Buckling and postbuckling of circular plates containing concentric penny-shaped delaminations

Buckling and postbuckling analyses of circular laminated composite plates with delaminations are presented. An axisymmetric finite element model based on a layer-wise laminated composite plate theory is developed to formulate the problem. Geometric nonlinearity in the sense of von Kármán and imperfections in the form of initial global deflection and initial delamination openings are included. A simple contact algorithm which precludes the physically inadmissible overlapping between delaminated surfaces is proposed and incorporated into the analysis.

Numerical results are obtained addressing the effects of the initial imperfections, the number of delaminations and their sizes on the critical buckling load and buckling mode shapes as well as postbuckling responses.     

Compressional stability behavior of composite plates with through-the-width and embedded delaminations by using first order shear deformation theory

In this paper, the compressive, i.e. bucking and post-buckling, behavior of composite laminates with through-the-width and embedded delaminations is investigated analytically. The analytical method is based on the first order shear deformation theory (FSDT) and its formulation is developed on the basis of the Rayleigh–Ritz approximation technique. In the case of the multiple delaminations, the contact phenomenon has significant effects on the compressional behavior of the laminates. Thus, the contact between the delaminated sublaminates is also considered in the presented FSDT analytical method. The method can handle both local buckling of the delaminated sublaminates and global buckling of the whole plate. Also, the three-dimensional finite element analysis is performed by using ANSYS5.4 general purpose commercial software, and the results are compared with those obtained by the analytical model. The agreement between the results is very good.     

Dynamic finite element analysis of laminated beams with delamination cracks using contact-impact conditions

A new finite element modeling technique is presented to investigate the static and dynamic behavior of laminated composite beams with partial delamination. In this study, a recently developed rectangular beam element is used. The element has lateral and axial displacements as degrees of freedom, but not rotation. For simplicity, linear shape functions are used for the beam element. As a result, the element has six degrees of freedom, four of which are the axial nodal displacements at the corner points and the other two are the lateral displacments at the ends. In addition, contact-impact conditions are applied to the finite element modeling to avoid overlapping of the upper and lower portions of a delaminated section. The numerical study shows that, depending on existence of an embedded delamination crack and its size, the response is different for a beam with a crack and subjected to a short impulse load. Hence, the present modeling technique may be used for detection of an embedded delamination crack.     

不同脱层位置下脱层屈曲梁振动实验研究

通过实验对一端固定一端夹支脱层屈曲梁在轴向周期激励作用下的非线性动力响应进行了实验研究.利用位移时间历程图,相图和频谱图,对多组不同脱层位置下脱层屈曲梁的非线性动力响应进行了分析.实验表明脱层梁结构存在倍周期以及混沌运动等非线性动力学行为.同时实验还表明,在相同的脱层长度下,脱层位置对脱层梁的动力学特性有明显影响,即脱层区域中心越靠近梁结构的中心位置,脱层梁的一阶自然频率越低,且越容易在较低的激励频率和激励荷载下发生周期分叉和混沌等行为.     

Characterization of delamination effect on composite laminates using a new generalized layerwise approach

A dynamic analysis method has been developed to investigate and characterize the effect due to presence of discrete single and multiple embedded delaminations on the dynamic response of composite laminated structures with balanced/unbalanced and arbitrary stacking sequences in terms of number, placement, mode shapes and natural frequencies. A new generalized layerwise finite element model is developed to model the presence of multiple finite delamination in laminated composites. The new theory accurately predicts the interlaminar shear stresses while maintaining computational efficiency.     

A penalty model for the analysis of curved composite beams

A simple one-dimensional mechanical model for curved laminated beams is presented. The laminae composing the beam are modelled as Timoshenko beams, perfectly bonded at the interfaces. Because the laminae can rotate differently from one to the other, the cross-sections of the composite beam can warp. The elasto-static problem of the beam is formulated through the principle of stationary potential energy, imposing constraint conditions between the displacements of adjacent laminae by a penalty technique. This approach produces an approximation of radial and tangential interactions between adjacent laminae. By using four-node isoparametric finite elements, numerical values of interlaminar stresses in straight and curved laminated beams are given. They are compared with the results obtained by other authors under different conditions.     

Simulation of multiple delaminations in composite laminates under mixed-mode deformations

A delamination analysis is developed in order to predict the defect evolution when a fiber composite laminate, with outer layers of equal or different thickness, is subjected to a compression load and multiple delaminations. In particular, the presence of two delaminated zones coaxially positioned on the two opposite sides of the laminate is analysed. In order to accurately predict the growth of delamination, when mode I and II are interacting, some fracture criteria have been proposed. Some results will be given to show the influence on the delamination buckling and on the growth phenomenon of the main geometrical and mechanical characteristics of the structure in order to show the pronounced role of the fracture modes on stable or unstable delamination growth.     

