Zhoulian Zheng

A Theoretical Study of Thin Film Delamination Using Clamped Punch-Loaded Blister Test: Energy Release Rate and Closed-Form Solution

Using an exact analytical solution of axisymmetric deformation of a circular membrane centrally connected to a rigid plate under the action of concentrated load at its center, we present an exact formula for the energy release rate applicable to ultrathin film–substrate systems without residual stresses or with small residual stresses. Also, a closed-form solution of axisymmetric deformation of circular membrane under the action of concentrated load at its center is presented.

DYNAMIC ANALYSIS FOR NONLINEAR VIBRATION OF PRESTRESSED ORTHOTROPIC MEMBRANES WITH VISCOUS DAMPING

This paper is concerned with the nonlinear damped vibration of prestressed orthotropic membrane structures. The Krylov–Bogolubov–Mitropolsky (KBM) perturbation method is employed for solving the governing equations of large amplitude nonlinear vibration of rectangular orthotropic membranes with viscous damping. Presented herein are asymptotic analytical solutions for the frequency and displacement function of large amplitude nonlinear damped vibration of rectangular orthotropic membranes with four edges simply supported or fixed. Through the computational example, we compared and analyzed the frequency results. Meanwhile, the vibration mode of the membrane and the displacement and time curve of each feature point on the membrane surface were analyzed. The results obtained herein provide a simple and convenient approach to calculate the frequency and lateral displacement of large amplitude nonlinear vibration of rectangular orthotropic membranes with low viscous damping. In addition, the results provide some computational basis for the vibration control and dynamic design of membrane structures.

Analytical Solutions for Bending Curved Beams with Different Moduli in Tension and Compression

When materials that exhibit different mechanical behaviors in tension and compression must be analyzed, Ambartsumyans bimodular model for isotropic materials can be adopted. It deals with the principal stress state in a point, which is particularly important in the analysis and design of structures. In this article, an equivalent section method is used to transform the bimodular curved beam into a classical one with singular modulus; consequently, the simplified solution for bending stresses may be easily determined only by changing a few parameters relating to section characteristics. For the determination of the unknown neutral layer, a perturbation method is used to obtain the explicit expression. Based on the known neutral layer, a stress function method is used to obtain the elasticity solution for stresses and displacements via boundary conditions and continuity conditions. Based on the elasticity solution, an initial stresses problem in a bimodular multiply-connected body is considered. The comparison between two solutions shows that the simplified solution agrees very well with the elasticity one. Moreover, the inclusion of shear stress and the application of the equivalent section method in reinforced-concrete curved beams are also discussed. The results indicate that the bimodularity of materials has definite influences on the bending behavior of a bimodular curved beam.

Large Displacement Analysis of Rectangular Orthotropic Membranes under Stochastic Impact Loading

This paper studies the calculation method about the displacement response mean function of rectangular orthotropic membranes with four edges fixed under stochastic impact loading. We set up the nonlinear stochastic governing differential equation, solve it according to the perturbation method and the random vibration theory and obtain the displacement response mean value function of the membrane surface. Furthermore, this paper makes a random simulation test for ZZF membrane material which is commonly applied in the membrane structural engineering and obtains abundant deflection response sample curves about the feature points of the membrane surface. For sample curves statistical analysis at some fixed time, sample means can be obtained, which verify the correctness of the theoretical calculation method. The calculation method provides a theoretical basis for vibration control of building membrane structures to control the occurrence of natural disasters.

Analytical and numerical studies on the nonlinear dynamic response of orthotropic membranes under impact load

Orthotropic membrane components and structures are widely used in building structures, instruments and meters, electronic engineering, space and aeronautics, etc., because of their light weights. However, the same lightweight combined with low stiffness make membranes prone to vibration under dynamic loads, and in some cases the vibration may lead to structural failure. Herein, the undamped nonlinear vibration response of pretension rectangular orthotropic membrane structures subjected to impact loading is studied by analytical and numerical methods. The analytical solution is obtained by solving the governing equations by the Bubnov-Galerkin method and the Lindstedt-Poincaré perturbation method. Numerical analysis has also been carried out based on the same theoretical model. The analytical and numerical results have been compared and analyzed, and the influence of various model parameters on membrane vibration discussed. The results obtained herein provide some theoretical basis for the vibration control and dynamic design of orthotropic membrane components and structures.

