exact three-dimensional beam theory. The influence of the relative height of the arch on the lateral buckling load is studied. The buckling load is determined by bisection method with observing the sign of the determinant of the tangent stiffness matrix. The post-critical load deflection path is traced by a modified arc–length method. Such influences are shown for arches with a constant cross-section or constant volume. After determining the most favorable height of the arch, the influence of the number and position of lateral supports is shown. We also compare the deflections, bending, and radial stresses at the lateral buckling states to the limit values which are recommended by European standards.

This paper deals with the lateral buckling behavior of an axially compressed beam interacting with the ground on which it is resting. Such a simple model is supposed to reproduce the same trends as observed during the lateral buckling of offshore pipelines on the seabed. In such practical analyses, the pipe-soil interaction relates the ground to the neutral axis of the pipeline. It is shown that, although such a constraint significantly affects the buckling behavior of the pipeline, it cannot reflect the torsional component of the buckling modes. However, this component is encountered in practice and may further modify the critical loads. Therefore, in this present preliminary study, the interaction between the beam in hand and the surrounding ground is modeled by a connection (a continuous distribution of lateral springs) related to the bottom line of the beam. In this way, the real contact between the soil and the bottom line of a pipe is mimicked, allowing for both flexural and torsional deformations in the buckling response. The problem is investigated analytically using an Euler–Bernoulli beam model with an isotropic linear elastic constitutive law and also an elastic interaction law. Original analytical solutions are derived and compared to numerical results obtained through finite element computations. In comparison with classical solutions (with the connection related to the neutral axis), new types of buckling modes may appear when considering torsional effects, depending on the boundary conditions, with generally much lower critical loads. These first results are certainly representative of some features of the global/localized lateral buckling of offshore pipelines, indicating that torsional effects should also be taken into account in such more comprehensive analyses.

Lateral buckling of cantilevered circular arches under various end moments is studied using an analytical approach. Three types of conservative moments are considered, i.e. the quasi-tangential moments of the 1st and 2nd kinds, and the semi-tangential moment. The induced moments associated with each of the moment mechanisms undergoing three-dimensional rotations are included in the Newman boundary conditions. Using the differential equations available for the out-of-plane buckling of curved beams, the analytical solutions are derived for a cantilevered circular arch, which can be used as the benchmarks for calibration of other methods of analysis.

The straight-beam approach is a simple and efficient means for analyzing the buckling of curved beams. Although previous researchers showed that the straight-beam approach is capable of simulating the lateral buckling of solid curved beams, the warping effect had been neglected and thus its practical application in engineering was limited. In this study, thin-walled curved I-beams will be dealt with by assuming the warping degrees of freedom (DOFs) to be identical at the common node for non-aligned connected elements. One feature of the present formulation is that the moments induced by initial nodal moments undergoing out-of-plane rotations are duly considered in the geometric stiffness matrix, while the compatibility and equilibrium are enforced for angled joints at the deformed position. With high computational efficiency, the present approach obtains buckling loads that agree well with the theoretical curved-beam solutions or the ones obtained by ABAQUS using shell elements. Compared with the modern curved-beam elements, the straight-beam element is locking free, invariant and simple in formulation, since the effect of curvature is not involved in global assembly.