薄片介质高速传动的动态仿真与分析

针对薄片介质在金融自动处理设备中传动和堆叠过程中常见的卡阻故障,采用RecurDyn计算薄片介质的力学特性,获得薄片介质的弹性模量与弯曲挠度之间的关系曲线,以用于确定不同新旧程度薄片介质的弹性模量;基于票券自动处理设备中的堆叠模块,对介质在传动过程中的变形和运动姿态进行仿真,计算支撑固件的不同长度所对应的介质弯曲挠度.结果表明：支撑固件长度越大,介质产生的弯曲挠度越大,有利于避免介质堆叠时发生卡阻问题.     

轴向可伸缩复合材料悬臂梁的非线性振动研究

以航空领域中可变体机翼的伸缩变形过程为研究对象,对可伸缩悬臂复合材料层合梁的时变非线性振动进行理论研究.建立可伸缩悬臂复合材料层合梁在外载荷作用下的非线性动力学模型;根据时变系数非线性动力学方程研究时变非线性振动特性.分析可伸缩悬臂复合材料层合梁在外伸与收缩变形过程中的非线性动力学特性.从数值结果上看:模型的外伸速度、飞行速度对振动的影响较大,初值对振动的影响较小.     

A new thickness parameterization for Discrete Material and Thickness Optimization

In this work, a new thickness parameterization which allows for internal ply-drops without intermediate voids is introduced in the Discrete Material and Thickness Optimization (DMTO) method. With the original DMTO formulation, material had to be removed from the top in order to prevent non-physical intermediate voids in the structure. The new thickness formulation relies on a relation between density variables and ply-thicknesses rather than constitutive properties. This new formulation allows internal ply-drops which is essential for composite structures as it is common practice to cover dropped plies as to avoid delaminations. Furthermore, it is demonstrated how the new thickness formulation in some cases improves the convergence characteristics. Finally, it is also shown how solid-shell elements can be utilized within the DMTO method for structural optimization of tapered laminated composite structures.     

Dynamic characterization of thin-walled laminated channel beams with warping

The dynamic characteristics of a round cornered C-channel beam made of laminated composite material are studied. The sharp corners are rounded for manufacturing considerations. Thin-walled beam theory is used to formulate the coupled vibration of a rounded C-channel beam with fixed-free end conditions. It is shown that cross-sectional properties used for isotropic case are applicable for laminated composites and the material properties needed for the formulation can be obtained using the law of average. A comparative study is conducted to show the advantage of using composites. The effect of radius of corner and warping on the natural frequency is investigated. The functional of the equations of motion is formed using the variational method. The Ritz method has been used to formulate an eigenvalue problem and its frequency equation. The method proposed is systematic. The computerized procedure can be used as a fast design tool in the design of composite channel beam structures.     

压电复合材料梁的全局分叉、混沌动力学分析

研究了简支压电复合材料层合梁在轴向、横向载荷共同作用下的非线性动力学、分叉和混沌动力学响应.基于yon Karman理论和Reddy高阶剪切变形理论,推导出了压电复合层合梁的动力学方程.利用Galerkin法离散偏微分方程,得到二个自由度非线性控制方程,并且利用多尺度法得到了平均方程.基于平均方程,研究了压电层合梁系统...     

Analysis of laminated shells with laminated stiffeners using rectangular shell finite elements

A finite element analysis of laminated shells reinforced with laminated stiffeners is described in this paper. A rectangular laminated anisotropic shallow thin shell finite element of 48 d.o.f. is used in conjunction with a laminated anisotropic curved beam and shell stiffening finite element having 16 d.o.f. Compatibility between the shell and the stiffener is maintained all along their junction line. Some problems of symmetrically stiffened isotropic plates and shells have been solved to evaluate the performance of the present method. Behaviour of an eccentrically stiffened laminated cantilever cylindrical shell has been predicted to show the ability of the present program. General shells amenable to rectangular meshes can also be solved in a similar manner.     

Optimal design of laminated composite beam structures

This work deals with design sensitivity analysis and optimal design of composite structures modelled as thin-walled beams. The structures are treated as a torsion-bending resistant beams. The analysis problem is discretized by a finite element technique. A two-node Hermitean beam element is used. The beam sections are made from an assembly of elements that correspond to flat layered laminated composite panels. Optimal design is performed with respect to the lamina orientations and thickness of the laminates. The structural weight is considered as the objective function. Constraints are imposed on stresses, displacements, critical load and natural frequencies. Two failure criteria are used to limit the structural strength: Tsai-Hill and maximum stress. The Tsai-Hill criterion is also adopted to predict the first-ply-failure loads. The design sensitivity analysis is analytically formulated and implemented. An adjoint variable method is used to derive the response sensitivities with respect to the design. A mathematical programming approach is used for the optimization process. Numerical examples are performed on three-dimensional structures.     