Nonlinear Instability of Dished Shallow Shells under Uniformly Distributed Load

In this paper, the nonlinear instability of dished shallow shells under a uniformly distributed load is investigated. The dimensionless governing differential equations for the problem are derived and the equations solved by using the Free-Parameter Perturbation Method with the Spline Function Method. By analyzing the instability modes of dished shallow shells, we obtain the variation rules of the maximum deflection area of initial instability of the uniformly loaded dished shallow shell, and discuss the relationship between the initial instability area and the maximum deflection area of initial instability. These results provide some theoretical basis for engineering design and instability prediction and control of shallow shell structures.

Aerodynamic Stability Analysis of Geometrically Nonlinear Orthotropic Membrane Structure with Hyperbolic Paraboloid

This paper studies the aerodynamic stability of a tensioned, geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid. The aerodynamic force acting on the membrane surface is determined by the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics. The interaction governing the equation of wind-structure is established on the basis of large-amplitude theory and the D’Alembert principle. Then, under the circumstance of single-mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction equation into a system of second-order nonlinear differential equations with constant coefficients. Through judging the stability of the system characteristic equation, the critical velocity of divergence instability is determined. Different parameter analysis shows that the orthotropy and geometrical nonlinearity is significant for preventing destructive aerodynamic instability in membrane structures. Compared to the planar model, there is a little inconsistency about the divergence instability regularities in the hyperbolic paraboloid model.

A nondestructive method for the pretension detection in membrane structures based on nonlinear vibration response to impact

The pretension of building membrane structures may relax over its service lifetime, which may cause engineering failure under external loads. Therefore, the pretension of building membrane structures should be monitored or estimated regularly to compare the actual pretension to its design pretension and then to adopt some strengthening measures to mitigate future problems. Based on the geometrically nonlinear vibration of a rectangular orthotropic membrane structure, a nondestructive detection method for monitoring its pretension is developed in this article. This method is achieved by impacting a low-velocity pellet onto the membrane surface to generate vibration and detecting its response amplitude. Then the detected amplitude is converted into a pretension estimate via a derived formula. In addition, experiments for three kinds of conventional membrane material (Heytex H5573, Xing Yi Da, and ZZF 3010) were carried out according to the theoretical idea. The experimental results proved this method is feasible and verified the theoretical derivation is reasonable.

A perturbation solution of von-Kármán circular plates with different moduli in tension and compression under concentrated force

ABSTRACT By modifying classical von-Kármán equations, we established bimodular von-Kármán equations of thin plates with different moduli in tension and compression. Adopting central deflection as a perturbation parameter, we used a perturbation method to solve the equations under various boundary conditions, including rigidly clamped, loosely clamped, simply hinged, and simply supported. The relation of load versus central deflection and stress formulas were derived via the perturbation solution obtained. The numerical simulation also shows that the perturbation solution based on central deflection is overall valid. The results indicate that when the compressive modulus of materials is greater than the tensile one, the bearing capacity of the plate will be further strengthened, which should be considered in the analysis and design of plate-like structures with obvious bimodular effect. Moreover, by comparing with the case under uniformly distributed load, the plate-membrane transition under centrally concentrated force presents discontinuity to some extent.

Nonlinear Free Vibration Analysis of Axisymmetric Polar Orthotropic Circular Membranes under the Fixed Boundary Condition

This paper presents the nonlinear free vibration analysis of axisymmetric polar orthotropic circular membrane, based on the large deflection theory of membrane and the principle of virtual displacement. We have derived the governing equations of nonlinear free vibration of circular membrane and solved them by the Galerkin method and the Bessel function to obtain the generally exact formula of nonlinear vibration frequency of circular membrane with outer edges fixed. The formula could be degraded into the solution from small deflection vibration; thus, its correctness has been verified. Finally, the paper gives the computational examples and comparative analysis with the other solution. The frequency is enlarged with the increase of the initial displacement, and the larger the initial displacement is, the larger the effect on the frequency is, and vice versa. When the initial displacement approaches zero, the result is consistent with that obtained on the basis of the small deflection theory. Results obtained from this paper provide the accurate theory for the measurement of the pretension of polar orthotropic composite materials by frequency method and some theoretical basis for the research of the dynamic response of membrane structure.