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• A novel non-intrusive sensitivity-based nonlinear finite element model updating method is proposed. • The nonlinear response sensitivity is computed using real and imaginary perturbation synchronously. • The nonlinear finite element model is updated using time history responses. • A cantilever beam with steel slice is conducted to illustrate the experimental application of the proposed method. This paper presents a novel non-intrusive sensitivity-based nonlinear finite element model updating method in which the local nonlinearity of structure is considered. The sensitivity analysis is conducted to determine the sensitivity of a dynamic response with respect to different nonlinear parameters using the real and imaginary perturbation method in one single calculation. The use of the imaginary perturbation is capable of second-order accuracy in imaginary perturbation sensitivity analysis of the nonlinear finite element model updating procedure. The nonlinear parameters in the finite element model are estimated by using the improved sensitivity-based optimization algorithm. A nonlinear multi-degree-of-freedom oscillator and a cantilever beam with multiple nonlinear supports are studied to verify the accuracy of the proposed method. The effects of measurement noise and initial parameters on the performance of the presented approach are further investigated. Then, the proposed approach is verified by an experimental test of a cantilever beam with a steel slice. The updated nonlinear finite element model is further evaluated by the structure subjected to new excitations. Results show that the proposed method can effectively update the nonlinear finite element model even in the presence of contaminated measurement data and different initial parameters in the finite element model. [ABSTRACT FROM AUTHOR]

An improved finite element modeling method is developed for isotropic curvilinearly stiffened plates under a thermal environment. The existing modeling method for curvilinearly stiffened plates avoids the difficulty of node overlap, which is suitable for plates with different thicknesses. By introducing the influence of temperature on material parameters and thermal stress on additional stiffness, the existing method is improved and extended to the study of thermodynamics. The proposed method is verified by modal test at normal temperature and commercial finite element software at the thermal environment. The variation of dynamic characteristics with temperature under different boundary conditions was studied. Results show that when the boundary conditions are asymmetric, the influence of temperature on the thermal mode shape is more significant than the case of symmetrical. [ABSTRACT FROM AUTHOR]

As research works of the transient statistical energy analysis (TSEA) and transient local energy approach (TLEA) mostly focus on simple structures, TSEA and TLEA are adopted to quantify the transient response of a complex vibro-acoustic system at the mid-high frequency range in this paper. Numerical examples of a coupled oscillator system, an L-shaped plate, and a launch vehicle fairing model are conducted to demonstrate the effectiveness and accuracy of TSEA and TLEA. The computational precision of TSEA and TLEA is verified by the analytical solution and finite element method. Furtherly, the transient energy responses of subsystems with different coupling ratios between subsystems are investigated. Results show that TLEA has a better performance than TSEA. With the increasing coupling ratio between subsystems, the rise time and peak energy of transient energy response of subsystems decrease gradually. Both ratios of rise time and peak energy predicted by TLEA to these of the TSEA increase as the rising of the coupling ratio. [ABSTRACT FROM AUTHOR]

The statistical energy analysis (SEA) is applied to predict the transient energy response of structures with time-varying parameters for the first time. With the energy governing equations derived by considering time-varying SEA parameters and energy flow item caused by time-varying damping loss factor, SEA method is firstly applied to predict transient energy response of time-varying systems. Then, numerical examples of a time-varying two-oscillator system, a time-varying L-shaped fold plate and a complex time-varying vibro-acoustic structure are investigated to demonstrate the effectiveness and accuracy of SEA method for time-varying system. The Newmark-beta method and finite element method are used to verify the accuracy of predicted transient energy response. Results show that SEA method for time-varying system is capable of predicting transient energy response of time-varying structures with sufficient accuracy and also applicable for transient analysis of complex time-varying structures with a small computational cost. [ABSTRACT FROM AUTHOR]

The out-of-plane crushing resistance of fractal-like honeycombs with self-similar hierarchy are investigated numerically and analytically. The hierarchical honeycombs are developed via replacing each three-edge vertex of a regular hexagonal honeycomb by a smaller hexagon. Hierarchical honeycombs with higher orders are constructed by repeating this process. Theoretical solutions are derived based on the Super Folding Element (SFE) theory to predict the mean crushing forces (MCFs) of the hierarchical honeycombs. Numerical simulations are also conducted in conjunction with the theoretical solutions. Crushing resistances of three groups of hierarchical honeycombs with different relative densities are explored subsequently. Good agreement between results obtained using theoretical and numerical methods indicates that the theoretical predictions are reliable. The results show that hierarchy can significantly improve the crushing resistance of honeycombs. It is found that the MCFs of first to fourth order hierarchical honeycombs are improved by 71%, 114%, 201% and 309% compared with the regular honeycomb under the same relative density, respectively. It reveals that the amplification of the MCF from one generation to the next approaches a constant (ξ n  ≈ 1.26) when the hierarchical order is sufficiently large. The potential maximum achievable amplifications of the MCF for hierarchical honeycombs of different relative densities are also discussed. [ABSTRACT FROM AUTHOR]

