Static and dynamic analysis of plates in cylindrical bending through displacement and mixed approaches

This work analyzes the influence of edge-boundary conditions on the static and dynamic behavior of isotropic and cross-ply plates in cylindrical bending conditions. The main concern of the analysis is addressed to dynamic problems (free vibrations) along with certain boundary conditions that seem to be mainly responsible for a low convergence of the eigenvalues to the exact values. The interest on the static behavior comes from the inherent sensitivity of related quantities, which can both be compared with previous studies and can better elucidate such a low convergence. The analysis is carried out within the frame of the three-dimensional theory by using different variational formulations based both on assumed displacements and/or stresses along with the attempt to unify the comparison of the different formulations. The numerical results/performance of such formulations are also compared to those achieved through alternative models.     

Improving bending characteristics of FRP sandwich structures with reinforcement webs

Sandwich-structure materials consist of a high-strength skin material and a lightweight core material. The advantages of sandwich structures are known to include excellent mechanical properties and low weight. Sandwich structures are lightweight because of their lightweight core; meanwhile, the skin structure provides mechanical strength and bears bending stress. Carbon-fiber-reinforced plastic (CFRP) is a high-specific-strength and high-specific-rigidity material. In recent years, CFRP sandwich structures have been used in aerospace applications due to their lightweight properties. However, soft-core members such as plastic foam materials have low rigidity and therefore may not exhibit adequate function as a sandwich structure. Webs can make up for the lack of rigidity of soft core members. Consequently, sandwich structures with reinforcement webs offer higher strength than sandwich structures without reinforcement webs. This study focused on reinforcement webs suitable for use in CFRP sandwich structures by evaluating the bending characteristics of CFRP sandwich structures with reinforcement webs. Experimental results demonstrated that CFRP sandwich structures with reinforcement webs had improved bending strength. The effects of the spacing interval of reinforcement webs and the number of layers of carbon fiber fabric on the bending characteristics of CFRP sandwich structures were also examined. Finally, an optimal condition model was created for CFRP sandwich structures with reinforcement webs.     

Geometrically nonlinear forced vibrations of the symmetric rectangular honeycomb sandwich panels with completed clamped supported boundaries

Geometrically nonlinear forced vibrations of symmetric rectangular honeycomb sandwich panels with clamped supported boundaries at the four edges are investigated using the homotopy analysis method (HAM). The honeycomb core of hexagonal cells is modeled as a thick layer of orthotropic material whose parameters of physical and mechanical properties are calculated by the corrected Gibson’s formula. The basic formulation of nonlinear forced vibrations has been developed based on the classical plate theory (CPT) and the nonlinear strain–displacement relation. The equilibrium equations have been obtained using Hamilton’s principle. Effects of axial half-waves, height and height ratio on the nonlinear free vibration response have been investigated for honeycomb sandwich panels.     

A BEM formulation based on Reissner’s theory to perform simple bending analysis of plates reinforced by rectangular beams

In this work, the plate bending formulation of the boundary element method (BEM), based on the Reissner’s hypothesis, is extended to the analysis of plates reinforced by rectangular beams. This composed structure is modelled by a zoned plate, being the beams represented by narrow sub-regions with larger thickness. The integral equations are derived by applying the weighted residual method to each sub-region, and summing them to get the equation for the whole plate. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to decrease the number of degrees of freedom, some approximations are considered for both displacements and tractions along the beam width. The accuracy of the proposed model is illustrated by simple examples whose exact solution are known as well as by more complex examples whose numerical results are compared with a well-known finite element code.     

An approach to optimization of shape memory alloy hybrid composite plates subjected to low-velocity impact

The paper presents an approach to the problem of optimum design of composite plates subjected to low velocity impact. The deflections and stresses are reduced by employing prestrained shape memory alloy (SMA) fibers which are in the martensitic phase when embedded within the plate. At an elevated temperature, the SMA fibers transform into the austenitic phase and tend to contract. However, due to a constraint, the contraction is either completely prevented or reduced resulting in significant tensile recovery stresses. This tension reduces deformations and stresses in the plate subjected to low-velocity impact.The solution in the paper addresses an impact of cross-ply plates with SMA fibers embedded within the layers oriented in both directions. An approach to optimization considered in the paper involves variations of the volume fractions of SMA fibers in each direction subject to a constraint on the total volume of the shape memory alloy. It is shown that an application of SMA fibers can significantly reduce deflections and stresses. A further benefit can be achieved by an optimization of a distribution of volume fractions of SMA fibers between the layers.     

