geometrical nonlinearity
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This paper analyzes the dynamic stability of an isotropic viscoelastic Euler–Bernoulli nano-beam using piezoelectric materials. For this purpose, the size-dependent theory was used in the framework of the modified couple stress theory (MCST) for piezoelectric materials. In order to capture the geometrical nonlinearity, the von Karman strain displacement relation was applied. Hamilton’s principle was also employed to obtain the governing equations. Furthermore, the Galerkin method was used in order to convert the governing partial differential equations (PDEs) to a nonlinear second-order ordinary differential one. Dynamic stability analysis was performed and the effects of such parameters as viscoelastic coefficients, size effect, and piezoelectric coefficient were investigated. The results showed that in this system, saddle points, central points, Hopf bifurcation points, and fork bifurcation points could be created, and the phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, and homoclinic orbits.

This paper presents a computationally efficient numerical model for the analysis of thin shells based on rotation-free triangular finite elements. The geometry of the structure in the vicinity of the observed triangular element is approximated through a controlled domain consisting of nodes of the observed finite element and nodes of three adjacent finite elements between which a second-order spatial polynomial is defined. The model considers large displacements, large rotations, small strains, and material and geometrical nonlinearity. Material nonlinearity is implemented by considering the von Mises yield criterion and the Levi-Mises flow rule. The model uses an explicit time integration scheme to integrate motion equations but an implicit radial returning algorithm to compute the plastic strain at the end of each time step. The presented numerical model has been embedded in the program Y based on the finite–discrete element method and tested on simple examples. The advantage of the presented numerical model is displayed through a series of analyses where the obtained results are compared with other results presented in the literature.

The Timoshenko beam model is applied to the analysis of the flexoelectric effect for a cantilever beam under large deformations. The geometric nonlinearity with von Kármán strains is considered. The nonlinear system of ordinary differential equations (ODE) for beam deflection and rotation are derived. Moreover, this nonlinear system is linearized for each load increment, where it is solved iteratively. For the vanishing flexoelectric coefficient, the governing equations lead to the classical Timoshenko beam model. Furthermore, the influence of the flexoelectricity coefficient and the microstructural length-scale parameter on the beam deflection and the induced electric intensity is investigated.

This study presents a unified approach to simulate the behavior of rectangular concrete-filled steel stub columns incorporating high strength and ultra-high strength materials subjected to concentric axial compression. The finite element model is developed based on Abaqus software, which is capable of accounting for geometrical nonlinearity, material plasticity, and interaction between multi-physics. The proposed model incorporates the influences of residual stress for welded-box steel sections and initial imperfection. A novel stress-strain relation of confined concrete is proposed to account for the composite action, which might increase the strength and ductility of infilled concrete under multi-axial compressive conditions. Various verification examples are conducted with wide ranges of geometrical and material properties. The simulation results show that the proposed model can accurately predict the ultimate strength, load-deformation relations, and failure mode of the experimental specimens.

AbstractAn investigation of dynamic behaviors of a sandwich plate containing an imperfect two dimensional functionally graded (2D-FG) core surrounded by two faces on a two-parameter elastic foundation and subjected to a moving load is carried out in this paper. The present sandwich solid is composed of a porous 2D-FG core covered by two homogenous layers. It is assumed that the middle layer has micro voids dispersed uniformly and unevenly through the layer thickness. The fundamental equations are governed within the framework of first-order-shear deformation theory by utilizing Hamilton’s principle, von-Karman geometrical nonlinearity and the principal of mixtures. Newmark direct integration procedure is implemented to transform the dynamic equations into a static form and then the kinetic dynamic relaxation numerical technique in conjunction with the finite difference discretization method are employed to solve the nonlinear partial differential governing equations. Finally, the effects of porosity fraction and scattering patterns, boundary constrains, the variation of materials’ grading indexes and elastic foundation constants on the transient performances of the plate are studied in detail.

In this study, harvesting energy from a nonlinear functionally graded (FG) piezoelectric cantilever beam under harmonic excitation is investigated. The material properties of the piezoelectric are assumed to be a combination of piezo-ceramic and piezo-polymer materials for high performance and flexibility. The neutral axis is obtained in order to eliminate bending–stretching coupling. The geometrical nonlinearity and electromechanical coupling are incorporated in the coupled nonlinear equations that are derived using the generalized Hamilton’s principle and solved using the combination of modal reduction and finite element methods. The shooting method is employed to obtain steady-state periodic response of an FG nonlinear harvester with appropriate initial conditions. Also it is shown that at least two-mode approximation is required for accurate estimation of nonlinear response and harvested power. Using the method of nonlinear modal reduction, the unstable branches for frequency domain solution are estimated and the computational time is reduced considerably compared to full finite element method. A case study is also accomplished in detail to analyze the effects of base amplitude values and material distribution on harvested power and bandwidth.

A smart-skin antenna structure is investigated for active flutter control with piezoelectric sensors and actuators. The skin antenna is designed as a multilayer sandwich structure with a dielectric polymer to perform the role of antenna or radar structures. The governing equations are developed according to the first-order shear deformation theory, and von Karman strain–displacement relationships are used for the moderate geometrical nonlinearity. To consider the supersonic airflow, first-order piston theory is performed for the aerodynamic pressures. The linear quadratic regulator (LQR) method is applied as a control algorithm, and Newmark’s method is studied to obtain the numerical results. In the present study, the effects of placements and shape of piezoelectric patches are discussed on the flutter control of the model in detail. In addition, the numerical results show that the skin antenna model can effectively suppress the panel flutter behaviors of the model, optimal conditions of piezoelectric patches are obtained for skin antenna structures.

In order to analyze the buckling behavior of lattice shells stiffened by cables or slender braces without pre-tension, it is necessary to consider the no-compression property of braces. This paper proposes an innovative method of linear buckling analysis that considers the no-compression property of braces. Moreover, in order to examine the proposed method's validity, its results are compared with the results from a nonlinear buckling analysis with geometrical nonlinearity and material nonlinearity to express the no-compression property of braces. The results show that the proposed method can well-predict the buckling behaviors of lattice shells stiffened by tension braces.

Abstract A novel passive asymmetric quasi-zero stiffness vibration isolator (AQZS-VI) comprising two linear springs acting in parallel with one negative stiffness element (NSE) is proposed, of which the NSE is mainly constructed by the combination of cantilever plate spring and L-shaped lever (CPS-LSL). The static model of the isolator is deduced considering the geometrical nonlinearity of the NSE and the bending deformation of plate spring. The nonlinear stiffness properties of the CPS-LSL and the AQZS-VI, as well as the nonlinear damping properties of the AQZS-VI are discussed. The absolute displacement transmissibility of the AQZS-VI under base displacement excitation is obtained using Harmonic Balance Method, and the effects of different excitation amplitudes and damping factors on the vibration isolation performance are analyzed. Better than other quasi-zero stiffness vibration isolators (QZS-VI) whose NSEs do not provide supporting force at zero stiffness point, the NSE of the AQZS-VI provides more supporting force than the parallel connected linear springs, which is very beneficial for improving the bearing capacity of the isolator. Compared with a typical symmetric QZS-VI with same damping property, the AQZS-VI has longer stroke with low stiffness and lower peak value of displacement transmissibility. The prototype experiments indicate that the AQZS-VI outperforms the linear counterpart with much smaller starting frequency of vibration isolation and lower displacement transmissibility. The proposed AQZS-VI has great potential for applying in various engineering practices with superior vibration isolation performance.