Nonlinear thermal and mechanical analysis of edge effects in angle-ply laminates

A method has been developed for the thermal analysis of materially nonlinear Carbon Fibre Reinforced Plastic (CFRP) laminated plates using a quasi-three-dimensional iso-parametric finite element. The variation of the linear expansitivity of CFRP lamina with temperature in the transverse direction is included. The nonlinear initial thermal stresses resulting from thermal cooling from the stress-free temperature of 132.22 to 20°C in the [0/90]_s and [±45]_s laminates were found. These two types of laminates were then subject to a uniform applied strain ε_x until failure was detected inside the laminate according to a maximum strain failure criterion. This nonlinear analysis was based on an initial stress iteration method formulated in a previous paper. The [±45]_s laminate analysis was carried out with and without resin layers between the laminae modelled. All results obtained were compared with those of previous investigators. It was found that with initial thermal stresses included the [0/90]_s laminate failed at an earlier stage than without initial thermal stresses included. The [±45], laminate with initial thermal stresses included failed at a later stage than that without initial thermal effects and the inclusion of resin layers delayed the failure even further.     

A traction-free-edge hybrid-stress element for the analysis of edge effects in cross-ply laminates

A hybrid-stress formulation is presented for the analysis of multilayer cross-ply laminates under uniform inplane strain and a special-purpose element is developed for which the traction-free edge conditions are exactly satisfied. Results obtained for interlaminar stress distributions are shown to converge to large, but finite, values near the free edge. The importance of exact representation of the traction-free edge conditions is examined by comparison of results with those obtained by other investigators and by using an analogous multilayer hybrid-stress element in which the free-edge conditions are approximately satisfied. It is concluded that exact representation of the free-edge conditions is required if accurate point-by-point stress distribution in the vicinity of the free-edge are essential, as in the study of laminate strength and failure.     

Minimum weight design of symmetric angle-ply laminates under multiple uncertain loads

An angle-ply laminated plate is optimized with the objective of minimizing the weight of the plate taking into account uncertainties in the multiple transverse loads. The weight is proportional to the laminate thickness which is minimized subject to deflection and buckling constraints under the least favourable loading with the ply angles taken as design variables. The convex modelling approach is employed to analyse the uncertain loading with the uncertain quantities allowed to vary arbitrarily around their average values subject to the requirements that these variations are bounded inL ₂ norm and represented by a finite number of eigenmodes. The effect of uncertainty on the optimal design is investigated quantitatively. It is shown that the minimum weight increases with increasing level of uncertainty and the optimal ply angles also depend on the level of uncertainty.     

Behaviour of paraboloid of revolution shell using cross-ply and anti-symmetric angle-ply laminates

A generalised formulation for the analysis of a doubly curved laminated composite shell using an eight-noded curved quadratic isoparametric finite element has already been presented. Based on that formulation, the behaviour of the shell characteristics of the paraboloid of revolution shell using eight types of cross-ply laminates and twelve types of anti-symmetric angle-ply laminates are presented in this paper. A detailed study of the variations of the deflections and other shell actions for the above laminates reveals that symmetric cross-ply laminates appear to be superior to anti-symmetric cross-ply laminates while 45/-45 laminates are superior to 30/-30 and 60/-60 laminates. An overall comparison between cross-ply and angle-ply laminates reveals that angle-ply laminates are more efficient than cross-ply laminates. In general, a decrease in the value of the shell actions is observed with an increase in the number of layers.     

Stress analysis of holes in angle-ply laminates: An efficient assumed stress “special-hole-element” approach and a simple estimation method

In the present paper, the development of “special hole-elements”, to enable an efficient and accurate analysis of stress concentration around through-thickness holes in angle-ply laminates, is presented. In these “hole-elements”, the development of which is based on a modified complementary energy principle, the analytical asymptotic solutions for the stress-state near the hole are embedded. The fully 3-D stress-state in the laminate is accounted for, and the interlaminar traction reciprocity is satisfied a priori, while the interelement reciprocity condition is satisfied a posteriori through a Lagrange multiplier method. In addition, a simple method of estimation of stress concentration factors is also given.Results obtained from the present “special-hole-element” procedure are compared with the solutions by the present simple estimation method as well as other available solutions in literature.     

