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The steady state response of a model of circular bladed disk with imperfection is investigated. Disk imperfection results from additional two groups of damping heads fixed on opposite ends of one diameter. These damping heads are introduced into the computing model as additional point mass, damping and stiffness. Such type of imperfection causes the bifurcation of double eigenfrequencies into pairs of close eigenfrequencies. The effect of imperfection is examined both numerically on three-dimensional nonrotating FE-model and analytically on a simplified split 2DOF model of rotating disk excited by single point harmonic force. Nonlinear friction connection is analyzed and equivalent linear damping coefficient is derived and used in the calculation procedure. It is shown that nonproportional distribution of damping strongly influences the high of resonance peaks. Some examples of response curves illustrate the dynamic properties of stationary and rotating disks with mass-damping-stiffness imperfection.

This paper presents a simplified model for predicting the nonlinear random response of flat and buckled plates. Based on a single mode representation of vibration response, r.m.s. values of the strain response to broadband excitation are evaluated for different static buckled configurations using the equivalent linearization technique. The dynamic effects on the overall strain response due to instability motion of snap-through are included. Parametric studies are performed in which the influences of the clamped and simply-supported boundaries, aspect ratio of the plate, thickness and length of the plate are considered. Using a simple single-model formula, the results of dynamic buckling motion were compared with finite-element models as well as experimental results. The comparisons between analytical results and experimental results help to assess the accuracy of the theory and the conditions under which deviations from the theory due to effects of imperfection and higher modes are significant. It is found that the theoretical model is useful for design and checking of computer results for curved plates in a slightly deflected form (initial deflection less than twice the thickness of plate) and the prediction accuracy on nonlinear analysis is higher than existing design formula based on linear response.

The paper is concerned with a new buckling problem of columns subjected to a central force produced by the tension of a string. The central force can be characterized by having a movable center fixed on the deformed axis of a column at its intermediate position. Equilibrium equations of the column, together with the boundary conditions and the conditions of continuity, lead to the characteristic determinant. The characteristic determinant yields the buckling load, and then the buckling mode. If the intermediate center is set at the midspan of the column, the characteristic equation yields a double root. The double root makes buckling mode indeterminate. This fact is an interesting aspect of the present buckling problem. The imperfection method is applied to discuss a possible buckling mode. Experiment of the column was conducted to check the theoretical prediction. The theoretical buckling load and the corresponding buckling modes are compared with the experimental results to find a good agreement between the theory and the experiment.

The discrepancy between the analytically determined buckling load of perfect cylindrical shells and experimental test results is traced back to imperfections. The most frequently used guideline for design of cylindrical shells, NASA SP-8007, proposes a deterministic calculation of a knockdown factor with respect to the ratio of radius and wall thickness, which turned out to be very conservative in numerous cases and which is not intended for composite shells. In order to determine a lower bound for the buckling load of an arbitrary type of shell, probabilistic design methods have been developed. Measured imperfection patterns are described using double Fourier series, whereas the Fourier coefficients characterize the scattering of geometry. In this paper, probabilistic analyses of buckling loads are performed regarding Fourier coefficients as random variables. A nonlinear finite element model is used to determine buckling loads, and Monte Carlo simulations are executed. The probabilistic approach is used for a set of six similarly manufactured composite shells. The results indicate that not only geometric but also nontraditional imperfections like loading imperfections have to be considered for obtaining a reliable lower limit of the buckling load. Finally, further Monte Carlo simulations are executed including traditional as well as loading imperfections, and lower bounds of buckling loads are obtained, which are less conservative than NASA SP-8007.

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.

This paper investigates the effects of applying different buckling modes obtained by linearized eigenvalue buckling analysis as the initial imperfection for double domes free form space structures. Nonlinear elastic–plastic analysis of rigidly jointed single layer double domes are carried out using the finite element method. Having verified the finite element modeling, several different collapse analyses have been undertaken in order to examine the stability behavior of these structures. By using the approximate-perturbed method, the results of the analyses show that in free form double domes, the lowest buckling modes could not be considered as the effective modes to change the bifurcation equilibrium path into the limit equilibrium one. Therefore, the generalized conformable imperfection mode method has been suggested in the present study in order to apply geometric imperfections in free form double domes. Also, one step method has been suggested in order to eliminate 60% of buckling modes, which are nonsensitive, before applying the approximate-perturbed method.

