粘贴片材加固混凝土梁的粘结剪应力分析

在受拉区表面粘贴加强片是加固混凝土梁的一种有效方法。本文在弹性理论的基础上,推导了受任意线性分布荷载作用下的混凝土梁采用粘贴加强片加固时,加强片端部粘结剪应力和最大粘结剪应力的计算公式。本文方法和有限元方法基本吻合。结果表明,最大锚固剪应力不但和粘胶层厚度、弹性模量有关,还和加强片厚度、弹性模量及长度有关。采用本文方法可以对加强片端部最大锚固剪应力进行验算,防止混凝土梁出现局部受拉破坏。本文研究结果将为进一步完善我国有关规范提供重要的参考资料。     

Interfacial fracture of piezoelectric multilayer actuators under mechanical and electrical loading

The elastic stress and strain fields in a plate of finite thickness containing an elliptical hole are systematically investigated using the 3D finite element method. It is found that the stress and strain concentrations are different in the plate of finite thickness even if the plate is in an elastic state. The relation between the stress and the strain concentration factors depends on Poisson’s ratio, the hole’s geometric configuration and the plate thickness. The stress concentration factor is equal to the strain concentration factor only at the notch root of the plate surface. The stress (or strain) concentration factor at the notch root of the plate surface decreases rapidly with increasing thickness and becomes lower than the stress and strain concentration factors corresponding to the plane stress state or at the notch root of the mid plane. It is too low to reflect the overall stress concentration as the thickness increases or as the b/a ratio decreases. The maximum stress concentration factor occurs on the mid plane only when the plate is thinner than the transition thickness of the stress concentration factor. When the plate is thicker than the transition thickness of the stress concentration factor, the distance between the location of the maximum stress concentration factor and plate surface tends to be constant with increasing thickness for the plate with a given  b/a ratio. The differences between the maximum value and the surface value of the stress and strain concentration factors increase rapidly and tend to their respective constant values with increasing plate thickness. The smaller the b/a ratio, the larger these differences. The difference of the stress concentration factor is larger than that of the strain concentration factor in the same plate.     

The effect of biaxial load on stress and strain concentrations in a finite thickness elastic plate containing a circular hole

The elastic stress and strain fields of a finite thickness plate containing a circular hole subjected to a biaxial load are systematically investigated using the finite element method. It is found that the stress and strain concentration factors of the finite thickness plate are different even if the plate is in elasticity state. The maximum stress and strain concentration factors do not always occur on the mid plane of the plate. The maximum stress and strain concentration factors of the notch root increase from their plane stress value to their peak values, then decrease gradually with increasing thickness and tend to constant values related to the load biaxiality ratio, respectively. The stress and strain concentration factors at the notch root of free surface are the monotonic descent functions of thickness. Their values decrease rapidly and tend to lower the limit values related to the load biaxiality ratio with increasing plate thickness. The differences of stress and strain concentration factors between maximum and surface value increase rapidly and tend to constant values related to the load biaxiality ratio with increasing plate thickness. The smaller the load biaxiality ratio, the larger these differences. Copyright © 2007 John Wiley & Sons, Ltd.     

Propagation of impact-induced stress waves in composite plates

A theoretical investigation is carried out of the response of a laminated plate to a surface impact. The plate consists of four layers of a uni-directional fiber composite in a symmetric cross-ply configuration. The composite material is modeled as a transversely isotropic, homogeneous, elastic continuum. The four layers are assumed to be of finite depth, infinite lateral extent, and perfectly bonded to each other. The surface impact has been modeled by three different conditions, namely, a delta function impulse, a square pulse, and a half-sine pulse. The variation with depth of the normal component of stress is examined as a step toward gaining insight into the through thickness response of the plate.     