FEM analysis of buckling and thermal buckling of antisymmetric angle-ply laminates according to transverse shear and normal deformable high order displacement theory

Buckling and thermal buckling of the antisymmetric angle-ply laminates clamped and subject to in-plane edge loads or a uniform temperature rise are analyzed by the finite element method. A higher order displacement theory including higher order terms along the transverse direction, taking into account transverse normal strain, is applied through the analysis. Effects of important parameters, such as ply angle, ratio of thickness to edge length, number of layers, ratio of in-plane to transverse modulus, etc. are studied. The numerical results are presented.     

Nonlinear dynamics of angle-ply composite laminated thin plate with third-order shear deformation

An asymptotic perturbation method is presented based on the Fourier expansion and temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported angle-ply composite laminated rectangular thin plate with parametric and external excitations.According to the Reddy's third-order plate theory,the governing equations of motion for the angle-ply composite laminated rectangular thin plate are derived by using the Hamilton's principle.Then,the Galerkin procedure is applied to...     

Nonlinear axisymmetric static analysis of orthotropic thin circular plates with elastically restrained edge

This study deals with the nonlinear axisymmetric static analysis of elastic orthotropic thin circular plates with elastically restrained edges for rotation as well as in-plane displacement. Von-Karman equations have been employed and spatial discretisation has been done by using the method of orthogonal point collocation. Numerical results have been presented for orthotropic plates with hinged edge, simply supported edge, movable clamped edge and immovable clamped edge. Results are given for the whole range of elastic edge restraints from the movable simply supported edge to the immovable clamped edge. The effect of a prescribed inplane force or an inplane displacement at the edge, on the static response under a uniformly distributed transverse load has been investigated. Several new results are presented. The present results are in good agreement with the available results.     

Reliability of the finite element method for calculating free edge stresses in composite laminates

The edge-stress problem for a [±45]_s graphite/epoxy laminate was examined in detail. A review of the literature on this problem showed that the interlaminar normal stress σ_z distributions along the interface between the +45° and -45° plies, obtained by various investigators, disagreed in magnitude and sign. In particular, a finite difference solution and a perturbation solution predicted a tensile σ_z, whereas the finite element methods predicted a compressive stress. Since a stress singularity exists at the intersection of the interface and the free edge, the differences in magnitude of the peak stress were expected, but not the difference in the sign.This paper investigates the reliability of the displacement-formulated finite element method in analyzing the edge-stress problem. Analyses of two well-known elasticity problems, one involving a stress discontinuity and one a singularity, showed that the finite element analysis yields accurate stress distributions everywhere except in two elements closest to the stress discontinuity or singularity. Stress distributions for a [±45]_s laminate showed the same behavior near the singularity as found in the well-known problems with exact solutions. The displacementformulated finite element method, therefore, appears to be a highly accurate technique for calculating interlaminar stresses in composite laminates. The disagreement among the numerical methods was attributed to the unsymmetric stress tensor at the singularity.     

Nonlinear image filtering with edge and corner enhancement

The authors describe a model of nonlinear image filtering for noise reduction and edge enhancement using anisotropic diffusion. The method is designed to enhance not only edges, but corners and T junctions as well. The method roughly corresponds to a nonlinear diffusion process with backward heat flow across the strong edges. Such a process is ill posed, making the results depend strongly on how the algorithm differs from the diffusion process. Two ways of modifying the equations using simulations on a variable grid are studied     

A first-ply failure analysis of composite laminates

A finite-element computational procedure is developed for the first-ply failure analysis of laminated composite plates. The procedure is based on the first-order shear deformation theory and a tensor polynomial failure criterion that contains the maximum stress, maximum strain, the Hill, Tsai-Wu and Hoffman failure criteria as special cases. By specifying the desired criterion, a first-ply failure analysis of composite laminates subjected to in-plane and/or bending loads can be achieved. A number of problems are presented to evaluate these failure criteria when applied to laminates subjected to in-plane and or bending loads.     

