有加强孔平板的剪切稳定性试验方法

本文对有加强孔平板的剪切稳定性试验方法进行了研究，提出了一种简单适用的试验装置和试验夹具。并对试验数据和理论计算值进行了比较，认为这种方法简单易行，便于工程应用     

Asymptotic analysis of perforated plates and membranes. Part 2: Static and dynamic problems for large holes

Static and dynamic problems for the elastic plates and membranes periodically perforated by holes of different shapes are solved using the combination of the singular perturbation technique and the multi-scale asymptotic homogenization method. The problems of bending and vibration of perforated plates are considered. Using the asymptotic homogenization method the original boundary-value problems are reduced to the combination of two types of problems. First one is a recurrent system of unit cell problems with the conditions of periodic continuation. And the second problem is a homogenized boundary-value problem for the entire domain, characterized by the constant effective coefficients obtained from the solution of the unit cell problems. In the present paper the perforated plates with large holes are considered, and the singular perturbation method is used to solve the pertinent unit cell problems. Matching of limiting solutions for small and large holes using the two-point Padé approximants is also accomplished, and the analytical expressions for the effective stiffnesses of perforated plates with holes of arbitrary sizes are obtained.     

基于均匀化理论的多孔板弯曲问题新解

由于订型分布孔的存在,通常的有限元法不能有效地分析多孔板的弯曲问题。该文基于均匀化理论建立了该类问题的新解法。对含密集型分布的阶梯型圆孔板的分析结果,说明了该文方法是有效的。     

Diffraction of stress waves by a free or reinforced hole in an orthotropic plate

Photoelastic plates made of an orthotropic material are used to model the dynamic stress state near free and reinforced circular holes under blast loading. The diffraction of stress waves by holes in a thin-walled plate is studied. Experimental data are used to analyze the dynamic stress concentration in a plate with a hole in which quasilongitudinal and quasitransverse waves propagate __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 73–78, July 2007.     

孔结构金属复合夹芯板抗爆炸冲击响应及吸能特性研究

采用有限元方法研究爆炸载荷下四边固支孔结构金属复合夹芯板的动力响应及吸能特性,给出了孔结构金属复合夹芯板的动力响应过程,得到夹芯板的变形模式,比较了孔结构金属复合夹芯板与非孔结构金属复合夹芯板的抗爆炸冲击性能,同时讨论了孔大小、间距、排布方式和面板质量分布等因素对孔结构金属复合夹芯板抗爆炸冲击性能的影响。研究结果表明,迎爆面外面板的孔设计使爆炸冲击波穿过孔洞直接作用在芯材上,增强了芯材的压缩,从而提高了夹芯板的能量吸收能力。同等面密度情况下,内外面板厚度比大于1的孔结构金属复合夹芯板变形挠度小于内外面板厚度比小于1的孔结构金属复合夹芯板。进一步研究发现,通过合理设计内外面板的质量分布,可以使孔结构金属复合夹芯板的抗爆炸冲击性能最优。     

Dynamical bending of rigid-plastic annular plates

Dynamical bending of circular rigid-plastic annular plates, fixed along the exterior boundary and free on the interior boundary, when subjected to instantaneously applied transverse uniformly distributed blast-type load[1], is investigated in this paper.It is shown that annular plates are preferable to plates without holes, since their load capacity increases while residual deflections decrease. A so-called boundary parameter is introduced to estimate the effect of boundary conditions on the radial bending moment.A procedure for determining the residual deflections at every point of a plate is developed for use on an electronic computer. Numerical examples are given. In the end of the paper, the particularities of solution of our problem for annular plates, corresponding to the setting of Wang[2], Wang and Hopkins[3] for plates without holes are discussed.     

Dynamic stress concentrations in thick plates with two holes based on refined theory

Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.     

Reissner板弯曲的复变函数分析方法

本文建立了Reissner板弯曲问题的复变函数分析方法,它可以有效地用于分析含一般孔洞板弯曲的应力集中问题。作为应用,文中还给出了一些计算实例。     

Homogenization-based method for bending analysis of perforated plate

Owing to the existence of distributed holes, it is difficult to solve the bending problem of perforated plates by the conventional finite element method. A homogenization-based method for this problem is presented in this paper. As an example, the bending analysis of a circular perforated plate with distributed step-wise cylindrical holes is made. The deflection and the fundamental frequency obtained by present method are in good agreement with experimental data, this implies that the method is effective. This project is supported by the National Natural Science Foundation (19602007) and National Outstanding Youth Foundation (19525206).     

Response of composite plates to blast loading

The transient response of composite plates, with and without central circular holes, to blast loading is studied. The modal-analysis approach has been used in the computation of numerical results, which have been obtained for isotropic and orthotropic plates, with and without holes. In order to verify the theoretical results, experiments have been conducted on aluminum and unidirectionally reinforced E-glassepoxy plates, using a shock tube as the loading device. The experimental peak dynamic strains (normalized with respect to the pressure) are compared with the theoretical values. The strain-time history is also shown for a particular gage location in the composite plate. Finally, a comparison of dynamic-amplification factors, defined as the ratio of the peak dynamic strains to the static strains, has been made between the isotropic and the composite plates.     