Kevlar短纤维增韧碳纤维/铝蜂窝夹芯板三点弯曲与面内压缩性能

介绍了碳纤维/铝蜂窝夹芯结构的Kevlar短纤维界面增韧方法。通过三点弯曲实验和面内压缩实验,对比增韧试件与未增韧试件的载荷位移曲线、破坏模式等特征,发现未增韧试件往往先发生界面分层破坏,继而面板和芯体分别发生局部破坏;而增韧试件通常发生整体破坏。实验数据显示,Kevlar短纤维界面增韧可以使碳纤维/铝蜂窝夹芯板的抗弯强度、压缩强度、能量吸收等力学性能分别至少提高14.06%、55.80%和61.53%。对破坏后界面的SEM观测发现:增韧试件并未发生界面脱粘,而是由于芯体撕裂造成面/芯剥离,揭示了Kevlar短纤维的界面增韧机制。对具有Kevlar短纤维界面增韧的碳纤维/铝蜂窝夹芯结构进行有限元建模,并分别对其在三点弯曲和面内压缩载荷下的力学行为进行数值分析,以指导该类夹芯结构的分析与设计。     

Contact force history analysis of composite sandwich plates subjected to low-velocity impact

Usually the modified Hertzian contact law or experimental static indentation law has been used to analyze low-velocity impact response of composite laminates. In composite laminated plates subjected to low-velocity impact, usually indentation by impact is very small and also energy absorption by indentation is negligible, so ‘spring element method’, which proposed by author recently, can be well applied to investigate impact response. In the present study ‘lumped mass method’ also had been proposed by author to approximately calculate contact force history of composite laminates will be conceptually described as well as the spring element method. And it will be discussed that how the spring element method can be applied to composite sandwich plates. Finally numerical results easily obtained from finite element analysis based on the spring element method using general-purpose commercial FEM software is compared with experimental results. The comparison shows overall agreement.     

Analytic homogenization for torsion of orthotropic sandwich plates: Application to corrugated cardboard

This paper presents an analytic homogenization model for the torsion of orthotropic sandwich plates and its application to the torsion modelling of corrugated cardboards. It is very difficult to determine the torsion rigidity of these kinds of 3D structures even numerically because of the boundary condition effects. Inspired by the gridwork homogenization model of Timoshenko, we decompose the plate torsion into two beam torsions. The plate torsion curvature is separated into two beam torsion rates and the beam torsion rigidities in these two directions are introduced to describe the torsion behaviour of the orthotropic plates. We demonstrate that the plate torsion rigidity is equal to a quarter of the sum of the two beam torsion rigidities, which are easily calculated analytically or numerically. This torsion homogenization model can be used not only for corrugated cardboard packaging structures, but also for naval and aeronautic composite structures.     

双向梯形夹芯板柱面弯曲成形回弹分析

整体弯曲成形是制造曲面夹芯板高效且经济的方法,其成形特点与回弹预测是重点研究方向。采用结合有限元的半解析法对双向梯形夹芯的力学参数进行推导,获得夹芯等效弹性常数,分析上、下面板不等厚夹芯板柱面弯曲成形时面板与夹芯的变形特点及应力中性层的变化,在此基础上建立夹芯板平面应变弯曲回弹理论计算模型,预测夹芯板弯曲成形的应力分布与回弹,并与数值模拟及多点弯曲成形实验结果进行对比。结果表明:夹芯板回弹量与中厚板十分接近,回弹量较小,易于控制成形精度;理论预测的横截面切向应力与回弹都偏大,其中上面板应力相对误差在2.9%以内,下面板应力相对误差在6.5%以内,下面板纵向中心截面线误差在1.0mm范围内,各项误差均在很小范围内,验证了本工作回弹计算模型的准确性。     