Hydroelastic Behavior of a Floating Ring-Shaped Plate

The interaction between incident surface water waves and floating elastic plate is studied. This paper considers the diffraction of plane incident waves on a floating flexible ring-shaped plate and its response to the incident waves. An analytic and numerical study of the hydroelastic behavior of the plate is presented. An integro-differential equation is derived for the problem and an algorithm of its numerical solution is proposed. The representation of the solution as a series of Hankel functions is the key ingredient of the approach. The problem is first formulated. The main integro-differential equation is derived on the basis of the Laplace equation and thin-plate theory. The free-surface elevation, plate deflection and Green’s function are expressed in polar coordinates as superpositions of Hankel and Bessel functions, respectively. These expressions are used in a further analysis of the integro-differential equation. The problem is solved for two cases of water depth infinite and finite. For the coefficients in the case of infinite depth a set of algebraic equations is obtained, yielding an approximate solution. Then a solution is obtained for the general and most interesting case of finite water depth analogously in the seventh section. The exact solution might be approximated by taking into account a finite number of the roots of the plate dispersion relation. Also, the influence of the plate’s motion on wave propagation in the open water field and within the gap of the ring is studied. Numerical results are presented for illustrative purposes.     

An Equation for Stress Concentration Factor in Countersunk Holes

A detailed three-dimensional finite element stress analysis was conducted on straight-shank and countersunk rivet holes in a plate subjected to tension loading. The study included a wide range of plate width to radius, thickness to radius, countersunk depth to thickness ratios and countersunk angles(θ_c). The stress concentration is maximum at or near the countersunk edge. The stress concentration depends on countersunk depth, plate thickness and width and it is nearly independent of the countersunk angle for 80° ≤ θ_c ≤ 120°. Using the finite element results and limiting conditions, an equation for stress concentration factor is developed and verified.     

波浪与弹性板作用的数值模拟

该文采用高阶有限元和边界元联合的方法求解波浪与弹性板的相互作用。其中流场采用边界元法求解,结构弹性响应方程采用基于Mindlin板理论的有限元方法求解,通过模态叠加技术实现了弹性板变形与流场相互作用的解耦。通过对一矩形板的计算,验证了该文方法与他人试验结果和数值模拟结果都吻合良好。利用这一模型进一步分析了波浪与弹性圆形板的作用问题,并对圆形板运动响应的收敛性进行了分析。     

The Wiener–Hopf and residue calculus solutions for a submerged semi-infinite elastic plate

We present a solution for the interaction of normally incident linear waves with a submerged elastic plate of semi-infinite extent, where the water has finite depth. While the problem has been solved previously by the eigenfunction-matching method, the present study shows that this problem is also amenable to the more analytical, and extremely efficient, Wiener–Hopf (WH) and residue calculus (RC) methods. We also show that the WH and RC solutions are actually equivalent for problems of this type, a result which applies to many other problems in linear wave theory. (e.g., the much-studied floating elastic plate scattering problem, or acoustic wave propagation in a duct where one wall has an abrupt change in properties.) We present numerical results and a detailed convergence study, and discuss as well the scattering by a submerged rigid dock, particularly the radiation condition beneath the dock.     

Sensitivity of Dynamic Response of a Simply Supported Functionally Graded Magneto-electro-elastic Plate to its Elastic Parameters

Dynamic response sensitivity of a simply supported functionally graded magneto-electro-elastic plates have been studied by combining analytical method with finite element method. The functionally graded material parameters are assumed to obey exponential law in the thickness direction. A series solution of double trigonometric function agreed with the simply supported boundary condition is adopted in the plane of the plate and finite element method is used across the thickness of the plate. The finite element model is established based on energy variational principle. The coupled electromagnetic dynamic characteristics of a simply supported functionally graded magneto- electro-elastic plate are decided by its dynamics differential equation into which displacement components, electric potential and magnetic potential as nodal degree of freedom are incorporated. Dynamic response sensitivity is defined as a partial differential of dynamic response with respect to material parameter. Sensitivity of dynamic response of a simply supported functionally graded magneto-electro-elastic plate to its elastic parameters has been studied. The influence of the different exponential factor on dynamic response sensitivity has also been investigated.     

Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates

In this paper, nonlinear static and free vibration analysis of functionally graded piezoelectric plates has been carried out using finite element method under different sets of mechanical and electrical loadings. The plate with functionally graded piezoelectric material (FGPM) is assumed to be graded through the thickness by a simple power law distribution in terms of the volume fractions of the constituents. Only the geometrical nonlinearity has been taken into account and electric potential is assumed to be quadratic across the FGPM plate thickness. The governing equations are obtained using potential energy and Hamilton’s principle that includes elastic and piezoelectric effects. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect using higher order plate elements. The present finite element is modeled with displacement components and electric potential as nodal degrees of freedom. Results are presented for two constituent FGPM plate under different mechanical boundary conditions. Numerical results for PZT-4/PZT-5H plate are given in dimensionless graphical forms. Effects of material composition and boundary conditions on nonlinear response are also studied. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.     