The static response of imperfect composites and sandwich laminates subjected to in-plane partial edge loading is studied. An efficient finite element model based on a refined plate theory is developed for the present purpose. In this theory, the transverse shear stresses are continuous at the layer interfaces along with stress free conditions at the top and bottom surfaces of the plate. The imperfection is considered in the form of in-plane displacement jumps at the layer interfaces, which is characterized by a linear spring-layer model. It is quite encouraging to note that the plate model having all these refined features requires unknowns only at the reference plane. However, this theory demands C¹ continuity of transverse displacement at the element edges, which is difficult to accommodate arbitrarily in any existing finite element. To deal with this problem a new triangular element developed by the authors is used in the present study.

Thin-walled structures are widely used in aeronautical and aerospace engineering. Conical and cylindrical shells structures, under axial compression, are prone to failure by buckling and typically show a snap-back phenomenon in the end-shortening curve. Path-following technologies based on Newton-type methods have difficulties to trace reliably the snap-back response due to the extremely sharp turning angle near the limit point. In this paper, a Koiter’s reduction finite element method, termed the Koiter–Newton (KN) method, is presented to trace reliably the post-buckling path of cylinders and cones considering either linear buckling modes or dimples from lateral perturbation loads as geometric imperfection. A robust algorithm based on the bifurcation-detection technique is applied during the solution of the reduced order model to achieve a successful path-tracing. The numerical results presented reveal that the nonlinear prediction obtained from Koiter’s perturbation theory at the unloaded state of the structure is numerically accurate up to the buckling load and the initial post-buckling path.

In the practical engineering applications of stiffened shell, the initial imperfection is inevitable and it could cause significant reduction in the load-carrying capacity of stiffened shell. The light-weight optimization of stiffened shell is generally performed under the constraint of fixed maximum load-carrying capacity. However, the load-carrying capacity of stiffened shell has been improved continuously as the promotion of manufacturing technology, which causes the previous strategies of light-weight optimization become conservative and outdated. Therefore, an improved hybrid framework of multi-objective optimization of stiffened shell with imperfection is necessary and presented in this paper, which focus on developing a general posterior design method to determine the optimal weight according to the different collapse loads. A new adaptive update criterion based on the Kriging model is developed to improve the efficiency and accuracy of the hybrid framework. The present optimal results provide a set of the Pareto optimal points and form a Pareto front, from which new posterior design can be achieved.

Connected carbon nanotubes (CNTs) with parallel longitudinal axes and with bending angles were simulated by a commercial finite element package and their buckling behavior was investigated by performing several computational examinations. In addition, the effect of defects on the structural stability of these heterojunctions was analyzed. For this purpose, two different nanotube hybrids (straight and kink heterojunction) were constructed in their perfect forms. In the second phase, three most likely atomic defects, i.e., impurities (doping with Si atoms), vacant sites (carbon vacancy) and introduced perturbations of the ideal geometry in different amounts to the perfect models, were simulated. To conclude our study, the buckling behavior of imperfect heterojunctions was numerically evaluated and compared with the behavior of the perfect ones. It was concluded that the existence of any type of defects in the configuration of nanotube hybrids leads to a lower critical load and as a result, lower buckling properties. This study provides a better insight into the prediction of straight and kink heterojunction CNTs behavior.

A coarse-grained molecular dynamics (MD) simulation approach based on a widely used fuse model is developed to study the mechanical behaviors of hierarchical brick and mortar bio-composites made from hard minerals and soft polymers. Massively parallel MD simulations are performed to investigate the toughness enhancement and the effect of stochastic variations in brick strength in representative bio-composites. Our simulations indicate that the hierarchical structure of bio-composites not only plays a key role in toughness optimization, but also reduces the sensitivity of the structure to biomineral imperfections. This work demonstrates a simple and efficient simulation platform for designing novel biomimetic materials.