An approach on determining elastic parameters and Coefficient of thermal expansion (CTE) of a 2.5-dimensional (2.5D) braided composites is proposed in this paper, by adopting mesoscopic mechanics integrated Finite element (FE) modeling. According to the geometric features of meso-structure, Representative volume cell (RVC) models of composite for predicting thermo-elastic parameters are established. On the basis of the models, homogenized parameter prediction is carried out in three steps: Firstly, equivalent elastic properties is predicted subject to periodic displacement boundary conditions; secondly, the equivalent thermal modulus is determined by using the periodic non-adiabatic temperature boundary conditions; thirdly, using the obtained elastic parameters and thermal modulus to calculate the equivalent coefficient of thermal expansion. A multiscale finite element analysis is conducted: The thermo-elastic parameters of yarn is calculated using the RVC model; subsequently, the equivalent parameters of the yarn are substituted into the RVC of 2.5D braided C/SiC composites, to predict the thermo-elastic parameters. Results indicate that the CTE determined by homogenized parameter prediction of 2.5D C/SiC composites shows good agreements with the experimental results. At last, the refined FE model and the equivalent homogeneous model are employed to verify the effectiveness of the predicted parameters in terms of effective modeling. After the comparative analysis on thermal modal data between refined model and equivalent model, the acquired results demonstrate the effectiveness of the proposed method in determining thermo-elastic parameters. [ABSTRACT FROM AUTHOR]

Substructure method has been widely applied in dynamic analysis of complex structures due to high computational efficiency. On the basis of Residual flexibility mixed-boundary (RFMB) substructure method, a model updating approach is proposed in this paper. Four major steps of the RFMB model updating method are summarized as: 1) Substructuring: Dividing the whole structure into residual part and reduced part according to the junction surface; 2) reduction: Using the RFMB component mode synthesis approach to reduce the order of each substructures; 3) assembly: Residual structure analysis by using the reduced assemble matrix; 4) updating: Model updating by solving the optimization problem. Numerical simulation is conducted to verify the effectiveness by adopting a cantilever plate in case I. In case II, the proposed method is applied to identify the elastic parameter of interface of a bolted joint structure using experimental data. After parameter identification, the maximum error between numerical results and the experimental data decreases to 2.44 %. And three component mode synthesis model updating methods: Craig-Bampton (CB), Mixed-boundary (MB) without considering residual flexibility and RFMB model updating approach, are applied to update the same bolted joint structure for comparing the accuracy. For comparing the computational efficiency, the RFMB model updating approach is applied to the complicated aero-engine casing structure. In case III, the average time-consuming of the Whole finite element model (WFEM) is 5.15 times to the Residual finite element model (RFEM) in the single updating iteration. Results show that the proposed approach has better performance in the finite element model updating. [ABSTRACT FROM AUTHOR]

Design optimization of dynamic properties, for example, modal frequencies, can be of much importance when structures are exposed to the shock and/or vibration environments. A modal strain based method is proposed for fast design of natural frequencies of plate-like structures. The basic theory of modal strains of thin plates is reviewed. The capability of determining the highly sensitive elements by means of modal strain analysis is theoretically demonstrated. Finite element models were constructed in numerical simulations. Firstly, the application of the proposed method is conducted on a central-massed flat plate which was topologically optimized by the Reference. The results of modal strain analysis at the first mode have good agreement with the results from the topology optimization. Furthermore, some features of the strain mode shapes (SMSs) of the flat plate are investigated. Finally, the SMSs are applied to the optimization of a stiffened plate. Attention is focused on the distributions of the SMSs of the stiffeners, which also shows good agreement with the results from the topology optimization in the previous study. Several higher orders of SMSs are extracted, which can visualize the most sensitive elements to the corresponding modal frequency. In summary, both the theory and simulations validate the correctness and convenience of applying SMSs to dynamic design of plate-like structures. [ABSTRACT FROM AUTHOR]