A hybrid numerical and imaging approach for characterizing defects in composite structures

In this study, a hybrid approach coupling hyperspectral near infrared imaging with a progressive finite element method is proposed for characterization of the elastic and failure response of composites with non-uniform variations of the wrinkles profile through the thickness and across the structure dimensions. In this approach, hyperspectral near infrared spectroscopy is used to create a 3D profile of the surface resin pockets with the capability of measuring resin thickness from approximately 125 to 2500 μm. These resin pockets are directly correlated to underlying ply level wrinkling as confirmed by optical microscopy. The 3D mapped resin plane obtained from the hyperspectral imaging is used to morph a ply-by-ply finite element model of a carbon-fiber/epoxy resin laminated plate using a progressive damage failure methodology. The results show the capability of the hybrid method to predict the structural response in laminated composites containing spatially distributed and non-uniform ply-level wrinkling.     

纯钛燃料电池双极板软模成形工艺研究

目的 研究软模成形过程中塑性应变比r值对双极板成形深度及壁厚的影响,探究不同工艺参数对双极板尺寸的影响规律。方法 通过单向拉伸实验得到纯钛极薄带的力学性能参数,然后采用橡胶软模成形方法制备纯钛燃料电池双极板,利用光学显微镜对制备的双极板尺寸及壁厚进行测量并深入分析。结果 TD取向的r值最大为2.56,沿该方向成形时,纯钛极薄带在载荷为300 kN、软模硬度为77HA条件下得到的双极板深度最大,为0.293 mm;同时,其壁厚减薄较小,在减薄最严重的位置壁厚减薄率仅为13.52%。结论 较大的载荷与适宜的软模硬度能得到较好的双极板深度,对双极板周期无影响;双极板深度、壁厚与r值有关,r值越大,纯钛极薄带抵抗壁厚减薄的能力越强,成形深度越大。     

Effect of the thickness on elastic deformation and quasi-brittle fracture of plate components

Plane theory of elasticity lays a foundation for many important results in science and engineering. However, the understanding of the elastic solutions derived under plane stress or plane strain assumption, is far from complete. In particular, it is not clear how adequate the classical two-dimensional solutions of the plane theory of elasticity are when applied to the analysis of actual plate components having a finite thickness. So far there is no generally accepted criterion for identifying what thickness would qualify as plane stress or plane strain and, in general, what effect on the stress distribution the plate thickness has. In this work we review some recent analytical efforts, numerical and experimental studies in order to throw light onto how the plate thickness, which is largely ignored by the classical plane solutions of the theory of elasticity, influences the elastic deformation and quasi-brittle fracture of plate components.     

Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation

The free vibration characteristics of rectangular continuous grading fiber reinforced (CGFR) plates resting on elastic foundations have been studied, based on the three-dimensional, linear and small strain elasticity theory. The foundation is described by the Pasternak or two-parameter model. The CGFR plate is simply supported at the edges and is assumed to have an arbitrary variation of fiber volume fraction in the thickness direction. Suitable displacement functions that identically satisfy the simply supported boundary conditions are used to reduce the equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which can be solved by differential quadrature method (DQM) to obtain natural frequencies. Convergence studies have been performed on CGFR plates on the elastic foundations. It is shown that the present method has a rapid convergent rate, stable numerical operation and very high accuracy. Besides results for CGFR plate with arbitrary variation of fiber volume fraction in the plate’s thickness are compared with discrete laminated composite plate. The main contribution of this work is to present useful results for continuous grading of fiber reinforcement in the thickness direction of a plate on elastic foundation and comparison with similar discrete laminate composite plate. Results indicate the advantages of using CGFR plate with graded fiber volume fractions over traditional discretely laminated plates.     