Thermomechanical bending analysis of functionally graded sandwich plates with both functionally graded face sheets and functionally graded cores

The bending response of functionally graded material (FGM) sandwich plates subjected to thermomechanical loads is investigated using a four-variable refined plate theory. A new type of FGM sandwich plate, namely, both FGM face sheets and an FGM hard core, is considered. Containing only four unknown functions, the governing equations are deduced based on the principle of virtual work and then these equations are solved via the Navier approach. Analytical solutions are obtained to predict the deflections and stresses of simply supported FGM sandwich plates. Benchmark comparisons of the solutions obtained for a degradation model (functionally graded face sheets and homogeneous cores) with ones computed by several other theories are conducted to verify the accuracy and efficiency of the present approach. The influences of volume fraction distribution, geometrical parameters, and thermal load on dimensionless deflections and normal and shear stresses of the FGM sandwich plates are studied.     

Smart damping of geometrically nonlinear vibrations of composite shells using fractional order derivative viscoelastic constitutive relations

In this article, a three-dimensional fractional order derivative model has been developed for the constrained viscoelastic layer of the active constrained layer damping (ACLD) treatment of laminated composite shells undergoing geometrically nonlinear vibrations. The constraining layer of the ACLD treatment is made of vertically/obliquely reinforced 1–3 piezoelectric composites and acts as the distributed actuator. A three-dimensional smart nonlinear finite element model has been developed. Several numerical results are presented to check the accuracy of the present three-dimensional fractional derivative model of the constrained viscoelastic layer for smart damping of geometrically nonlinear vibrations of laminated composite shells.     

铝合金-聚合物复合层板弯曲回弹理论分析

针对铝合金-聚合物复合层板弯曲回弹问题,分析了复合层板弯曲过程表面层铝板及中心层聚合物的变形特征,建立了复合层板平面应变纯弯曲回弹理论分析模型.采用建立的模型预测了复合层板纯弯曲过程回弹角变化,并与实验结果进行了对比,分析了聚合物层厚度及铝合金板材力学性能对回弹的影响规律.结果表明:随着中心聚合物层厚度的增加,复合层板回弹角降低;随着表面层铝板强度的降低,复合层板回弹角减小.理论预测结果与实验结果一致,说明了本文推导的理论模型的可靠性.     

Generation of transient vibrations on aluminum honeycomb sandwich panels subjected to hypervelocity impacts

This paper presents the results of a set of experiments aimed at discovering the main features of impact-induced vibrations on all-aluminum honeycomb sandwich panels, representative of the GOCE satellite's top floor, which is exposed to the orbital debris environment. The activity focused on the characterization of the vibrations induced in the vicinity of internal payloads by hypervelocity impacts occurring on the vehicle's external shell. More than 30 tests were realized by launching 0.8–2.3 mm aluminum projectiles in the velocity range 4–5.5 km/s on targets with tri-axial accelerometer assemblies mounted on both the front and rear face of the panel, at a nominal distance of 150 mm from the impact point. It was found that a hypervelocity impact produces in both the front and rear side of the sandwich panel a vibration environment which can be described through the shock response spectrum (SRS) of three different types of waves that can be distinguished on the basis of the acceleration direction: out-of-plane, in-plane longitudinal and in-plane shear. The influence of projectile mass and velocity on SRS appeared to vary with frequency, with the most significant difference in the range between ∼10³ and ∼10⁴ Hz. The results of whole experimental set were used to derive an interpolation law through standard techniques of nonlinear fit. The empirical equation obtained makes it possible to predict the near-field vibration environment produced by hypervelocity impacts with debris having given size and velocity, reproducing all the test data with an average uncertainty of ±6 dB.     

