• Structural Engineering and Mechanics
• /
• v.11 no.2
• /
• pp.199-210
• /
• 2001

Axially compressed circular cylinders repeat symmetry-breaking bifurcation in the postbuckling region. There exist stable equilibria with all symmetry broken in the buckled configuration, and the minimum postbuckling strength is attained at the deep bottom of closely spaced equilibrium branches. The load level corresponding to such postbuckling stable solutions is usually much lower than the initial buckling load and may serve as a strength limit in shell stability design. The primary concern in the present paper is to compute these possible postbuckling stable solutions at the deep bottom of the postbuckling region. Two computational approaches are used for this purpose. One is the application of individual procedures in computational bifurcation theory. Path-tracing, pinpointing bifurcation points and (local) branch-switching are all applied to follow carefully the postbuckling branches with the decreasing load in order to attain the target at the bottom of the postbuckling region. The buckled shell configuration loses its symmetry stepwise after each (local) branch-switching procedure. The other is to introduce the idea of path jumping (namely, generalized global branch-switching) with static imperfection. The static response of the cylinder under two-parameter loading is computed to enable a direct access to postbuckling equilibria from the prebuckling state. In the numerical example of an elastic perfect circular cylinder, stable postbuckling solutions are computed in these two approaches. It is demonstrated that a direct path jump from the undeformed state to postbuckling stable equilibria is possible for an appropriate choice of static perturbations.

• Structural Engineering and Mechanics
• /
• v.67 no.6
• /
• pp.629-641
• /
• 2018

The paper describes the development of a two-dimensional (2D) co-rotational nonlinear beam finite element that includes advanced path-following capabilities for detecting bifurcation instability in elasto-plasticity of steel elements subjected to fire without introducing imperfections. The advantage is twofold: i) no need to assume the magnitude of the imperfections and consequent reduction of the model complexity; ii) the presence of possible critical points is checked at each converged time step based on the actual load and stiffness distribution in the structure that is affected by the temperature field in the elements. In this way, the buckling modes at elevated temperature, that may be different from the ones at ambient temperature, can be properly taken into account. Moreover, an improved displacement predictor for estimating the displacement field allowed significant reduction of the computational cost. A co-rotational framework was exploited for describing the beam kinematic. In order to highlight the potential practical implications of the developed finite element, a parametric analysis was performed to investigate how the beam element compares both with the EN1993-1-2 buckling curve and with experimental tests on axially compressed steel members. Validation against experimental data and numerical outcomes obtained with commercial software is thoroughly described.

• Industrial Engineering and Management Systems
• /
• v.3 no.2
• /
• pp.92-99
• /
• 2004

We consider the ATM switching node location problem (ANLP). In this problem, there are two kinds of facilities, hub facilities and remote facilities, with different capacities and installation costs. We are given a set of customers with each demand requirements, a set of candidate installation sites of facilities, and connection costs between facilities. We need to determine the locations to place facilities, the number of facilities for each selected location, the set of customers who are connected to each installed hub via installed remote facilities with minimum cost, while satisfying demand requirements of each customer. We formulate this problem as a general integer programming problem and solve it to optimality. In this paper, we present a preprocessing procedure to tighten the formulation and develop a branch-and-price algorithm. In the algorithm, we consider the integer knapsack problem as the column generation problem. Computational experiments show that the algorithm gives optimal solutions in a reasonable time.