International Journal of Structural Stability and Dynamics

This paper deals with a two-temperature thermoelastic material subjected to a laser heating pulse as the heat source. Closed form solutions for the temperature and stress fields due to time exponentially decaying laser pulse are presented using the state-space approach. The Laplace transformation method is employed in deriving the governing equations. The inversion of Laplace transform is obtained numerically by using the Riemann-sum approximation method. The results have been presented in figures to show the effect of the time exponentially decaying laser pulse, the two-temperature parameter and the absorption coefficient on all the fields studied. The results show that the two-temperature parameter and the absorption coefficient parameter have significant effects on all the field parameters studied.

The corotational (CR) kinematic description was a recent method for formulation of geometric nonlinear structural problems. Based on the consistent symmetrizable equilibrated (CSE) CR formulation, a linear triangular flat shell element with three translational and three rotational degrees of freedom (DOFs) at each of the three nodes was derived by the assumed natural deviatoric strain (ANDES) formulation, which can be used to the geometric nonlinear analysis of shell structures with large rotations and small strains. By taking variations of the internal energy with respect to nodal freedoms, the equations for the CR nonlinear finite element, including the tangent stiffness matrix and the internal force vector in the global coordinate system, were derived. The nonlinear equations were solved by using the generalized displacement control (GDC) method. It was shown through numerical examples that combing CR formulation and ANDES elements can accurately solve complex geometric nonlinear problems with large body motions. As revealed by the efficiency and reliability of the ANDES elements in tracing the nonlinear structural load–deflection response, it is demonstrated that some membrane elements and plate elements give better performance in the geometric nonlinear analysis of shell structures.

The critical buckling load of a functionally-graded simply-supported beam with partially delaminated piezoelectric layers is discussed. The governing equations of motion are derived using two different, i.e. Euler–Bernoulli and Timoshenko beam theories, and the buckling load was evaluated from the exact solution to the corresponding eigenvalue equation. The equations were simplified to some extent by shifting the coordinate origin such that there is zero bending-extension coupling. Effects induced by the delaminated length, asymmetry, piezoelectric thickness, voltage, and the functionally graded materials (FGMs) volume fraction are evaluated. The validity of results and the invoked assumptions were successfully verified with existing results and finite element calculations. There is some difference between the analytical buckling load and that calculated with the finite element method (FEM), proven small in amount but predictable in terms of the piezoelectric thickness. Further, a general formula is derived to evaluate the dimensionless critical buckling load with the parameters obtained from regression analysis of the solution that can be utilized for all cases where the materials are not far different in their mechanical properties. The results can be utilized as benchmark design tool.

Large amplitude vibration problem of laminated composite spherical shell panel under combined temperature and moisture environment is analyzed in this paper. A general nonlinear mathematical model of laminated composite panel is developed based on higher-order shear deformation theory (HSDT) by taking the geometric nonlinearity in the Green–Lagrange sense. The sets of nonlinear governing differential equations are obtained using Hamilton’s principle and discretized via finite element steps. The nonlinear vibration responses are computed using a direct iterative method by incorporating hygral and/or temperature dependent material properties for laminated composite. The convergence behavior of the developed model has been checked and validated by comparing the responses with those available published results. Finally, some new examples are computed for different parameters (geometry, support condition and lamination scheme, etc.) and their effects on nonlinear free vibration responses under uneven environment are discussed.

Flapwise flexural vibration of rotating beams has been extensively studied since the 1970s. Existing methods for solving the aforementioned vibration problem range from the conventional finite element method to variable-order finite element method, Frobenius method, differential transformation method and dynamic stiffness method (DSM). Although various approximation methods are available, most of these methods are based on perturbation or discretization of the governing equation, often leading to tedious calculations. This paper re-examines flapwise flexural vibration of rotating beams using the method of variational iteration, which is relatively new and capable of providing accurate solutions for eigenvalue problems. The extracted natural frequencies and mode shapes for sample rotating beams with various rotational speeds and hub radii are compared with existing results that were published in the open literature.

This paper investigates the combined effect of flexural and shear actions on the failure modes of the high strength reinforced concrete (HRC) members using the proposed algorithm for plastic hinge formation. The accuracy of the present procedure for the HRC columns was verified by comparing the results obtained with those of the cyclic loading tests performed in Japan. To evaluate the seismic performance of the HRC high-rise buildings, a seismic performance checklist for the HRC buildings was recommended. Based on the proposed algorithm for formation of plastic hinges, the seismic performance of HRC buildings based on the static pushover analysis is evaluated. From the results of the pushover analysis, a simplified lumped-mass stick model was developed, which is adopted to evaluate the seismic performance using the nonlinear time history analysis. For the purpose of illustration, the seismic performance of a high-rise building constructed with HRC was investigated by both the nonlinear pushover and nonlinear dynamic analyses using the proposed procedure and concepts. The results of this paper serve as a useful reference for the seismic design and evaluation of HRC high-rise structures.

