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The in-plane buckling behavior of funicular arches is investigated numerically in this paper. A finite strain Timoshenko beam-type formulation that incorporates shear deformations is developed for generic funicular arches. The elastic constitutive relationships for the internal beam actions are based on a hyperelastic constitutive model, and the funicular arch equilibrium equations are derived. The problems of a submerged arch under hydrostatic pressure, a parabolic arch under gravity load and a catenary arch loaded by overburden are investigated. Buckling solutions are derived for the parabolic and catenary arch. Subsequent investigation addresses the effects of axial deformation prior to buckling and shear deformation during buckling. An approximate buckling solution is then obtained based on the maximum axial force in the arch. The obtained buckling solutions are compared with the numerical solutions of Dinnik (Stability of arches, 1946) [] and the finite element package ANSYS. The effects of shear deformation are also evaluated. [ABSTRACT FROM AUTHOR]

A low-order mimetic finite difference method for Reissner-Mindlin plate problems is considered. Together with the source problem, the free vibration and the buckling problems are investigated. Details about the scheme implementation are provided, and the numerical results on several different types of meshes are reported. [ABSTRACT FROM AUTHOR]

Thin-walled members that have one dimension relatively large in comparison to the cross-sectional dimensions are usually modelled by using beam-type one-dimensional finite elements. Beam-type elements, however, are based on the assumption of rigid cross-section, thus they only allow considerations associated with the beam axis behaviour such as flexural-, torsional- or lateral-buckling and cannot consider the effects of local deformations such as flange local buckling or distortional buckling. In order to capture the local effects of this type shell-type finite element models can be used. Based on the Bridging multi-scale approach, this study proposes a numerical technique that is able to split the global analysis, which is performed by using simple beam-type elements, from the local analysis which is based on more sophisticated shell-type elements. As a result, the proposed multi-scale method allows the usage of shell elements in a local region to incorporate the local deformation effects on the overall behaviour of thin-walled members without necessitating a shell-type model for the whole member. Comparisons with full shell-type analysis are provided in order to illustrate the efficiency of the method developed herein. [ABSTRACT FROM AUTHOR]

The factors responsible for the errors often encountered in the stability analysis of elastic systems are found by testing the Bubnov-Galerkin method for the buckling problem of a single-layer flexible elastic bar. Refined formulas are obtained for the maximum deflection of a longitudinally compressed hinged three-layer bar. [ABSTRACT FROM AUTHOR]

We developed analytical models of the buckling failure of initially rectilinear pipeline in the environment. We specify the drawbacks of available analytical methods, which take no account of the possible longitudinal displacement of the pipeline points or the limited length of the pipeline portion, as well as, in the limiting case, fail to describe the experimental results of buckling failure in the air. The proposed models make it possible to provide analytical evaluation of the critical load, length and shape of the deformed pipeline in cases of its horizontal and vertical transversal deformations with the account of the above factors. The results obtained are corroborated by the numerical simulation of the deformation process, based on the procedure described by the authors in Part 1, as well as by the full-scale test results. [ABSTRACT FROM AUTHOR]

The problem of a rod and a plate subjected to plane strain in the interval of the direct phase transformation is formulated as a nonlinear boundary-value thermoelastic problem with an implicit dependence on temperature (through a phase parameter simulating the volume fraction of new-phase crystals). An analytical solution of the problem of a rod bent into a ring and a plate bent into a tube as a result of phase strains under the action of a small end bending moment is given. A numerical analysis of the buckling problem of a titanium nickelide (alloy) rod (plate) under longitudinal compression in the interval of the direct phase transformation shows that buckling becomes possible if the compressive load is much lower than the Euler critical load calculated before the transformation. Branches of buckled equilibrium states corresponding to loads lower than the Euler load are plotted as functions of the phase parameter. In all cases considered, the deflections increase abruptly in the neighborhood of the critical points. The evolution of buckling modes is studied, and the phase-strain distributions along the rod (plate) are shown. [ABSTRACT FROM AUTHOR]

The nonlinear boundary-value problem of the axisymmetric buckling of a simply supported conical shell (dome) under a radial compressive load applied to the supported edge is formulated for a system of six first-order ordinary differential equations for independent fields of finite displacements and rotations. Multivalued solutions are obtained using the shooting method with specified accuracy. For various values of the loading parameter, bifurcation of the solutions of the problem is studied and a parametric branching diagram is constructed. The buckling modes are obtained for three branches of the solution. Curves of the buckling modes corresponding to three isolated branches of the solution are given. [ABSTRACT FROM AUTHOR]