This paper presents the influence of various random system parameters on dynamics response of imperfection sensitive higher order shear deformable functionally graded material (FGM) plates. Young’s moduli, Poisson’s ratio and volume fraction index are considered as random system parameters. The material properties of the FGM plates are assumed to vary along the thickness direction using simple power-law distribution in terms of the volume fraction of the constituents. The plate kinematics is based on Reddy’s higher order shear deformation theory. Finite element method (FEM) is employed in conjunction with first-order perturbation technique (FOPT) and Newmark integration scheme to explore the influence of different system parameters, like volume fraction indices, aspect ratio, material uncertainties, and imperfection amplitude on the dynamic responses of the FGM plates.

In this study, a laminated composite shell with uniformly applied hydrostatic pressure on its external surface is investigated numerically and experimentally. A numerical buckling analysis is carried out on a laminated composite shell with various nonlinearities including geometrical nonlinearity, material nonlinearity and geometric imperfection to obtain the critical buckling pressure using the commercially available software ANSYS^Ⓡ. The eigen mode shape imperfection in the geometry is considered for the nonlinear buckling analysis of composite shell. The force-induced inward dimple (FID) and eigen affine imperfections are also considered for the numerical analysis. The nonlinear governing differential equations of the buckling performance of the shell are solved using the arc-length method coupled with nonlinear finite element analysis. The developed nonlinear finite element modeling of the composite shell is validated by comparing the critical buckling pressures available in the literature obtained for the composite cylinder and prolate and oblate composite domes. Further, the effectiveness of the developed numerical modeling and analysis is demonstrated by performing an experimental investigation on a prototype shell made up of GFRP composites and subjected to external hydrostatic pressure. Various parametric studies are also performed to study the effect of aspect ratio of the shell and ply configuration of the composite shell. It was shown that the buckling pressure of the composite shell is decreased if the FIDs are located at the apex of the shell and eigen affine imperfection amplitude of the shell is increased. However, a substantial effect in the critical pressure of the composite shell could not be observed, if the position of FIDs is located towards the bottom of the shell. It is also found that the composite shell with all 90° ply orientation having aspect ratio of 0.5 yields higher critical buckling pressure.

In this work, the mixed local/nonlocal elasticity theory is developed for the investigation of the vibration of a circular graphene sheet with a structural defect located in a magnetic field. When graphene is placed in a magnetic field, the Lorentz force is applied to it, which is calculated using Maxwell’s equations. The insufficiency of Eringen’s nonlocal theory (ENT) caused some authors to employ the two-phase theory (TPT) to study nanostructures. Geometric imperfections can happen in the manufacturing process of graphene sheets. Lots of these imperfections can be modeled as a hole. So, in this work, an imperfection is considered as the centric hole. Governing equations, in Newtonian formulation, are extracted in the integrodifferential form. The boundary conditions are selected as clamped at inner and outer edges. To discretize the equation of motion we employ Galerkin’s approach. The solution is validated using a comparison study between the presented results and those that exist in the literature, and the accuracy of the suggested approach is verified. The effectiveness of the mixture parameter, magnetic field, radius of imperfection, and nonlocal parameter is examined on the natural frequency. The results exhibit that an increase in the mixture parameter and magnetic field increases the natural frequency of the graphene sheet.

In this paper the finite element procedure for analysing the postbuckling behaviours of shallow spherical shells is developed. The numerical simulations for the previously tested experimental data of pressurised thin-walled shallow spherical shells have been done by using a degenerated nine-node shell element with mixed interpolation functions. The nonlinear pre-buckling paths have been statically calculated, and then the corresponding postbuckling behaviours have also been obtained through nonlinear dynamic analysis. It is shown that if both an internal and an external viscous damping are considered, the good simulations even for the dynamic postbukling paths can be obtained.