International Journal of Structural Stability and Dynamics

In this paper, a C^o finite element has been employed for deriving an eigenvalue problem using higher order shear deformation theory. The uncertain material and geometric properties are modeled as basic random variables. A mean-centered first order perturbation technique is used to find the mean and standard derivation of the buckling temperature of laminated composite plates — subjected to a uniform temperature rise — with random material and geometric properties. The effects of the modulus ratio, fiber orientation, length-to-thickness ratio, aspect ratio and various boundary conditions on the critical temperature are examined. It is found that small variations in material and geometric properties of the composite plate significantly affect the buckling temperature of the laminated composite plate. The results have been validated with independent Monte Carlo simulation and those available in the literature.

The elastic response of curved beams subjected to moving vertical loads and dynamic loads is investigated. Incremental dynamic equilibrium equations are derived by using the principle of virtual work. Newmark's step-by-step procedure is adopted to discretise the dynamic equilibrium equations and obtain the time history response. Geometric nonlinearities due to large deflections and rotations are taken into account. A total Lagrangian finite element formulation is developed. The numerical models are compared with the existing analytical solutions and employed to show the effects of geometric nonlinearities as well as the initial curvature on the dynamic behaviour of curved I-beams. It is shown that the geometric nonlinearities are significant even for service loads. The nonlinear behaviour of a curved beam is substantially different from the nonlinear behaviour of a straight beam when the initial curvature is not small.

This paper presents a substructural approach to parameter identification of structures, with the simultaneous identification of structural parameters and input time history of the applied excitation. The substructural approach reduces the computational effort when dealing with large structures. The substructural parameters, including the unknown interface forces at the ends of the substructure, are identified iteratively. The locations of input forces must be known; however, their magnitudes can be unknown. The method requires the measurement of accelerations at the interior DOFs but not interface DOFs of the substructure. Numerical simulations are performed for three examples, viz. global models of a 15 DOF shear building model, a planar truss of 55 members and a cantilever beam of 20 elements. The examples are excited with harmonic, random and impulse excitations. The effect of noisy data is studied. Even with noise, the proposed substructural method is found to identify the structural parameters with appreciable accuracy and with a considerable saving of CPU time. However, the identification of damping parameters is found to be prone to more errors than for the stiffness parameters.

This paper presents the free vibration analysis of annular sector plates based on Mindlin's first-order shear deformation theory using the discrete singular convolution (DSC) method. In the solution process, the governing equations of the motions and boundary conditions of the plate are discretized by the method. The effect of some geometric parameters on frequencies is investigated. Comparisons are made with existing numerical and analytical solutions in the literature. It is found that the DSC method yields accurate results for the plate problems under investigation.

In this paper, the effects of different parameters on the nonlinear aeroelastic behavior of functionally graded flat plates are investigated. Considering the through-the-thickness continuous variation of the material properties, a combination of the simple rule of mixtures and the Mori–Tanaka scheme is used for estimating the effective properties at each point. The von-Karman large strains and the piston theory are used to model the structural nonlinearity and aerodynamic loading, respectively. By Hamilton's principle the governing nonlinear partial differential equations of motion are derived and then converted to a set of nonlinear ordinary differential equations using the Galerkin method. The system of nonlinear ordinary differential equations is solved in the time domain using the time integration schemes to determine the aeroelastic response. It is shown that for in-plane-loaded functionally graded plates with temperature-independent material properties, less stability capacity is predicted by the Mori–Tanaka scheme than by the simple rule of mixtures.

This paper investigates the influence of anchor rods, planks and inner knee braces on the critical load of scaffolding systems under concentric and eccentric loads in construction. The steel rebar of grade 3 is used in place of the patent anchor rod in this study. The results show that the critical load of the scaffolding system increases by 1.5 times when anchor rods of a length of 30 cm are used on two sides of each story of the scaffolding system. The critical load increases by 4 times when the scaffolding system has both the anchor rods and plank. The critical load of the scaffolding system with the anchor rods placed on each story is twice as large as that with anchor rods added every two stories; the failure mode of the system also switches from the in-plane to out-of-plane mode. The 30-cm-long anchor rod, used in place of a steel bar of grade 3, provides a good lateral restraint to the scaffolding system. Moreover, the setup plank can significantly elevate the critical load of the scaffolding system; the critical load increases approximately 1.5 times under the concentric load, and increases up to 2.2 times under the TL/4 eccentric load, defined as a load applied at a quarter distance from the end. The anchor rod and the plank should always be included in a scaffolding system to improve its stability, especially under the eccentric loads in construction.

In this research, a seismic retrofitting method for chevron-braced frames (CBFs) is proposed. The key idea here is to prevent the buckling of the chevron braces via a conventional construction technique that involves a hysteretic energy-dissipating element installed between the braces and the connected beam. The energy-dissipating element is designed to yield prior to buckling of the braces, thereby preventing the lateral stiffness and strength degradation of the CBF caused by buckling, while effectively dissipating the earthquake input energy. Nonlinear static pushover, time history and damage analyses of the CBF and retrofitted CBF (RCBF) are conducted to assess the performance of the RCBF compared with that of the CBF. The results of the analyses reveal that the proposed retrofitting method can efficiently alleviate the detrimental effects of earthquakes on the CBF. The RCBF has a more stable lateral force–deformation behavior with enhanced energy dissipation capability than the CBF. For small-to-moderate intensity ground motions, the maximum interstory drift of the RCBF is close to that of the CBF. But, for high intensity ground motions, it is considerably smaller than that of the CBF. Compared with the CBF under medium-to-large intensity ground motions, the RCBF experiences significantly less damage due to prevention of buckling of the braces.

It is well-known that the domains of static stability and dynamic stability (even for a linear approach) do not match each other when the system is no more conservative and the dynamic approach is usually privileged, meaning that the dynamic stability domain is included in the static one. Following previous works proposing a new criterion of static stability of nonconservative systems and prolonging a paper of Gallina devoted to linear dynamic instability (flutter), we show in this paper some remarkable relations between the two approaches: contrary to the common thought, the new static stability criterion implies partially the dynamic one.

For systems with parallel components, the variable of primary importance is the maximum of the failure times of the different components. In this paper, we study the exact probability distribution of the maximum failure time. Explicit expressions are derived for the cumulative distribution function, probability density function, hazard rate function, moment-generating function, nth moment, variance, skewness, kurtosis, mean deviation, Shannon entropy, and the order statistics. Estimation procedures are derived by the methods of moments and maximum likelihood. We expect that these results could be useful for performance assessment of parallel systems.

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.