基于边缘扩散的医学图像非线性去噪算法*

在对医学图像去噪的同时保留边缘信息,对于后期的诊断具有重要的意义。分析了ＰＭ和Ｃａｔｔｅ算法 以及它们的不足,提出了一种基于边缘扩散的非线性去噪方法,通过边缘检测把图像分为边缘和非边缘两部分, 非边缘区域通过各向同性算法去噪;边缘区域通过各向异性算法去噪,改进扩散形式,只沿边缘方向扩散去噪。 实验表明方法非常有效,带噪声的医学图像经过改进后的算法去噪处理,图像质量得到明显的改善。     

Object-oriented stochastic finite element analysis of fibre metal laminates

This paper deals with issues arising from the stochastic simulation of fibre metal laminates. The elasticity modulus of the composite layer is assumed to be a random process. An object-oriented computational framework is proposed, which can be integrated with an existing object-oriented deterministic infrastructure. This framework is utilized to implement a spectral stochastic version of the solid-like shell element. Modelling aspects particular to the layered nature of the fibre metal laminates are discussed and implemented in the proposed framework. Practical application of the software is illustrated by computations on panels of GLARE (fibre metal laminate).     

Three-dimensional finite element analysis of interlaminar stresses in thick composite laminates

The three-dimensional finite element computer program has been developed to investigate interlaminar stresses in thick composite laminates. The finite element analysis is based on displacement formulation employing curved isoparametric 16-node elements. By using substructure technique, the program developed is capable of handling any composite laminates which consist of any number of orthotropic laminae and any orientations. In this paper, solid laminates and laminates with a circular hole were taken to study interlaminar stresses at the straight edge and the curved edge, respectively. Various solid laminates such as [45_n/0_n − 45_n/90_n]_s, [45/0/ − 45/90]_ns, and [45/0/ − 45/90]_sn (n = 1˜4) were analyzed. Also, [45/0/ − 45/90]_sn laminates with a circular hole were studied for n = 1 ˜ 20. The effect of laminate thickness and stacking sequence on the interlaminar stresses near the free edge was investigated. Interlaminar stresses were governed by stacking sequence rather than laminate thickness. The boundary layer width did not increase with laminate thickness but with the number of plies in the repeating unit.     

Probabilistic buckling analysis of fiber metal laminates under shear loading condition

The design allowables for compressive and shear buckling of fiber metal laminate (FML) panels need to be developed for the certification of these materials. In this paper, the shear buckling behavior of the two FML panels, ARALL3-3/2 and GLARE3-2/1, is investigated using a probabilistic analysis method in order to predict the distributions of the buckling load. The scatter associated with the material properties and the randomness in the loading conditions are accounted for in the probabilistic analysis. The shear buckling load of the panel is taken as the response function of the material properties and the load parameter. The response surface methodology (RSM) is employed for the development of the response function based on limited finite element data. Three RSM design methods: full factorial design, CCD design and saturated D-optimum design, are applied to construct the response function following which the shear buckling load distributions of the two FML panels are predicted. The predicted results are verified using independently generated finite element data.     

Nonlinear analysis of tension structures

This paper describes a nonlinear finite element procedure for form finding and load analysis of tension structures. Three methods are presented for form finding of the initial equilibrium configuration. The behaviour of tension structures under a variety of loading conditions is also investigated. The complete procedure for both form finding and load analysis functions is implemented in a program and is verified through applications to typical tension structures.     

Nonlinear analysis of reinforced concrete

This paper discusses the development of two different computer programs for nonlinear analysis of reinforced concrete structures.The first program handles plane stress problems. Flow theory of plasticity is used in the modelling of concrete and reinforcement. General four-noded quadrilateral elements with selective sampling of strain are used in the discretization.The second program is developed for analysis of plates and shells. Endochronic theory is used in the constitutive law for concrete whereas an overlay model is utilized for the reinforcement. Geometric nonlinearities are accounted for through updating of coordinates for the triangular shell elements.Several examples of applications of the two programs are given. The plane stress program is used for analysis of a beam and two different corbels, while the shell program has been applied to a square plate and a shell with geometric nonlinearities.     

一种基于块的图像边缘分析方法

边缘检测是图像处理和计算机视觉中的基本问题,人眼视觉系统对图像中的边缘信息非常敏感,经常作为描述图像特征的一种重要手段。基于运动补偿和DCT变换编码的视频编码标准中,一幅图像分成大小相同不重叠的块进行编码,基于块的图像边缘分析在图像处理、去块效应滤波、模式选择以及基于内容的视频检索等方面有较广泛应用。提出了一种基于分析块边缘方向的边缘分析算法。实验结果表明,与其他算法相比,该算法在分析性能与计算复杂方面具有较明显的优越性。