Based on the assumption of quasibrittle failure under high-cycle fatigue for the metal material, the damage constitutive equation and the modified damage evolution equation are obtained with continuum damage mechanics. Then, finite element method (FEM) is used to describe the failure process of metal material. The increment of specimen’s life and damage state can be researched using damage mechanics-FEM. Finally, the lifetime of the specimen is got at the given stress level. The damage mechanics-FEM is inserted into ABAQUS with subroutine USDFLD and the Python language is used to simulate the fatigue process of titanium alloy specimens. The simulation results have a good agreement with the testing results under constant amplitude loading, which proves the accuracy of the method. [ABSTRACT FROM AUTHOR]

Abstract: Structural stability is an vital aspect for structural health monitoring of transmission lines. This paper presents a novel method to evaluate the structural status of transmission line based on dynamic and stability analysis. A newly built long-span transmission tower-line system that crosses the Huaihe River in China with a span of 1083m was studied as an example. Finite element model of the transmission tower-line system was constructed. Nonlinear buckling analysis for both the tower and tower-line system were performed to determine the critical wind loads. Dynamic properties of both the tower and tower-line system under different levels of wind loads were analyzed. Numerical results show the law that modal frequency of low order modes decreases when the wind velocity increases before the structural instability happens for both cases. Therefore, for the structural health monitoring of transmission lines, frequency decrease of low order mode is an useful indicator to predict the happening of structural instability. This conclusion could be taken as the reference in the design of structural health monitoring system for transmission lines. [Copyright &y& Elsevier]

The efficient Wave-Based Method (WBM) is extended to predict the bending vibration response of thin-walled rectangular plates under thermal load. Governing equations of dynamic plate bending problems considering thermal effects are first introduced. The general solution and particular solution of governing equation are derived by the separate variable method and residue theorem, respectively. Then novel wave functions and particular solution function are selected to establish the wave-based model of dynamic plate bending problems under thermal load. The accuracy of WBM is verified by finite element method (FEM) for a simply supported plate and a clamped plate. Then the influence of thermal load on the dynamic bending responses of a clamped plate is investigated. Simulation results prove that WBM achieves higher convergence rate than FEM. The thermal load significantly changes the structural dynamic behaviors. When both the temperature-dependent material properties and thermal stresses are considered, the increase of environment temperature leads to the resonant peak of displacement response shifts toward lower frequency. • The WBM is developed to predict the bending vibration response of thin-walled structures under thermal environment. • Novel wave functions and particular solution function are derived to establish the wave-based model. • The proposed method is validated on two cases with different boundary conditions. • The developed WBM achieves high accuracy and reduces computing time effectively. • The influence of thermal environment on the dynamic bending responses is investigated. [ABSTRACT FROM AUTHOR]

• A modeling method of curvilinearly stiffened plates suitable for both thin and thick plates is established and verified by experimental and existing numerical results. • Similar accuracy can be obtained when fewer mesh is used than finite element software. • The stiffeners can be arranged on the plate in any form without changing the mesh of the plate. Curvilinearly stiffened plates can have superior mechanical properties than traditional straight-line stiffened plates. To avoid the shear locking problem in the modeling of stiffened thick plates by Reissner-Mindlin theory when the thickness of plate decrease, discrete shear triangle element was introduced by employing the discrete shear constraints on each side. The discrete shear triangle element is employed for the plate and the Timoshenko beam theory is employed for the curvilinearly stiffeners, respectively. The FE equations are established through displacement interpolation function of plate and the displacement compatibility conditions at the plate-stiffened interfaces. The plate and stiffener are modeled separately in the present method, which allows the nodes of stiffener element not coincide with nodes of the plate's shell-element. Based on the newly proposed modeling technique, the statics, vibration and buckling behavior of curvilinearly stiffened plates are investigated. Numerical and experimental investigations are conducted to verify the mechanical properties of proposed model for stiffened plates. Results from the proposed method show good agreements with the numerical and experimental results. The present method can conduct static and dynamic analysis for both stiffened thick and thin plates and guarantee the accuracy of calculation with less number of elements. Image, graphical abstract [ABSTRACT FROM AUTHOR]

An algorithm that integrates Karhunen–Loeve expansion (KLE), finite element method (FEM), and boundary element method (BEM) is proposed to carry out a vibro-acoustic analysis under stationary and non-stationary random excitations which are uncorrelated or correlated. In the KLE, a set of orthogonal basis functions is employed to discretize the auto-covariance function of the excitations and obtain the eigenvalues and eigenfunctions of the auto-covariances. The KLE for correlated random excitation relies on the expansions of correlated random variables. During the response calculation, the FEM and BEM are employed to obtain structural and acoustic responses. A circular piston in an infinite baffle and a stiffened panel excited by stationary or non-stationary random processes are used to illustrate the proposed algorithm's accuracy. Results show that the statistics of vibro-acoustic response are accurately obtained with the proposed method and this method is also applicable for the vibro-acoustic analysis of more complex structures under various types of random excitations. [ABSTRACT FROM AUTHOR]

