An analytical symplectic approach to the vibration analysis of orthotropic graphene sheets

A nonlocal continuum orthotropic plate model is proposed to study the vibration behavior of single-layer graphene sheets (SLGSs) using an analytical symplectic approach. A Hamiltonian system is established by introducing a total unknown vector consisting of the displacement amplitude, rotation angle, shear force, and bending moment. The high-order governing differential equation of the vibration of SLGSs is transformed into a set of ordinary differential equations in symplectic space. Exact solutions for free vibration are obtianed by the method of separation of variables without any trial shape functions and can be expanded in series of symplectic eigenfunctions. Analytical frequency equations are derived for all six possible boundary conditions. Vibration modes are expressed in terms of the symplectic eigenfunctions. In the numerical examples, comparison is presented to verify the accuracy of the proposed method. Comprehensive numerical examples for graphene sheets with Levy-type boundary conditions are given. A parametric study of the natural frequency is also included.

Accurate and straightforward symplectic approach for fracture analysis of fractional viscoelastic media

An accurate and straightforward symplectic method is presented for the fracture analysis of fractional two-dimensional(2D)viscoelastic media.The fractional Kelvin-Zener constitutive model is used to describe the time-dependent behavior of viscoelastic materials.Within the framework of symplectic elasticity,the governing equations in the Hamiltonian form for the frequency domain(s-domain)can be directly and rigorously calculated.In the s-domain,the analytical solutions of the displacement and stress fields are constructed by superposing the symplectic eigensolutions without any trial function,and the explicit expressions of the intensity factors and J-integral are derived simultaneously.Comparison studies are provided to validate the accuracy and effectiveness of the present solutions.A detailed analysis is made to reveal the effects of viscoelastic parameters and applied loads on the intensity factors and J-integral.

Inverse Load Identification in Stiffened Plate Structure Based on in situ Strain Measurement

For practical engineering structures,it is usually difficult to measure external load distribution in a direct manner,which makes inverse load identification important.Specifically,load identification is a typical inverse problem,for which the models(e.g.,response matrix)are often ill-posed,resulting in degraded accuracy and impaired noise immunity of load identification.This study aims at identifying external loads in a stiffened plate structure,through comparing the effectiveness of different methods for parameter selection in regulation problems,including the Generalized Cross Validation(GCV)method,the Ordinary Cross Validation method and the truncated singular value decomposition method.With demonstrated high accuracy,the GCV method is used to identify concentrated loads in three different directions(e.g.,vertical,lateral and longitudinal)exerted on a stiffened plate.The results show that the GCV method is able to effectively identify multi-source static loads,with relative errors less than 5%.Moreover,under the situation of swept frequency excitation,when the excitation frequency is near the natural frequency of the structure,the GCV method can achieve much higher accuracy compared with direct inversion.At other excitation frequencies,the average recognition error of the GCV method load identification less than 10%.

Fracture analysis of magnetoelectroelastic bimaterials with imperfect interfaces by symplectic expansion

A Hamiltonian-based analytical method is used to study the mode Ⅲ interface cracks in magnetoelectroelastic bimaterials with an imperfect interface. By introducing an unknown vector, the governing equations are reformulated in sets of first-order ordinary differential equations. Using separation of variables, eigensolutions in the symplectic space are obtained. An exact solution of the unknown vector is obtained and expressed in terms of symplectic eigensolutions. Singularities of mechanical, electric, and magnetic fields are evaluated with the generalized intensity factors. Comparisons are made to verify accuracy and stability of the proposed method. Numerical examples including mixed boundary conditions are given.

Prediction of Postbuckling Characteristics of Perforated Metamaterial Cylindrical Shells Under Axial Compression

Large deflection postbuckling responses of metamaterial cylindrical shells perforated by arrayed circular holes are investigated through a newly proposed theoretical model incorporating with finite element method and experiment.The triggering of an unusual pattern transformation under compressive load(that shows special hyperelastic metamaterial characteristics)contributes to the particularity of the postbucklingmodes,in which the axisymmetric waisted and non-axisymmetric postbuckling configurations of perforated cylindrical shells are identified.The transformations of postbucking modes are mainly affected by global outline sizes of the shell and local geometrical parameters of holes.The structural load-carrying capacity for the waisted postbuckling response suffers a sudden drop and recovers when the holes collapse.Comparatively,the shell would undergo a sustained fall off under non-axisymmetric postbuckling states.The negative Poisson’s ratio induced by pattern transformation plays a key role and a critical effective threshold value exists,inducing the waisted postbuckling mode.The revealed principles would be of benefit for achieving a controllable structural stability that is usually difficult to implement on those conventional structures.

An Optimal Design of the Two-Staged Square Sectional Combined Energy Absorption Structure with Local Surface Nanocrystallization

In this paper,a local surface nanocrystallization technology is used for thin-walled structures with square cross sections,and an energy absorption device of two-staged combined energy absorption structure is proposed.In virtue of the surface nanocrystallization that enables to change the material on local positions,the structural deformation is induced and controlled to maximize the energy absorption capacity.A numerical model of the two-staged combined energy absorption structure is established,and the local surface nanocrystallization layout is optimized.The results show that the specific energy absorption of two-staged combined structure with local surface nanocrystallization can be increased by 34.36%compared with the untreated counterpart of the same material and structural shape.The ratio between the first and second peak crushing forces and the energy absorption allocation ratio between the two stages can be adjusted in the ranges of 0.26–0.55 and 0.31–0.45,respectively,which can be controlled by the local surface nanocrystallization designs.The numerical simulation and experimental results are in good agreement,which shows that the design for energy absorption device with local surface nanocrystallization is feasible and effective.