International Journal of Structural Stability and Dynamics

A geometrically nonlinear formulation to analyze structures in the hypotheses of large displacements and rotations and small strains is presented. In this formulation, applied to low-order elements and based on the total Lagrangian kinematics, the use of the rotation matrices is bypassed. A selectively based definition of the strain tensor, used in order to avoid shear-locking problems, is effected by the linear definition of deformations because it is element reference system independent. In addition, complex manipulations required to obtain conservative descriptions and well-posed transformation matrices are avoided. Numerical tests have been carried out to validate the developed technique both in the statical and in the quasi-statical context.

This paper investigates the active control of the supersonic flutter motion of an elastically supported rectangular sandwich plate, which has a tunable electrorheological (ER) fluid core and rests on a Winkler–Pasternak elastic foundation, subjected to an arbitrary flow of various yaw angles. The classical thin plate theory is adopted. The ER fluid core is modeled as a first order Kelvin–Voigt material, and the quasi-steady first order supersonic piston theory is employed for the aerodynamic loading. The generalized Fourier expansions in conjunction with Galerkin method are employed to formulate the governing equations in the state-space domain. The critical dynamic pressures at which unstable panel oscillations occur are obtained for a square sandwich plate, with or without an interacting soft/stiff elastic foundation, for selected applied electric field strengths and flow yaw angles. The Runge–Kutta method is then used to calculate the open-loop aeroelastic response of the system in various basic loading configurations. Subsequently, a sliding mode control (SMC) synthesis is set up to actively suppress the closed loop system response in yawed supersonic flight conditions with imposed excitations. The results demonstrate the performance, effectiveness, and insensitivity with respect to the spillover of the proposed SMC-based control system.

Restrained distortional buckling (RDB) is different from overall buckling and distortional buckling, and it usually occurs in the hogging moment region of composite beams. It may govern the member design for some cases, and should be taken into consideration. The present paper investigates the elastic RDB of composite beams based on elastically supported column method. First, Svensson's elastically supported column model is improved by including the participation of the web as part of the buckling column. The corresponding theoretical expressions for the improved elastically support column subjected to a varying axial force are derived by the potential energy expression and equilibrium differential equation, respectively. Then, the precision of several elastically supported column methods for the RDB problem is discussed, based on the finite element method (FEM). The results show that elastically supported columns subjected to a negative uniform moment or a triangular moment have a good agreement with FEM results, but they are not valid for the cases of nonlinear moment distributions. In order to consider the complicated load conditions of composite beams, the equivalent moment assumption is introduced and proved to be suitable for the RDB problem. However, there is an applicable range of the length of the hogging moment region. Thus, a critical length formula of equivalent moment assumption of RDB is put forward and verified by FEM. Furthermore, a three-step simplified method is presented which can solve the elastic RDB problem of continuous composite beams. The proposed method, in which values of elastically supported column methods can be tabulated previously, is simple and suitable for design purposes.

The objective of this study is to investigate the resonance and sub-resonance acceleration response of a two-span continuous railway bridge under the passage of moving train loadings. The continuous bridge is modeled as a Bernoulli–Euler beam with uniform span length and the moving train is simulated as a series of equidistant two degrees-of-freedom (2-DOF) mass–spring–damper units. The modal superposition method is adopted to compute the interaction dynamics of the train–bridge system. The numerical analyses indicate that (1) the train-induced resonance of the two-span continuous beam may result in significant amplification of the dynamic response of the train/bridge system; (2) for a two-span continuous beam, the first two resonant speeds may fall in the range of operating speeds of high-speed trains, which can lead to highly amplified vehicle responses; (3) due to the presence of sub-resonant peaks, the maximum acceleration of the two-span continuous beam need not occur at the midpoint of the beam; (4) inclusion of damping of a beam is helpful for reducing the train-induced resonant response on the beam, but the first two resonant peaks of the coupling system remain unchanged.

The in-plane free vibration of circular arches with continuously varying cross-sections is studied by means of the exact solution. The exact solution can be obtained only for a circular arch with constant cross-section. As an approximation, the circular arch with varying cross-sections is divided into a number of arch elements with constant cross-sections. The cross-section of each arch element is determined by averaging the upper and lower cross-sections. Then, the exact solution of free vibrations for each arch element can be obtained by using the initial value method. The axial extension, transverse shear deformation and rotatory inertia effects are included in the analysis. As the number of the arch elements increases, the fast convergence of the frequencies to those of the original arch is observed. Clamped–clamped (CC), hinged–hinged (HH), hinged–clamped (HC), clamped–free (CF) and free–free (FF) boundary conditions are studied for different opening angles, taper types and taper ratios. A detailed parametric study is performed, by which the mode transition phenomenon is observed. The results obtained are compared with those available in the literature.

Free vibration analysis of functionally graded elastic, rectangular, and simply supported (diaphragm) plates is presented based on a higher-order shear and normal deformation theory (HOSNT). Although functionally graded materials (FGMs) are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to the spatial coordinates. The material properties of functionally graded (FG) plates are assumed here to be varying through the thickness of the plate in a continuous manner. The Poisson ratios of the FG plates are assumed to be constant, but their Young's modulii and densities vary continuously in the thickness direction according to the volume fraction of constituents which is mathematically modeled as a power law function. The equations of motion are derived using Hamilton's principle for the FG plates on the basis of a HOSNT assuming varying material properties. Numerical solutions are obtained by the use of Navier solution method. The accuracy of the numerical solutions is first established through comparison with the exact three-dimensional (3D) elasticity solutions and the present solutions are then compared with available solutions of other models.