Elastic-Plastic Analysis Under Proportional and Non-Proportional Loading Paths Using Deformation Plasticity Theory

Abstract

An estimation of elastic-plastic stresses and strains is presented for mechanical components, using pseudo elastic analysis based on the deformation theory of plasticity. Analysis of two applications, one under proportional loading and other under non-proportional loading paths using pseudo elastic finite element method, is presented. A rectangular plate with a hole under tension loading and a rectangular plate fixed at one end under bending-tension non-proportional loading are considered for analysis. Pseudo Elastic finite element analysis for proportional loading uses elastic solutions and varies material properties for elements in plastic zone to estimate elastic-plastic solution. A finite element code is developed based on pseudo elastic analysis method. An attempt is made to extend pseudo elastic analysis to analyze bending-tension non-proportional loading problem. Both applications in consideration are assumed to be of Von Mises material and follow isotropic hardening rule with elastic-linear hardening material model. Non-linear analysis of the plate with a hole under proportional tensile loading and that of rectangular plate under bending-tension non-proportional loading are performed in ANSYS and results are compared for validation and are observed to be in good agreement with present analysis.     

高速船舱壁加筋板流固耦合振动分析

将结构有限元法和流体有限元法结合起来,根据Garlerkin法和Hamilton变分原理分别推导出离散的流体和结构的运动方程,用湿模态法求得流体附加质量矩阵,对高速船舱壁加筋板流固耦合系统进行了模态分析。并进行模态试验,研究不同水深时舱壁加筋板结构流固耦合振动模态,同时与有限元计算结果进行比较,从而揭示了该类结构流固耦合振动的动力特性,对舱壁加筋板结构的动力设计具有指导意义。     

Numerical and experimental studies on aluminum sandwich plates of variable thickness

Abstract

The elastic flexural behavior of static deformation and free vibration of sandwich plates of variable thickness is investigated numerically and experimentally. In the analysis, the face plates are treated as Marguerre shells, and the core is assumed to be an antiplane core and to provide resistance to transverse shear and normal stresses only. Displacement continuity conditions are used at the interfaces between face plates and the core to derive the displacement field. Energy formulations are obtained and solved by the isoparametric finite element method. The numerical results are obtained to compare with the results in the existing literature and to show the effects of taper constant and face plate thickness on deflections and natural frequencies. Finally, experimental works based on the method of holographic interferometry are conducted to confirm the theoretical findings. Experimental and numerical data agree quite well in this work.     

A numerical study of a plate with a hole for a new class of elastic bodies

It has been shown recently that the class of elastic bodies is much larger than the classical Cauchy and Green elastic bodies, if by an elastic body one means a body incapable of dissipation (converting working into heat). In this paper, we study the boundary value problem of a hole in a finite nonlinear elastic plate that belongs to a subset of this class of the generalization of elastic bodies, subject to a uniaxial state of traction at the boundary (see Fig. 1). We consider several different specific models, including one that exhibits limiting strain. As the plate is finite, we have to solve the problem numerically, and we use the finite element method to solve the problem. In marked contrast to the results for the classical linearized elastic body, we find that the strains grow far slower than the stress.     

Stress distribution,crack shape and energy for a penny-shaped crack in a plate of finite thickness

The shape of a penny-shaped crack located at the center of an elastic plate of finite thickness is related to the arbitrary axisymmetrical internal pressures applied to the crack surfaces in the form of a Fredholm integral equation, without using the methods of dual-integral equations. General expressions for the stresses in the plane containing the crack are written as the sums of the associated infinite solid stresses and the integrals accounting for the effect of plate thickness. The crack shape due to uniform crack pressures and the fracture criterion for brittle plates subjected to uniform stresses are obtained for various plate thicknesses.     

On the reduce of interfacial shear stresses in fiber reinforced polymer plate retrofitted concrete beams

One major problem when using bonded fiber reinforced polymer (FRP) plate is the presence of high interfacial shear stresses near the end of the composite (edge effect) which might govern the failure of the strengthening schedule. It is known that the decrease of plate thickness reduces the magnitude of stress concentration at plate ends. Another way is to use a plate end tapering. In this paper, the analytical solution of interfacial shear stresses obtained has been extended by a numerical procedure using the modal analysis of finite element method (FEM) in a retrofitted concrete (RC) beam with the FRP plate with tapered end, which can significantly reduce the stress concentration. This approach allows taking into consideration the variation of elastic properties of adhesive and plate as well as the complicated geometrical configurations and effects of thermal loads.