含孔平板弹性波散射问题的复变函数方法

本文采用平板弯曲波动理论及复变函数方法，对平板开孔弹性波的散射及动应力集中问题进行了分析研究，得到了传播急剧记波时此种平板弯曲波动问题的分析解。若同时采用保角射技术，就为主解平板任意形状开孔弹性波的散射及动应力集中问题提供了一种统一规范的方法。作为算例，本文给出了平板开圆孔和椭圆孔附近的动应力集中系数的数值结果，并对其进行了讨论。     

Three-dimensional stress and free vibration analyses of functionally graded plates with circular holes by the use of the graded finite element method

Static and free vibration analyses of plates with circular holes are performed based on the three-dimensional theory of elasticity. The plates are made of a functionally graded material (FGM), and the volume fractions of the constituent materials vary continuously across the plate. The effective properties of the FGM plate are estimated by using the Mori–Tanaka homogenization method. A graded finite element method based on the Rayleigh–Ritz energy formulation is used to solve the problem. Effects of different volume fractions of the materials and hole sizes on the behavior of FGM plates under uniaxial tension are investigated. Natural frequencies of a fully clamped FGM plate with a circular cutout are derived. The results obtained are compared with available experimental data.     

Stress wave fields in plates weakened by curvilinear holes with edge cracks

The dynamic fracture of plates weakened by holes with edge cracks and subjected to impulsive loading is studied using the dynamic photoelastic method. The time dependences of the stress intensity factors and the crack growth rate are examined for three models of plates with circular holes and edge cracks __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 79–84, February 2006.     

Stability and limit states of elastoplastic spherical shells under static and dynamic loading

The problem of elastoplastic deformation, buckling, and postcritical behavior of spherical shells is solved using a finite element method and a cross-type explicit scheme of time integration. Stability problems for hemispherical shells under external pressure and compression between rigid plates are considered. The influence of holes and boundary conditions on shell deformation is investigated. It is shown that the calculation results are in good agreement with experimental data.     

Stress Concentration Factor in Functionally Graded Plates with Circular Holes Subjected to Anti-plane Shear Loading

Stress concentration factors due to the presence of geometrical discontinuities (circular holes) in functionally graded plates are derived. The material property inhomogeneity is assumed to be in the radial direction originating at the center of the plate. Variable separable closed-form solutions are obtained for the stresses and displacements in functionally graded plates (without and with holes) subjected to anti-plane shear loading. The stresses in functionally graded plates without a hole are not homogeneous as it is in the case of homogeneous plates. Either a stress concentration (more than the applied stress) or dilution (less than the applied stress) occurs depending on whether the modulus increases (hardening graded material) or decreases (softening graded material) away from the center of the graded plate without a hole. A novel definition of the stress concentration factor due to the geometrical discontinuity in functionally graded plates is derived. The effect of the circular hole in functionally graded plates is to magnify (compared to homogeneous plates) the stress concentration when the modulus decreases away from the center of the hole (softening material). Beneficial reduction of the stress concentration factor is achieved in hardening functionally graded materials.     

Minimizing stress concentrations around circular holes in uniaxially loaded plates

The problem of determining stress distributions and reducing stress concentrations around holes in plates occurs in numerous design situations. One method for reducing the stress concentration around a central circular hole in a uniaxially loaded plate was demonstrated by Heywood. With this approach, smaller holes are introduced on either side of the original hole to help smooth the flow of the tensile principal-stress trajectories past the original hole. For the one case reported by Heywood (which did not produce the greatest reduction possible), the maximum stress was reduced to 84 percent of that due to a single hole. In the present program, a systematic study was undertaken using two-dimensional photoelasticity method to determine the optimum sizes and locations for the auxiliary holes for a number of plates with different central-hole diameter-to-plate width ratios. Maximum stress reductions from 13 to 21 percent were demonstrated for plates with hole diameter-to-plate width ratios between 0.1 and 0.6. With such reductions in maximum stress level, the improvement in fatigue life of a part can be very significant.     

各向异性弹性体中矩形孔边缘应力分布

推导了各向异性平面弹性体中矩形孔洞边缘的应力分布公式并给出了数值计算结果。工程中会遇到矩形孔洞的问题，而矩形孔导致的应力集中增加了工程问题的复杂性。目前尚没有简单实用的公式计算矩形孔在各向异性体中应力的分布。本文采用复变函数保角变换的方法推导了矩形孔边缘的应力公式。在利用本文给出的方法，可以计算矩形孔在不同性质的各向异性材料中，承受任意的双轴荷载下孔边缘的应力分布情况。     

Solution of nonstationary problems in the mechanics of anisotropic bodies by the method of dynamic photoelasticity

The results obtained in developing and applying the method of dynamic photoelasticity to two-dimensional problems in the mechanics of anisotropic bodies are reviewed. The theory behind the method and its engineering implementation are described. The capabilities of the method are illustrated by solving specific nonstationary problems: dynamic stress concentration, diffraction of longitudinal and transverse waves by free and reinforced holes, dynamic fracture of orthotropic plates with holes and cracks under impulsive and explosive loads     

Determination of individual stresses thermoelastically

Hybrid methods are developed for determining individual stress components under plane stress from thermoelastically measured isopachics. Some of the techniques depend only on stress equilibrium and are independent of constitutive response. Applications are to a partially loaded half-plane, and tensile plates containing side notches and holes. These are believed to represent the first examples of separating stresses from thermoelastically measured data.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Stress analysis of finite composite laminate with multiple loaded holes

Based on the classical laminated plate theory, a finite composite plate weakened by multiple elliptical holes is treated as an anisotropic multiple connected plate. Using the complex potential method in the plane theory of elasticity of an anisotropic body, an analytical study concerned with the stress distributions around multiple loaded holes in finite composite laminated plates subjected to arbitrary loads was performed. The analysis makes use of the Faber series expansion, conformal mapping and the least squares boundary collocation techniques. The effects of plate and hole sizes, layups, the relative distance between holes, the total number of holes and their locations on the stress distribution are studied in detail. Some conclusions are drawn.