In this paper, all the parameters affecting the nonlinear behavior of S-FGM plates under lateral stochastic white noise excitations are investigated. First the governing equation for a general S-FGM plate is derived for the assumed problem. Then it is rewritten by introducing some nondimensional parameters such that the results are applicable for a wide range of plates. Without loss of generality and using an example, the effective parameters on the instability and bifurcation of the transverse vibration of plates are studied, including the mean value of the lateral load with the in-plane forces and the material property. Especially, the role of material property is highlighted and some analogical figures are drawn to compare the behavior of the FGM plates with the homogenous ones. It is shown that the material property can affect the behavior of instability and bifurcation of the plate and its occurrence.

In this paper, a semi-analytical solution to the problem of a simply supported beam subjected to a moving sprung mass with initial velocity and constant acceleration or deceleration was presented, which serves as a benchmark for checking the performance of other numerical methods. Herein, a finite element modeling procedure was adopted to tackle the vehicle–bridge interaction, and the responses of the vehicle and bridge were computed by time integration schemes such as the Newmark average acceleration, HHT-$\alpha$, and Wilson-$\theta$ methods. In comparison with the semi-analytical solution, the acceleration response of the beam solved by the Newmark average acceleration method shows spurious high-frequency oscillations caused by the finite element discretization. In contrast, the HHT-$\alpha$ and Wilson-$\theta$ methods can dissipate these oscillations and show more accurate results. Moreover, we found that the dynamic responses of the beam and sprung mass were mainly determined by the initial velocity of the sprung mass, but not by the acceleration or deceleration.

This paper studies the dynamic interaction for two adjacent rigid foundations embedded in a viscoelastic soil layer. The vibrations originate from one of the rigid foundations placed in the soil layer, which are subjected to harmonic loads of translation, rocking, and torsion. The dynamic responses of the rigid surface foundations are solved from the wave equations by taking into account their interaction. The solution is formulated using the frequency domain boundary element method (BEM), in conjunction with Kausel–Peek Green’s function for a layered stratum and the thin layer method (TLM) to account for the interaction between the two foundations. This approach allows us to establish a mathematical model for determining the compliance functions of the two adjacent foundations with regard to their spacing, substratum depth, masses, shapes, embedding, load intensity, and frequencies of excitation. The soil heterogeneity was taken into account for the cases of one or two layers of soils over a rigid bedrock and semi-infinite soil. The analysis of the present study indicates that the effect of several parameters on the dynamic interaction response of two adjacent foundations is nonnegligible. In particular, the dominant influence of some parameters, such as the heterogeneity of the soil, shape of the foundations, and the load intensity, compared to the other ones is clearly revealed.

In this paper, a discrete model of the planar Cosserat rod is presented. Based on the calculus of variations, the equilibrium equations of the model are derived for potential forces and hyperelastic material. Buckling of the structure under axial loading is thoroughly studied assuming linear elasticity. Dimensionless stiffness parameters are introduced, and analytical solutions are given for the critical loads and the corresponding buckled shapes of the model. Classification of the axially loaded structure is accomplished based on the number, sign, and physical admissibility of its buckling loads. It is revealed that the model can possess several buckling modes under tension.

A thermal buckling analysis is presented for simply-supported rectangular symmetric cross-ply laminated composite plates that are integrated with surface-mounted piezoelectric actuators and subjected to the combined action of thermal load and constant applied actuator voltage. The material properties of the composite and piezoelectric layers are assumed to be functions of temperature. Derivations of the equations are based on the classical laminated plate theory, using the von-Karman nonlinear kinematic relations. The Ritz method is adopted to obtain closed-form solutions for the critical buckling temperature. Numerical examples are presented to verify the proposed method. The effects of the applied actuator voltage, plate geometry and stacking sequence of laminates are investigated.

This paper presents an innovative technique for structural damage detection based on time series analysis with feedback controllers incorporated into the structure. The sensitivity of autoregressive (AR) coefficients to element stiffness is first derived, and it is proposed that the sensitivity of the AR coefficients can be enhanced by intentionally assigning the poles of the detection system. Finally, an $\bar{x}$ control chart is constructed based on the sensitivity-enhanced AR coefficient. Identification of the occurrence of damage is achieved by monitoring statistically significant changes in the control chart. The proposed methodology is validated by examples including a cantilever Euler beam and Phase I of the IASC-ASCE benchmark structure. The simulation results show that by utilizing the sensitivity-enhanced AR coefficients, the control charts are more sensitive to damage and are capable of detecting small levels of structural damage even in the presence of measurement noise.