Near-Boundary Stress Wave Field in Anisotropic Plates under Impulsive Load

The stress wave field and the behavior of waves near the free boundary in an orthotropic plate and at the interface between two anisotropic media are studied. The results presented were obtained using the dynamic photoelastic method and optically sensitive fibrous models. Experimental data for impulsively loaded plates with various boundary conditions are analyzed     

Stochastic boundary element method for reliability analysis of plate and beams composite structures

I.IntroductionTheengineeringstructuresareoftells,'1>:'rectcdtotheactionofthestochasticloadingthatvarieswiththetime,forexample,theengineeringstructuresactedonbytheearthquake,theoceanstructuresactedonbydynamicpressure,andthevehiclesofthetransportationinflue…     

板结构计算模型的新发展

现代复合材料层合板具有高强和轻型的突出优点,从而在军工和民用等诸多领域发挥着重要作用。这种板结构的特点是随着纤维走向的不同,层间材料的物理-力学特性发生剧烈变化。沿板厚方向变形的梯度比较陡峭,并在层间结合面处发生强不连续,呈现zig-zag （锯齿状）现象。这导致横向剪应变在板的静态和动态响应中发生重要作用,不计横向变形的经典组合板计算模型CLPT难以适应现代多层板计算分析的需要。考虑横向剪切变形影响的板的计算模型得到重视和发展。需要指出,现有各种考虑剪切变形影响的计算模型虽然有了很大的发展,但在全面和准确性上仍然存在一定的不足,难以适应现代多层组合板横向力和物理性能多变的情况。模型预测的沿板厚方向位移和应力的变化规律难以通过严格的检验。本文提出的以比例边界有限元为基础的正交各向异性板的数值计算模型,同时可适用于各种薄板与厚板的分析,对现代复合材料层合板的分析具有特殊的优越性。所得到的板的位移、正应力和剪应力沿板厚方向的变化,与三维弹性理论的标准解高度吻合。数值算例进一步表明,随着层间纤维走向的变化,板内位移场和应力场沿板厚方向剧烈变化所呈现的锯齿现象均可以精准地进行模拟。据此,本文建议方法对现代板分析的广泛适应性和高度准确性得到了充分论证。     

Winkler地基上四边自由正交各向异性矩形薄板弯曲问题的辛叠加解

研究Winkler地基上正交各向异性矩形薄板弯曲方程所对应的Hamilton正则方程, 计算出其对边滑支条件下相应Hamilton算子的本征值和本征函数系, 证明该本征函数系的辛正交性以及在Cauchy主值意义下的完备性, 进而给出对边滑支边界条件下Hamilton正则方程的通解, 之后利用辛叠加方法求出Winkler地基上四边自由正交各向异性矩形薄板弯曲问题的解析解. 最后通过两个具体算例验证了所得解析解的正确性.     

多层正交异性矩形薄板弯曲振动稳定解析解

构造了带有补充项的双重正弦傅里叶级数通解来求解各种边界条件的多层正交各向异性矩形薄板的弯曲、振动和稳定问题.将坐标轴取在中性面上,求出用挠度表示的应力表达式,然后由横截面上每单位宽度的应力合成板的内力;再将层合板的内力代入板的平衡方程中得到板的控制方程,将多层板的物理参数折算为等价的单层板物理参数;最后联立控制方程与边界条件,求得未知量的系数并代入本文的通解中.本文的通解不需要叠加即可求解各种边界条件的板的弯曲、振动和稳定问题;现有的对于单层板的研究都可以用本文的方法拓展到多层板领域;对于复杂边界条件的板,也可以使用该通解分析.     

基于近场动力学微分算子的含裂纹正交各向异性板热传导分析方法

采用近场动力学微分算子(Peridynamic Differential Operator, PDDO)理论建立正交各向异性板热传导的非局部模型。通过构造近场动力学函数,将边界条件和热传导方程由局部微分形式转化为非局部积分形式,引入Lagrange乘子,采用变分分析对含裂纹正交各向异性板温度及裂纹尖端的热通量分布进行求解。通过对比算例,验证了该模型具有较好的收敛性和有效性。分析了正交各向因子、材料铺设角、裂纹倾角及间距对裂纹尖端热通量的影响。结果表明,基于PDDO建立的含裂纹正交各向异性板热传导模型,考虑了热传导问题中的非局部性,能有效提高计算精度,预测含裂纹板中裂纹尖端出现的奇异性。     

Natural frequencies of thin,rectangular plates with holes or orthotropic “patches” carrying an elastically mounted mass

