Response of Elliptical Composite Cylinders to Axial Compression Loading

The results from semianalytical predictions and experiments are used to study the response of composite cylinders with elliptical cross sections loaded axially to a significant percentage of their buckling load. The semianalytical approach is based on the methods of Marguerre, Rayleigh-Ritz, and Kantorovich. The radius of curvature and the displacements are approximated by expansions in harmonic series in the circumferential arc-length coordinate, and the coefficients of the displacement series are unknown functions of x which are solved for using the finite-difference method. The primary features of the predicted response are first described. Then the experiments are described and results for elliptical cylinders with varying degrees of orthotropy are compared with predictions. Where appropriate, calculations based on the analysis of circular cylinders are compared with the semianalytical calculations for the ellipse. Correlation between experiments and predictions is good, and it is demonstrated that despite the noncircular cross section, many responses of an ellipse are very similar to the axisymmetric response of circular cylinders subjected to an axial load. The similarity is independent of the degree of orthotropy of the elliptical cylinder.     

Multi-objective design optimization of variable stiffness composite cylinders

The bending-induced buckling improvement in a variable stiffness (VS) composite cylinder (made by fiber steering) is studied. For such a cylinder, the effect of the variation of the direction of the load on its buckling performance of the cylinder is also examined. Compromise programming, as a multi-objective optimization method, is used to design for buckling of the VS cylinder subjected to bending load in either of the two opposite directions. Different combinations of weight factors for the structural performance in the two opposite directions were also applied to obtain the Pareto frontier as the main decision making tool for the designers in a multi-objective design problem.     

Optimal design of general stiffened composite circular cylinders for global buckling with strength constraints

A design strategy for optimal design of composite grid-stiffened cylinders subjected to global and local buckling constraints and strength constraints was developed using a discrete optimizer based on a genetic algorithm. An improved smeared stiffener theory was used for the global analysis. Local buckling of skin segments were assessed using a Rayleigh-Ritz method that accounts for material anisotropy. The local buckling of stiffener segments were also assessed. Constraints on the axial membrane strain in the skin and stiffener segments were imposed to include strength criteria in the grid-stiffened cylinder design. Design variables used in this study were the axial and transverse stiffener spacings, stiffener height and thickness, skin laminate stacking sequence and stiffening configuration, where stiffening configuration is a design variable that indicates the combination of axial, transverse and diagonal stiffener in the grid-stiffened cylinder. The design optimization process was adapted to identify the best suited stiffening configurations and stiffener spacings for grid-stiffened composite cylinder with the length and radius of the cylinder, the design in-plane loads and material properties as inputs. The effect of having axial membrane strain constraints in the skin and stiffener segments in the optimization process is also studied for selected stiffening configurations.     

复合载荷作用变刚度复合材料回转壳屈曲优化

通过曲线纤维轨迹设计,变刚度复合材料回转壳将拥有比常刚度（直线纤维）回转壳更好的抗屈曲稳定性,为此,研究了复合载荷作用下曲线纤维铺层形式和几何参数对变刚度复合材料回转壳屈曲性能的影响规律。首先根据回转壳横截面圆弧变化改进曲线纤维角度线性描述方法,建立了变刚度复合材料回转壳的参数化有限元模型;其次,结合序列二次响应面方法和回转壳屈曲优化模型,搭建了复合材料回转壳曲线纤维轨迹优化的设计流程;最后,以准各向同性铺层复合材料回转壳为比较基准,对弯扭载荷作用变刚度圆柱壳和轴压、弯矩和扭矩分别作用变刚度椭圆柱壳在不同铺层方式、不同几何参数下的屈曲性能进行了优化比较。结果表明:弯扭载荷作用下,变刚度圆柱壳的屈曲性能随弯矩载荷占比增加而提高,且均好于准各向同性圆柱壳,但扭矩载荷占优时,优化常刚度圆柱壳的屈曲性能更具有优势;不同载荷作用下,具有较小截面方向比的变刚度椭圆柱壳屈曲性能要明显好于对应的准各向同性椭圆柱壳,且横截面越接近圆形,曲线纤维对椭圆柱壳屈曲性能的改善越弱。      

