Narrow Results

With the widespread application of fiber-metal laminates in various aerospace fields and the inherent presence of both material and geometric nonlinearities in composites, the prediction of nonlinear vibration characteristics of these structures holds particular importance. This study, based on the Jones–Nelson–Hui and von Kármán theories, utilizes the energy method and the orthogonal polynomial method to solve the differential equations and iteratively obtain the nonlinear natural frequencies and responses. Additionally, the complex modulus method is employed to calculate the nonlinear modal damping ratios. Experimental validation demonstrates the effectiveness of the proposed model, with a frequency error of less than 3.7%, a response error of less than 15.4%, and a damping error of less than 11.5% when compared with experimental results. Finally, the influence of elastic modulus, thickness, and ply configuration on the nonlinear vibration characteristics of the structure is investigated. The discussion reveals that titanium reduces vibrations but should not be too thick, while fiber thickness can be appropriately increased.

A pseudo-elastic local meshless formulation is developed in this paper for elasto-plastic analysis of solids. The moving least square (MLS) is used to construct the meshless shape functions, and the weighted local weak-form is employed to derive the system of equations. Hencky's total deformation theory is applied to define the effective Young's modulus and Poisson's ratio in the nonlinear analysis, which are obtained in an iterative manner using the strain controlled projection method. Numerical studies are presented for the elasto-plastic analysis of solids by the newly developed meshless formulation. It has demonstrated that the present pseudo-elastic local meshless approach is very effective for the elasto-plastic analysis of solids.

This paper is concerned with an analytical model for column analysis of concrete-filled tubular beam-columns subjected to the combined action of axial load and monotonic or cyclic bending. A method of segmentation is adopted in the analysis of beam-columns. The flexural and axial rigidities of the beam-column segments are derived from M–P–φ and M–P–ε relations obtained through fibre-analysis explained in Part 1¹ of the paper. Geometric and material nonlinearities are taken into account and incremental equilibrium equations are formulated based on an updated Lagrangian formulation. An incremental-iterative Newton–Raphson iteration technique is adopted to obtain the solution of the equations. The limitation of Newton–Raphson technique in approaching the limit points is overcome by using a generalized stiffness parameter, thereby tracing the post-buckling response. The accuracy of the model is verified by comparing the results with the experimental values available in published literature.

This paper presents a method for nonlinear dynamic analysis of frames with material and geometric nonlinearities which is based on the semirigid technique. The plastic hinge that accounts for the material nonlinearity is modeled as a pseudo-semirigid connection with nonlinear hysteretic moment-curvature characteristics at the element ends. The stiffness matrix of a frame element with material and geometric nonlinearities is expressed as the sum of products of the standard stiffness matrix and the geometric stiffness matrix of the element, with their corresponding correction matrices based on the plasticity factors developed from the section flexural stiffness at the plastic hinge locations. The combined stress yield condition is used for the force state determination of plastic hinges, and force equilibrium iterations and geometry updating for frames are carried out in every time step. When the key parameters of a structure are updated in a time step, the time step is split up into substeps to ensure accuracy while keeping the computations to a reasonable amount. The plastic rotation history can be calculated directly or in an approximate indirect way. The method is computationally efficient and it needs no additional connection elements, which makes it convenient for incorporation into existing linear dynamic analysis programs. Besides, the method can handle accurately and efficiently the dynamic analysis of nonlinear frames using relatively large time steps in conjunction with time step subdivision to cope with key parameter changes. A portal frame is used to verify the correctness of the proposed method. A more complicated five-story frame is used to illustrate the applicability and performance of the proposed method.

Currently, four grouped 177 m super-large cooling towers, i.e. column-supported hyperboloidal shells, are to be constructed in a typical electric power plant in Southeast China. To this end, simultaneous pressure measurements on 1:200 rigid tower models are carried out in an atmospheric boundary layer (ABL) wind tunnel, aimed at accurately obtaining the external/internal cladding wind loads on these shells. The wind-induced static behavior of the cooling towers is analyzed by applying the wind loads acquired via the pressure model tests, using both linear elastic and nonlinear elastic finite element (FE) analyses. The corresponding responses (structural deformation, internal force and local buckling state) are compared with those obtained by the traditional design approach, focused on the effects of internal suction and external pressure distribution. Besides, the tower group interference effects are studied by comparing the results computed of a freestanding tower, with those of the tower groups during two different construction stages. The main findings about the loading effects on the static performance of the super-large cooling towers are helpful for improving the current Chinese Codes that govern the design of super-large cooling towers.