The approximate solution for the title problem is obtained in the case of simply supported and clamped rectangular plates made of isotropic or orthotropic materials. A variational approach (the well known Rayleigh–Ritz method) is used, where the displacement amplitude is expressed in terms of beam functions. This means that each coordinate function satisfies identically all the boundary conditions at the outer edge of the plate. Free vibration analysis has been performed on various different cases; solid isotropic and orthotropic plates, orthotropic plates with a hole and isotropic plates with an orthotropic inclusion or “patch”, carrying an elastically mounted concentrated mass. It is important to point out that the case of an orthotropic patch is interesting from a technological viewpoint since it constitutes a model of a repair implemented on the virgin structural element when it has suffered damage. This approach has been implemented by the aeronautical industry in some instances. The obtained results are in very good agreement with those of particular cases of simply supported plates available in the literature.     

正交各向异性厚板的边界元解法

本文利用 Hormander 算子法和平面波分解法导出了计入剪切变形的正交各向异性厚板的基本解。建立了计入剪切变形的正交各向异性厚板的边界积分方程。文中详细地讨论了基本解的数值计算,并用边界元法分析了一些算例。     

Photoelastic stress analysis of orthtropic materials by using an isotropic plate

Based on the two-dimensional theory of elasticity for an orthotropic plate, relations between stress components produced in two different orthotropic plates are considered and the conditions to realize the similar stress fields in different orthotropic plates are studied. On the basis of the similarity law, a convenient photoelastic method to analyze stress fields in an orthotropic plate, using an isotropic plate, is presented. Two examples are treated. One deals with the stress-concentration problem around a circular hole in a strip with edges parallel to the symmetric axis of elasticity. In the second example, the edges of the strip are assumed to be inclined by 30 deg to the elastically symmetric axes. The experimental results are compared with theoretical calculations. Paper was presented at the SEM VII International Congress on Experimental Mechanics held in Las Vegas, NV on June 8–11, 1992.     

Elastodynamic behavior of laminated orthotropic plates under initial stress

A finite element method of analysis of the vibrational and wave propagational characteristics is presented for a laminated orthotropic plate under initial stress. The plate may have an arbitrary number of bonded elastic orthotropic layers, each with distinct thickness, density and mechanical properties, and the analysis is capable of treating a completely arbitrary three-dimensional state of initial stress. Biot's theory for incremental elastic deformations of a stressed solid forms the basis for this study. A homogeneous, isotropic plate under two different states of initial stress was analyzed and their numerical results showed excellent correlation with those from an exact solution. Further examples of a three layer composite plate and a sandwich plate are offered to add some general insight to the physical behavior of such plates.     

Analytical bending solutions of free orthotropic rectangular thin plates under arbitrary loading

This paper presents the analytical solutions for the bending of orthotropic rectangular thin plates by the double finite integral transform, which, as an effective tool in solving plate problems, should have received attention. As a representative and difficult problem in the theory of plates, free plates’ bending is successfully solved to demonstrate the accuracy of the method by comparing the present analytical solutions with those from the literature as well as those by the finite element method. With the proper integral transform kernels, the proposed solution procedure is applicable to the bending of orthotropic rectangular plates with all combinations of simply supported, clamped and free boundary conditions, which serves as an elegant approach to analytical solutions of plate bending problems.     

Dynamic buckling of thin-walled composite plates with varying widthwise material properties

The paper deals with dynamic response of a thin-walled rectangular plate subjected to in-plane pulse loading. The plate is made of orthotropic (fibre composite) material in which the principal directions of orthotropy are parallel to the plate edges. The plate is characterised by a widthwise varying fibre volume fraction. The structures are assumed to be simply supported at the loaded ends and at non-loaded ends with five different boundary conditions (both simply supported, both fixed, simply supported fixed, simply supported free edge, fixed free edge). In order to obtain the equations of motion the non-linear theory of orthotropic thin-walled plates has been modified in such a way that it additionally accounts for all components of inertial forces. The differential equations of motion have been obtained from Hamilton’s Principle. The problem of nonlinear static stability was solved with the second order of the Koiter’s asymptotic stability theory of conservative systems. The results obtained from analytical–numerical method were compared with the results from finite element method (FEM).     

Exact solutions for variable-thickness inhomogeneous elastic plates under various boundary conditions

In this paper, an exact solution to the governing equations of the bending of a variable-thickness inhomogeneous rectangular plate is presented. The procedure is applicable to variable-thickness inhomogeneous rectangular plates with two opposite edges simply supported. The remaining ones subjected to a combination of clamped, simply supported, and free boundary conditions and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for variable-thickness inhomogeneous orthotropic plates as for uniform-thickness homogeneous isotropic plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of the inhomogeneity, aspect ratio, thickness parameter and degree of non-uniformity on the deflections and stresses are investigated. This paper is partially supported by the Deanship of Scientific Research at King AbdulAziz University (Grant no. 172/427).     