A homogeneous elliptical shaft may not warp under torsion

Summary. When a homogeneous prismatic shaft of an arbitrary cross section is subjected to a twisting moment at its end, an axial displacement, referred to as warping displacement, will be induced in it. The only exception known to date is that the shaft is an isotropic one with circular cross sections. In this work we find that elliptical cross sections may also exhibit zero warping. But now the shafts need to be rectilinearly orthotropic in which the ratio of two associated shear rigidities equals to the square of the aspect ratio of the ellipse. Physically, this means that the elastic orthotropy of the shaft can serve to compensate the geometric deviation from a circular cross-section to an elliptical one. The idea can be further generalized to show that the zero warping property also holds for a number of composite cylinders consisting of an elliptical core or cavity coated with many similarly elliptical layers of different materials.     

An optimization of composite lattice cylinder using the approximate method

Recently, the approximate methods based on continuous models have been developed to perform structural analysis of composite lattice structures due to their relative simplicity and computational efficiency. This paper defines the modified effective stiffness considering the directionally dependent mechanical properties to an intersection of ribs and mode shape function of a composite lattice cylinder. It subsequently presents an approximate method based on the continuous model of conducting a buckling analysis of the composite lattice cylinder with various boundary conditions under uniform compression. This method considers the coupled buckling mode as well as the global and local buckling modes. The validity of the present method is verified by comparing the results of the finite element analysis. In addition, a parametric analysis is performed to investigate the effects of the design parameters on the critical load and buckling mode shape of the composite lattice cylinder based on the present method. Finally, we apply the present method to perform the optimization of a composite lattice cylinder for a high-speed vehicle to minimize the mass. Consequently, it is concluded that the present method is very suitable to optimization of composite lattice cylinders due to their relative simplicity and computational efficiency.     

Local cross-sections and energy efficiencies in the multiple electromagnetic/optical scattering by two perfect electrically-conducting cylindrical particles

Exact mathematical expressions for the intrinsic electromagnetic (EM) cross–sections (i.e. extinction, scattering and absorption) for a pair of perfectly conducting circular cylinders in a homogeneous non–absorptive medium are derived. The multipole expansion method in cylindrical coordinates and the translational addition theorem, applicable to any range of frequencies or particle sizes are used. An effective EM field, incident on the probed cylinder is defined first, which includes the initial and re-scattered field from the second cylinder. It is used jointly with the scattered field to derive the mathematical expressions for the intrinsic/local cross–sections. Numerical computations for the intrinsic extinction (or scattering) energy efficiencies per unit-length for a pair of conducting circular cylinders with different radii in a homogeneous medium are considered. The results computed a priori can be useful in the full characterization of a multiple scattering system of many particles, in conjunction with experimental data for the extrinsic cross–sections.     

Buckling load analysis of grid stiffened composite cylinders

Stiffened cylindrical shells are the major components of aerospace structures. In this study global buckling load for a generally cross and horizontal grid stiffened composite cylinder was determined. This was accomplished by developing an analytical model for determination of the equivalent stiffness parameters of a grid stiffened composite cylindrical shell. This was performed by taking out a unit cell and smearing the forces and moments due to the stiffeners onto the shell. Based on this analysis the extensional, coupling and bending matrices (A, B and D matrices, respectively) associated with the stiffeners were determined. This stiffness contribution of the stiffeners was superimposed with the stiffness contribution of the shell to obtain the equivalent stiffness parameters of the whole panel. Making use of the energy method the buckling load was solved for a particular stiffener configuration. Buckling test was also performed on a stiffened composite cylinder and compared with analytical results. Finally, using the analytical model developed, parametric analysis of some of the important design variables was performed and based on these results conclusions were drawn.     