Advanced carbon fiber reinforced polymer (CFRP) demonstrates promise for the fatigue strengthening of steel structures. By decreasing the stress field at the crack tip, the stress intensity factors (SIFs) can be effectively reduced by CFRP reinforcement. In this paper, the mode I SIF of CFRP-reinforced center-cracked tensile (CCT) steel plate is proposed based on a series of fatigue tests. The selected fatigue tests include experiments conducted by the authors as well as fatigue tests reported in the literature, covering different CFRP systems (low/high modulus, CFRP sheeting/plate) with various CFRP strengthening dimensions. The classical mode I SIF of CCT steel plate without CFRP strengthening is selected as the basis of the proposed solution. Then two reduction factors, similar to the correction factors given in the Japanese Society of Steel Construction (JSSC) standard, are introduced to study the effects of the mechanical properties of CFRP composites and the geometries of the CFRP reinforcement, respectively. Modified SIFs for both single-side CFRP-reinforced and double-side CFRP-reinforced CCT steel plates are proposed. It is found that the experimental SIFs of CFRP-reinforced CCT steel plates can be reasonably captured by the proposed mode I SIF formula. Finally, parametric studies for investigating the sensitivity of SIF to various mechanical and geometric factors are presented.

In this paper, we investigate the buckling capacity of a hybrid grid shell, which is made of quadrangular meshes diagonally stiffened by pre-tensioned thin cables. The eigenvalue buckling, geometrical nonlinear elastic buckling and elasto-plastic buckling analyses of the hybrid structure were carried out. Then the influences of the shape and scale of imperfections on the elasto-plastic buckling loads were discussed. Also, the effects of different structural parameters, such as the rise-to-span ratio, cross-section of beams, area and pre-stress of cables and boundary conditions, on the failure load were investigated. The results show that the buckling capacity is reduced when taking into account the material nonlinearity. Furthermore, the hybrid structure is highly imperfection sensitive and the reduction of the failure load due to imperfections can be considerable. The proper shape and scale of the imperfection are also important. It is also shown that there exists an optimal rise-to-span ratio resulting in a relatively high buckling capacity for a specific span. Moreover, the enlarging of the cross-section of steel beams notably improves the stability performance of the structure. However, the area and pre-stress of cables pose small effect on the structural stability.

Owing to its good approximation characteristics of trigonometric functions and the multi-resolution local characteristics of wavelet, the trigonometric Hermite wavelet function is used as the element interpolation function. The corresponding trigonometric wavelet beam element is formulated based on the principle of minimum potential energy. As the order of wavelet can be enhanced easily and the multi-resolution can be achieved by the multi-scale of wavelet, the hierarchical and multi-resolution trigonometric wavelet beam element methods are proposed for the adaptive analysis. Numerical examples have demonstrated that the aforementioned two methods are effective in improving the computational accuracy. The trigonometric wavelet finite element method (WFEM) proposed herein provides an alternative approach for improving the computational accuracy, which can be tailored for the problem considered.

Attention is drawn to the fact that the recent increase in axle loads, speed and traffic volume in railway tracks, as well as concerns over passengers' riding comfort and safety have resulted in fresh challenges that are needed to be addressed. These challenges can only be successfully tackled with a more accurate modeling of the dynamic behavior of railway tracks. Although a significant amount of research involving mathematical modeling of railway track dynamics has been conducted in the last two decades, the nonlinearity of track support systems has not been given sufficient attention. This paper is concerned with the effect of nonlinearity of the support sub-layers on the dynamic responses of the railway track. To this end, a railway track model that considers the nonlinear properties of the track sub-layers is developed. Then, a field investigation into the dynamic responses of the railway track system under moving trains is conducted. The effect of the nonlinearity properties of the track support system on the track responses is investigated by comparing the results obtained by the numerical model, with or without consideration of track support nonlinearity, with those from the field tests. It is illustrated that consideration of the nonlinear properties of the track support system improves the accuracy of the calculated responses by a factor of three. It is also shown that the train axle loads and track accumulative loading have a significant effect on the nonlinearity of the track support system and, as a result, on the modeling of track responses.

A semi-analytical solution for the tip-off response of a vehicle moving along a guideway is obtained, considering the dynamic interaction between the two subsystems. The guideway is modeled as an inclined simply-supported uniform flexible beam, and the vehicle as a flexible free-free beam under a pre-specified thrust force. The equations of motion for the vehicle and guideway are developed using the Lagrangian approach and the assumed mode method based on the Euler–Bernoulli hypothesis. In the form of nonlinear differential equations, they are solved by the Petzold-Gear backward differentiation formula (BDF) method. The solutions obtained are validated by comparing them with the published results for the models with a rigid vehicle running over a rigid guideway or a flexible guideway. Comparisons of the present solutions with the existing ones for the vehicle and guideway reveal the advantages of the approach proposed herein. Other effects on the tip-off responses of the vehicle that are investigated include the length of the guideway, distance between the shoes of the vehicle, and mass and rigidity ratios of the vehicle to the guideway. The results presented herein provide valuable information for the design of the vehicle launch system.

Telescopic cranes are usually steel beam systems carrying a load at the tip while comprising at least one constant and one moving part. In this work, an analytical model suitable for the dynamic analysis of telescopic cranes boom is presented. The system considered herein is composed — without losing generality — of two beams. The first one is a jut-out beam on which a variable in time force is moving with constant velocity and the second one is a cantilever with length varying in time that is subjected to its self-weight and a force at the tip also changing with time. As a result, the eigenfrequencies and modal shapes of the second beam are also varying in time. The theoretical formulation is based on a continuum approach employing the modal superposition technique. Various cases of telescopic cranes boom are studied and the analytical results obtained in this work are tabulated in the form of dynamic response diagrams.