Differential quadrature method for bending of orthotropic plates with finite deformation and transverse shear effects

Based on the Reddy ‘s theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature ( DQ ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert ( DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.     

Transient response of laminated plates with arbitrary laminations and boundary conditions under general dynamic loadings

The dynamic analysis of laminated plates with various loading and boundary conditions is presented employing generalized differential quadrature (GDQ) method. The first-order shear deformation theory is considered to model the transient response of the plate. The GDQ technique together with Newmark integration scheme is employed to solve the system of transient equations governing dynamics of the plate. Different symmetric and asymmetric lamination sequences together with various combinations of clamped, simply supported, and free boundary conditions are considered. Particular interest of this study regards to asymmetric orthotropic plates having free edge and mixed boundary conditions. It is shown that the method provides reasonably accurate results with relatively small number of grid points. Comparison of the results with those of other methods demonstrates a very good agreement. It is also revealed that the present method offers similar order of accuracy for all variables including displacements and stress resultants.     

Symplectic system based analytical solution for bending of rectangular orthotropic plates on Winkler elastic foundation

This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation.Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish dual variables and dual equations in the symplectic space.The operator matrix of the equation set is proven to be a Hamilton operator matrix.Separation of variables and eigenfunction expansion creates a basis for analyzing the bending of rectangular orthotropic plates on Winkler elastic foundation and obtaining solutions for plates having any boundary condition.There is discussion of symplectic eigenvalue problems of orthotropic plates under two typical boundary conditions,with opposite sides simply supported and opposite sides clamped.Transcendental equations of eigenvalues and symplectic eigenvectors in analytical form given.Analytical solutions using two examples are presented to show the use of the new methods described in this paper.To verify the accuracy and convergence,a fully simply supported plate that is fully and simply supported under uniformly distributed load is used to compare the classical Navier method,the Levy method and the new method.Results show that the new technique has good accuracy and better convergence speed than other methods,especially in relation to internal forces.A fully clamped rectangular plate on Winkler foundation is solved to validate application of the new methods,with solutions compared to those produced by the Galerkin method.     

Multiple mode large amplitude vibration of thick orthotropic circular plates

This paper is analytically concerned with the large amplitude vibration of thick orthotropic circular plates incorporating the effects of transverse shear and rotatory inertia. Von Kármán-type field equations written in terms of the three displacement components of the plate are utilized to obtain solutions to clamped stress-free and immovable plates. By means of Galerkin's technique and a numerical Runge-Kutta procedure a multiple-mode analysis is carried out in both cases. Exact solutions are reported for two of the three governing equations. Effects of transverse shear deformation and modal interaction are found to be significant for orthotropic thick plates. The method given here could be extended to the multiple-mode analysis of circular plates with other boundary conditions.     

Spline-Approximation Method Applied to Solve Natural-Vibration Problems for Rectangular Plates of Varying Thickness

The natural vibrations of anisotropic rectangular plates of varying thickness with complex boundary conditions are studied using the spline-collocation and discrete-orthogonalization methods. The basic principles of the approach are outlined. The natural vibrations of orthotropic plates with parabolically varying thickness are calculated. The results (natural frequencies and modes) obtained with different boundary conditions are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 90–99, October 2005.     

Perturbation analysis for the postbuckling of rectangular orthotropic plates

In this paper, applying perturbation method to von Kármán-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, thé postbuckling behavior of simply supported rectangular orthotropic plates under inplane compression is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. Numerical results are presented for various cases of orthotropic composite plates having different elastic properties. It is found that the results obtained are in good agreement with those of experiments.     

A Higher Order Asymptotic Analysis for Orthotropic Plates in Stress Edge Conditions

A higher order asymptotic analysis for orthotropic plates is presented with the leading order interior solution reduced to the well-known Kirchhoff plate theory. The boundary-layer solutions are decoupled into the plane strain and torsional deformations of a boundary-layer plane strip, which is analyzed by the Laplace transform method to formulate Saint-Venant’s principle in plate studies. The necessary and sufficient conditions for stress edge-data generating exponentially decaying solutions are established to derive the stress edge conditions for the higher order plate theory. Mathematics Subject Classifications (2000) 74K20, 74B05, 74G10, 74G50.