Localized approximation for gaussian beams in elliptical cylinder coordinates

We establish a localized approximation to evaluate the beam-shape coefficients of a Gaussian beam in elliptical cylinder coordinates. As for the case of spherical coordinates and of circular cylinder coordinates, this approximation provides an efficient way to speed up computations within the framework of a generalized Lorenz-Mie theory for elliptical cylinders.     

Buckling of Cracked Laminated Composite Cylindrical Shells Subjected to Combined Loading

A series of finite element analysis on the cracked composite cylindrical shells under combined loading is carried out to study the effect of loading condition, crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, bending, internal pressure and external pressure are obtained, using the finite element method. Results show that the internal pressure increases the critical buckling load of the CFRP cylindrical shells and bending and external pressure decrease it. Numerical analysis show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell and results show that for lower values of the axial compressive load and higher values of the external pressure, the buckling is usually in the global mode and for higher values of axial compressive load and lower levels of external pressure the buckling mode is mostly in the local mode.     

外压作用下椭圆截面柱壳的弹性屈曲

基于能量法推导了外压作用下椭圆截面柱壳弹性屈曲临界荷载的理论解,推导中考虑了椭圆截面连续变化的曲率,引入带有衰减系数的位移函数以反映外压作用下椭圆柱壳的变形特点,并利用里兹法求解外压椭圆柱壳的能量方程。由椭圆柱壳理论解退化求得的圆柱壳外压屈曲荷载与已有文献的经典解吻合良好,与有限元分析结果的比较进一步验证了该文理论解的准确性。基于理论解的参数分析表明:在外压作用下,椭圆柱壳具备比圆柱壳更优越的力学性能;椭圆柱壳的外压屈曲荷载随椭圆截面比的增大而增大,随壳体名义径厚比的减小而增大;椭圆柱壳的外压屈曲荷载随壳体长度的增大而降低,但当名义长径比大于1左右后,屈曲荷载基本保持不变。     

复合材料机翼整体成型技术研究

对给定外型与尺寸的整体成型复合材料机翼进行了设计、 制备及力学性能实验研究。采用有限元分析软件, 对空心复合材料机翼进行静力学分析, 得到了承载效率与机翼几何尺寸的关系, 并确定了最优结构尺寸与复合材料纤维铺层厚度。采用石蜡芯模辅助气囊法成型技术, 制备了整体成型复合材料机翼, 并进行了三点弯曲实验测定, 分析了其破坏机制。三点弯曲实验研究发现, 整体成型复合材料机翼的破坏模式为上蒙皮的局部屈曲失效, 屈曲后仍有一定的承载能力。      

Buckling behavior of fiber reinforced plastic–metal hybrid-composite beam

It is known that the buckling is characterized by a sudden failure of a structural member subjected to high compressive load. In this study, the buckling behavior of the aluminum tubular beam (ATB) was analyzed using finite element (FE) method, and the reinforcing arrangements as well as its combinations were decided for the composite beams based on the FE results. Buckling and bending behaviors of thin-walled ATBs with internal cast polyamide (PA6) and external glass and carbon fiber reinforcement polymers (GFRPs and CFRPs) were investigated systematically. Experimental studies showed that the 219% increase in buckling load and 661% in bending load were obtained with reinforcements. The use of plastics and metal together as a reinforced structure yields better mechanical performance properties such as high resistance to buckling and bending loads, dimensional stability and high energy absorption capacity, including weight reduction. While the thin-walled metallic component provides required strength and stiffness, the plastic component provides the support necessary to prevent premature buckling without adding significant weight to the structure. It is thought that the combination of these materials will offer a promising new focus of attention for designers seeking more appropriate composite beams with high buckling loads beside light weight. The developed plastic–metal hybrid-composite structure is promising especially for critical parts serving as a support member of vehicles for which light weight is a critical design consideration.     