Laminated glass beams: Strength factor and temperature effect

Glass design charts are available for annealed, monolithic glasses. In order to use these design charts, strength of a laminated glass unit needs to be adjusted by a strength factor. This paper presents a study on strength factor and the effect of various factors on the strength factor, like ambient temperature, width and length of the beam. The effect of nonlinearity on the strength factor is also investigated by considering the nonlinear behavior of fixed end laminated glass beams since the simply supported glass plates behaves nonlinearly. From the study, two factors are crucial in the estimation of relative strength of laminated glass with respect to monolithic glass: one of two factors is the plasticizer content and therefore the transition temperature of the PVB layer used in the manufacture of laminated glass unit, and the other is the effect of nonlinearity as observed in the analysis conducted with fixed end beams in this study.     

Identification and elimination of parasitic shear in a laminated composite beam finite element

A displacement-based finite element for the analysis of laminated composite beams is formulated using strain gradient notation. The definition of the beam’s longitudinal displacement possesses only the independent term (axial displacement) and a term which is linear in the thickness coordinate z. Thus, the finite element is first-order shear deformable. As strain gradient notation is physically interpretable, the contents of the coefficients of the polynomial expansions are identified a priori. Thus, the modeling capabilities as well as modeling deficiencies of the element are identified during the formulation procedure. A single parasitic shear term (spurious) is found to be present in the transverse shear strain expression of the element, which is responsible for locking. This parasitic shear term is also found to be the cause of a qualitative error existing in the representation of transverse shear strain along the length of a typical beam model. As the spurious term has been clearly identified, it can easily be removed to correct the element. The effectiveness of the procedure is shown through numerical analyses performed using the element containing the spurious term and then corrected for it. The beam model is validated by comparing numerical solutions with analytical solutions provided by the minimization of the total potential energy for a given laminated composite beam.     

Detection of delamination in laminated composites with limited measurements combining PCA and dynamic QPSO

This paper presents an output only damage diagnostic algorithm based on frequency response functions and the principal components for health monitoring of laminated composite structures. The principal components evaluated from frequency response data, are employed as dynamical invariants to handle the effects of operational/environmental variability on the dynamic response of the structure. Finite element models of a laminated composite beam and plate are used to generate vibration data for healthy and damaged structures. Three numerical examples include a laminated composite beam, cantilever plate made of carbon–epoxy and a laminated composite simply supported plate. Varied levels of delamination of laminated composite plies and matrix cracking at varied locations in the plies are simulated at different spatial locations of the structure. Numerical investigations have been carried out to identify the spatial location of damage using the proposed principal component analysis (PCA) based algorithm. In order to limit the number of sensors on the structure, an optimal sensor placement algorithm based on PCA is employed in the present work and the effectiveness of the proposed algorithm with a limited number of sensors is also investigated. Finally, the inverse problem associated with the detection of delamination and matrix cracking is formulated as an optimization problem and is solved using the newly developed dynamic quantum particle swarm optimization (DQPSO) algorithm. Studies carried out and presented in this paper clearly indicate that the proposed SHM scheme can robustly identify the instant of damage, spatial location, the extent of delamination and matrix cracking even with limited sensor measurements and also with noisy data.     

Design of laminated composite plates for optimal dynamic characteristics using a constrained global optimization technique

The lamination arrangements of moderately thick laminated composite plates for optimal dynamic characteristics are studied via a constrained multi-start global optimization technique. In the optimization process, the dynamical analysis of laminated composite plates is accomplished by utilizing a shear deformable laminated composite finite element, in which the exact expressions for determining shear correction factors were adopted and the modal damping model constructed based on an energy concept. The optimal layups of laminated composite plates with maximum fundamental frequency or modal damping are then designed by maximizing the frequency or modal damping capacity of the plate via the multi-start global optimization technique. The effects of length-to-thickness ratio, aspect ratio and number of layer groups upon the optimum fiber orientations or layer group thicknesses are investigated by means of a number of examples of the design of symmetrically laminated composite plates.     

Wave propagation in delaminated beam

The wave propagation model investigated herein is based on the known fact that material discontinuities affect the propagation of elastic waves in solids. The change in certain material characteristics, such as a local change in stiffness or inertia caused by a crack or the presence of material damage, will affect the propagation of transmitted elastic waves and will modify the received signal. Wave frequencies associated with the highest detection sensitivity depend, among other things, on the type of structure, the type of material, and the type of damage. This paper presents a method of wave propagation, which can be further used to detect small delaminations in beam-like structures. The considered beam is modelled by spectral finite elements.     

Finite element analysis of laminated anisotropic beams of bimodulus materials

This paper presents finite element analysis of laminated anisotropic beams of bimodulus materials. The finite element has 16 d.o.f. and uses the displacement field in terms of first order Hermite interpolation polynomials. As the neutral axis position may change from point to point along the length of the beam, an iterative procedure is employed to determine the location of zero strain points along the length. Using this element some problems of laminated beams of bimodulus materials are solved for concentrated loads/moments perpendicular and parallel to the layering planes as well as combined loads.