The mechanical behavior of honeycomb sandwich structures under low-velocity impact is of great significance. An experimental and numerical investigation on surface deformation and energy absorption subjected to low-velocity impact is undertaken. A high-speed camera system is employed to record the acceleration attenuation process of the impactor, a projection profile system is introduced to measure the surface profiles of the panel and the depth of the ultimate indentation is obtained. A three-dimensional finite element model is constructed and validated by the experimental results. Indentation characteristics and energy absorption are analyzed and in good agreement with experimental data. Effect of adhesive layers on energy absorption is discussed and the contribution of the facesheets and the honeycomb core to the energy absorption process is analyzed separately. Results shown that the effect of adhesive layers on energy absorption is non-ignorable and the honeycomb core plays a dominant role in energy absorption. Most of the energy absorbed by the honeycomb sandwich panel is expended as plastic dissipation, and the rest is transformed into strain energy. [ABSTRACT FROM AUTHOR]

The honeycomb sandwich composite material has been widely applied in engineering due to its excellent mechanical performance. The elastic properties of honeycomb core is of crucial importance in efficient mechanical analysis. An approach on determining the equivalent elastic modulus of honeycomb core using experimental modal data is proposed in this paper. Based on analytically predicted elastic constants of the pure core, the initial finite element model of a honeycomb panel is constructed using a three-layer sandwich theory; according to errors that exist in analytically estimated equivalent parameters and the sensitivity analysis of modal frequencies with respect to system parameters, the out-of-plane shear moduli G cxz and G cyz are selected to be determined. Consequently, the two parameters are determined by minimizing an objective function which is formulated with vibration test and numerical modal data. Comparative investigations are conducted to illustrate that the initial values of the parameters with physical significance play an important role in the identification procedure. The presented method can provide accurate and reliable predictions of material constitutive parameters of honeycomb core. [ABSTRACT FROM AUTHOR]

An algorithm that integrates Karhunen-Loeve expansion (KLE) and the finite element method (FEM) is proposed to perform non-stationary random vibration analysis of structures under excitations, represented by multiple random processes that are correlated in both time and spatial domains. In KLE, the auto-covariance functions of random excitations are discretized using orthogonal basis functions. The KLE for multiple correlated random excitations relies on expansions in terms of correlated sets of random variables reflecting the cross-covariance of the random processes. During the response calculations, the eigenfunctions of KLE used to represent excitations are applied as forcing functions to the structure. The proposed algorithm is applied to a 2DOF system, a 2D cantilever beam and a 3D aircraft wing under both stationary and non-stationary correlated random excitations. Two methods are adopted to obtain the structural responses: a) the modal method and b) the direct method. Both the methods provide the statistics of the dynamic response with sufficient accuracy. The structural responses under the same type of correlated random excitations are bounded by the response obtained by perfectly correlated and uncorrelated random excitations. The structural response increases with a decrease in the correlation length and with an increase in the correlation magnitude. The proposed methodology can be applied for the analysis of any complex structure under any type of random excitation. [ABSTRACT FROM AUTHOR]

An algorithm that integrates Karhunen–Loeve expansion (KLE) and finite element method (FEM) is proposed to carry out random vibration analysis of complex dynamic systems excited by stationary or non-stationary random processes. In KLE, the auto-covariance function of random process is discretized using orthogonal basis functions. During the response calculations, the eigenvectors of KLE are applied as forcing functions. Three methods are proposed to carry out the random vibration analysis termed as, Method 1A , Method 1B and Method 2 . In Method 1A and Method 1B , the basis functions are chosen such that they include multiples of complete or half-cosine and sine functions over the selected time. In Method 2 , the basis functions are chosen to be simple piecewise constants. The proposed algorithm is applied to a 2DOF system, a cantilever beam and a stiffened panel for both stationary and non-stationary excitations. Results show that three methods can describe the statistics of the dynamic response with sufficient accuracy. However, Method 1A results have a relatively larger error than that for Method 1B and Method 2 during initial transient time. The Method 2 results have an excellent agreement with analytical results. Moreover, the runtime of Method 2 algorithm is significantly less than both Method 1A and Method 1B algorithms even though its usage results in an increase in the number of KLE terms. Furthermore, Method 2 , unlike Method 1A and 1B , neither yields negative and/or infinite eigenvalues for the auto-covariance function nor large inaccuracies. [ABSTRACT FROM AUTHOR]