Ultimate strength of a composite cylinder subjected to three-point bending: correlation of beam theory with experiment

This paper investigates the ultimate bending response of a solid composite cylinder reinforced with uniaxially aligned continuous fibers. Experiments exhibited remarkable nonlinear load–deflections up to failure, indicating that a progressive failure process must have occurred in the cylinder. Thus, the failure of the outmost filament initially subjected to the maximum bending stress does not correspond to the ultimate failure, and additional loads should be still applicable to the cylinder. To reveal this progressive failure process, the cylinder is discretized into a number of parallel layers of different widths. Each layer is considered as a unidirectional lamina, whose overall load component is determined within the framework of classical beam theory. However, the lamina nonlinearity has been incorporated in the analysis using an instantaneous stiffness element defined by the micromechanics bridging model. The benefit of this model is in that only the constituent fiber and matrix properties are required in the analysis. As neither the first ply nor the last ply failure corresponds to the ultimate failure, in addition to the stress failure criterion used to detect the failure of an individual ply another deformation related parameter must be also employed to govern the ultimate failure and then to determine the ultimate strength. In the present case when a 16 layers discretization has been employed, the predicted fourth ply failure strength has been found to work for the ultimate strength and to correlate reasonably well with the experimental counterpart.     

Numerical modeling of composite laminated cylinders in compression using a novel imperfections modeling method

The present study presents the finite element modeling procedure of two composite laminated cylinders exhibiting initial geometric imperfections. Using as input a set of experimental measurements of the cylinder geometry, the application of the skinning method leads to the analytical representation of the cylinder imperfect internal, external and middle surfaces. A finite element mesh is then easily constructed over these surfaces. The results of the analysis are in very good agreement with the experimental strains and buckling load measurements and are used to estimate the knockdown effect of the imperfections on the cylinder buckling behaviour. They are also compared to results obtained by other simpler finite element models, in an effort to evaluate the accuracy of various modeling simplifications.     

Application of DQM as an effective simulation tool for buckling response of delaminated composite plates

The application of differential quadrature method (DQM), as an effective and robust numerical method, for the analysis of buckling of delaminated composite plates is introduced. The analysis investigated the response of laminated composite plates hosting a circular or an elliptical delamination. The delaminations were assumed to be fairly thinner than the plate hosting them, and thus, they could be treated as plates with clamped edges. Several case studies were used to verify the integrity of DQM in predicting the buckling strain of the plates. The investigation included the examination of several parameters influencing the buckling strength. The results obtained from DQM were compared with those obtained by the Rayleigh–Ritz and finite element solutions of other workers.     

Buckling of a composite cantilever circular cylindrical shell subjected to uniform external lateral pressure

In this paper a solution is presented for a buckling problem formulated for the cantilever circular cylindrical composite shell subjected to uniform external lateral pressure. The edge of the shell is fully clamped at one end of the cylinder and is free at the open section of the other end. An analytical formula for critical pressure has been derived using the generalised Galerkin method. The approach is illustrated by the buckling analyses of composite, orthotropic and isotropic shells. The results are verified using the finite-element method. It has been shown that the analytical solution provides an accurate estimate of the critical load and does not involve any computationally expensive procedures. This is particularly useful in the design optimisation of composite structures.     

Design and Optimization of Variable Stiffness Composite Cylinders With the Consideration of Manufacturing Interaction

Applied Composite Materials - In this study, a variable stiffness (VS) composite cylinder subjected to bending load is designed and optimized for maximum buckling load incorporating the effect of...     

Isotropic scattering by penetrable cylinders

Isotropic scattering is considered for infinite cylinders thin in the sense that ka < 1, although ?k'a? and cross-sectional shape can be arbitrary within limits (k and k' are, respectively, free-space and interior propagation constants, and a is a characteristic dimension of the cylinder). For circular cylinders, scattering width is found to saturate at its perfectly conducting value, and absorption width is found to peak, when skin depth becomes comparable with cylinder diameter. For a variety of cylinders with and without edges, both scattering and absorption widths are then found to be effectively identical to those of the circular cylinder with equal cross-sectional area. A new analytical formula is obtained for high but not infinite conductivity, and the connection with scattering cross sections of corresponding finite cylinders is discussed.