The improved direct stiffness calculation (DSC) is a simple and relatively practical technique to estimate the bending stiffness along beam-type structures based on modal parameters and thus to assess damage in the structure. Application of this technique to a real continuous bridge, named Truckee River Bridge (TRB) in California, is presented in this paper. Comparing the stiffness estimated from baseline condition with that obtained from different damage scenarios in consideration of measurement errors, the damage location and its severity were reliably estimated. Moreover, the improved DSC technique is extended to detect the damage with material nonlinearity, which is simulated with pushover and time-history analyses using one earthquake event. The results of this case study show that the DSC is valid and efficient for identifying the damage with material nonlinearity in beam-type bridges using low-order mode shapes, which is advantageous for in-suit structural health monitoring applications.

Delamination fracture in multilayered functionally graded, split cantilever beams is analyzed with account taken of the nonlinear behavior of the material. The fracture is studied analytically in terms of the strain energy release rate. The mechanical behavior of the material is described by a power-law stress–strain relation that is not symmetric for tension and compression. The beam can have an arbitrary number of vertical layers of different thickness. Each layer can have different material properties. Besides, the material in each layer is functionally graded along the layer thickness. Also, the delamination fracture can occur at any interface. The strain energy release rate is derived by analyzing the complementary strain energy of the beam. The solution obtained is applied to elucidating the effects of crack location, material gradient and material nonlinearity on the delamination fracture behavior of multilayered functionally graded beam configuration. It is found that the material nonlinearity leads to increase of the strain energy release rate, which implies that the material nonlinearity should be taken into account in the fracture mechanics based safety design of multilayered functionally graded structural members and components.

This study proposes a time-domain spectral finite element (SFE) method for simulating the second harmonic generation (SHG) of nonlinear guided wave due to material, geometric and contact nonlinearities in beams. The time-domain SFE method is developed based on the Mindlin–Hermann rod and Timoshenko beam theory. The material and geometric nonlinearities are modeled by adapting the constitutive relation between stress and strain using a second-order approximation. The contact nonlinearity induced by breathing crack is simulated by bilinear crack mechanism. The material and geometric nonlinearities of the SFE model are validated analytically and the contact nonlinearity is verified numerically using three-dimensional (3D) finite element (FE) simulation. There is good agreement between the analytical, numerical and SFE results, demonstrating the accuracy of the proposed method. Numerical case studies are conducted to investigate the influence of number of cycles and amplitude of the excitation signal on the SHG and its performance in damage detection. The results show that the amplitude of the SHG increases with the numbers of cycles and amplitude of the excitation signal. The amplitudes of the SHG due to material and geometric nonlinearities are also compared with the contact nonlinearity when a breathing crack exists in the beam. It shows that the material and geometric nonlinearities have much less contribution to the SHG than the contact nonlinearity. In addition, the SHG can accurately determine the crack location without using the reference data. Overall, the findings of this study help further advance the use of SHG for damage detection.

In order to realistically restore the mechanical properties of the arch bridge under load and damage processes, a coupled dual nonlinear analysis method is established for the arch-bridge load–carrying capacity by considering the effects of bidirectional force transfer and adaptive section stiffness. First, based on the geometric nonlinear theoretical method of bidirectional force transfer, the macroscopic structural deformation of arch ribs under different loading conditions and load levels is preliminarily calculated, including the bending and axial deformation of each section of the arch, which is used to characterize the development of plasticity. According to deformation or strain, the fiber model analysis method is used to determine the true moment–curvature and axial force–curvature development paths of key sections, and then the elastic–plastic flexural and compressive stiffnesses of each section under different deformation states are derived. The elastic–plastic stiffness is substituted back to the geometric nonlinear equations to obtain the deformation and internal force along the arch ribs considering the cross-sectional plasticity. Finally, the above process is cycled until the equivalence condition is satisfied between the structural internal force/deformation and cross-sectional ones. In order to verify the rationality and accuracy of such a coupling method, a model test is carried out on a stiff skeletal concrete suspension chain line arch with a span of 12m, whose results match satisfactorily with that of calculated by the coupling dual nonlinearity method. Compared with the method suggested in the code JTG3362-2018, the proposed method can better predict the development of deflection of different arch rib sections, as well as the actual internal force state. The bending moment calculated as per the code is 7–16% larger than the test result at the ultimate capacity state, while the method of this paper is within 5%.

A pseudo-elastic local meshless formulation is developed in this paper for elasto-plastic analysis of solids. The moving least square (MLS) is used to construct the meshless shape functions, and the weighted local weak-form is employed to derive the system of equations. Hencky's total deformation theory is applied to define the effective Young's modulus and Poisson's ratio in the nonlinear analysis, which are obtained in an iterative manner using the strain controlled projection method. Numerical studies are presented for the elasto-plastic analysis of solids by the newly developed meshless formulation. It has demonstrated that the present pseudo-elastic local meshless approach is very effective for the elasto-plastic analysis of solids.