Xiao-ting He

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.

Nonlinear large deflection problems of beams with gradient: A biparametric perturbation method

For beams with gradient, due to the combined influences introduced by loads and gradient, the first derivative item in Euler-Bernoulli equation can not be neglected thus making the solution of the problem be a nonlinear large deflection one. In this paper, we use a new perturbation method with two small parameters, one describes the loads effect and another describes the geometrical nature of the problem, to solve the nonlinear large deflection problem of beams with gradient under the two different boundary conditions. We derive the first and second order approximate analytical solution of the deflection, the rotation and the arc length of the beam, as well as the internal forces of the beam at the end. The results indicate that the choice of two independent parameters may describe comprehensively the nonlinear effects caused by loads and gradient, which enables the approximate solution to be precise enough to be used for the analysis of large-deflection beam with gradient.

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.

One-Dimensional and Two-Dimensional Analytical Solutions for Functionally Graded Beams with Different Moduli in Tension and Compression

The material considered in this study not only has a functionally graded characteristic but also exhibits different tensile and compressive moduli of elasticity. One-dimensional and two-dimensional mechanical models for a functionally graded beam with a bimodular effect were established first. By taking the grade function as an exponential expression, the analytical solutions of a bimodular functionally graded beam under pure bending and lateral-force bending were obtained. The regression from a two-dimensional solution to a one-dimensional solution is verified. The physical quantities in a bimodular functionally graded beam are compared with their counterparts in a classical problem and a functionally graded beam without a bimodular effect. The validity of the plane section assumption under pure bending and lateral-force bending is analyzed. Three typical cases that the tensile modulus is greater than, equal to, or less than the compressive modulus are discussed. The result indicates that due to the introduction of the bimodular functionally graded effect of the materials, the maximum tensile and compressive bending stresses may not take place at the bottom and top of the beam. The real location at which the maximum bending stress takes place is determined via the extreme condition for the analytical solution.

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.

An elasticity solution of functionally graded beams with different moduli in tension and compression

ABSTRACT In this study, we analytically solved the problem of a functionally graded beam with different moduli in tension and compression under the action of uniformly distributed loads. By determining the location of the unknown neutral layer of the beam, we first established a simplified mechanical model based on complete partition of tension and compression. Using boundary conditions and continuity conditions of the neutral layer, we obtained an elasticity solution of the problem, in which grade functions of tensile and compressive moduli of elasticity are assumed to be two different exponential expressions while Poissons ratio is unchanged. The numerical results and comparison also verified the validity of the analytical solution. By changing the grade parameters of the material, the stress and displacement of the beam in three cases, i.e., the tensile modulus is greater than, equal to, or less than the compressive modulus, are discussed, respectively. The result shows that due to the introduction of bimodular effect and functional grade of materials, the maximum tensile and compressive bending stresses may not take place at the bottom and top of the beam, which should be given more attention in the analysis and design of structures made of functionally graded materials with bimodular effect.

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.

Theoretical Study on Synchronous Characterization of Surface and Interfacial Mechanical Properties of Thin-Film/Substrate Systems with Residual Stress Based on Pressure Blister Test Technique

In this study, based on the pressure blister test technique, a theoretical study on the synchronous characterization of surface and interfacial mechanical properties of thin-film/substrate systems with residual stress was presented, where the problem of axisymmetric deformation of a blistering film with initial stress was analytically solved and its closed-form solution was presented. The expressions to determine Poisson’s ratios, Young’s modulus, and residual stress of surface thin films were derived; the work done by the applied external load and the elastic energy stored in the blistering thin film were analyzed in detail and their expressions were derived; and the interfacial adhesion energy released per unit delamination area of thin-film/substrate (i.e., energy release rate) was finally presented. The synchronous characterization technique presented here has theoretically made a big step forward, due to the consideration for the residual stress in surface thin films.