泡沫铝层合梁的三点弯曲变形

研究了泡沫铝层合梁三点弯曲的载荷(P)-位移(δ)曲线、变形过程及面板破坏、夹芯剪切破坏、凹陷破坏等破坏模式。用极限载荷公式得到的计算值与实验值符合良好。实验所得的加载和卸载刚度(P/δ)与计算结果吻合较好。泡沫铝层合梁具有较低的密度((0.42～0.92)×10~3kg/m~3)和很高的弯曲比刚度(E~(1/2)/ρ)。利用极限载荷公式建立了破坏模式图。     

Analysis of local bending effects in sandwich plates with orthotropic face layers subjected to localised loads

This paper presents a method for the approximate analysis of local bending effects in sandwich plates with specially orthotropic face layers subjected to localised external loads. The local bending analysis is based on the assumption that the relative deflection of the loaded face against the deflection of the face not loaded can be modelled by application of an elastic foundation model. This is achieved by introducing a two-parameter elastic foundation model which takes into account the shearing interaction effects between the loaded face and the core material. An approximate solution to the complete problem is achieved by superposition of the local solution and an overall solution derived by application of classical sandwich plate theory. The results obtained are compared with finite element analysis results, and a good match between the solutions is observed. Finally a brief parametric study shows that the local bending effects are strongly influenced by the modular ratio and the thickness of the loaded face.     

复合材料蜂窝夹层板结构的多工况优化设计研究

以复合材料蜂窝夹层板结构作为研究对象,建立了多工况优化模型,对众多的材料设计变量进行必要的取舍,通过优化分析确定复合材料蜂窝夹层板面板各分层的厚度以及蜂窝芯层的厚度等,使结构满足相应的频率约束、屈曲约束,以及强度约束、位移约束和尺寸限制等,同时达到结构的重量最轻。采用序列二次规划法对某卫星的承力筒结构进行了优化设计,优化结果表明:在满足其振动特性以及静力学特性的条件下,复合材料蜂窝承力筒的各面板层厚度以及蜂窝芯层的厚度均有所减小,减重效果显著,较好地实现了复合材料蜂窝夹层板结构的多工况优化设计。     

Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations

A nonlinear bending analysis is presented for a simply supported, functionally graded plate resting on an elastic foundation of Pasternak-type. The plate is exposed to elevated temperature and is subjected to a transverse uniform or sinusoidal load combined with initial compressive edge loads. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The formulations are based on a higher-order shear deformation plate theory and general von Kármán-type equation that includes the plate-foundation interaction and thermal effects. A two step perturbation technique is employed to determine the load–deflection and load–bending moment curves. The numerical illustrations concern nonlinear bending response of functional graded plates with two constituent materials resting on Pasternak elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The results reveal that the characteristics of nonlinear bending are significantly influenced by foundation stiffness, temperature rise, transverse shear deformation, the character of in-plane boundary conditions and the amount of initial compressive load. In contrast, the effect of volume fraction index N becomes weaker when the plate is supported by an elastic foundation.     

球形孔泡沫铝合金三明治梁的三点弯曲变形

研究了球形孔泡沫铝合金的单轴压缩性能,得到了抗压强度与相对密度的关系;与多边形孔泡沫铝合金和泡沫纯铝作了对比,发现球形孔使力学性能有了较大的提高.根据球形孔泡沫铝合金三明治梁三点弯曲的载荷(P)位移(δ)曲线研究了四种常见破坏模式并建立了破坏模式图.用极限载荷公式得到的计算值与极限载荷的实验值吻合良好.球形孔泡沫铝合金力学性能高于多边形孔泡沫铝合金及泡沫纯铝,因而其三明治梁的力学性能最好.     

拉压弹性模量差异对泡沫铝夹芯板三点弯曲模拟的影响

泡沫铝材料是一种典型的拉压双模量材料,即受拉与受压时弹性模量不同。使用ABAQUS有限元软件对泡沫铝夹芯板的三点弯曲行为进行了模拟。首先,对泡沫铝芯层采用可压缩泡沫模型,通过对芯层的受拉区和受压区采用不同的弹性模量来讨论拉压弹性模量差异对夹芯板三点弯曲行为的影响。同时,在泡沫铝压缩响应一致的情况下,对可反映拉压弹性模量差异的孔洞模型和未考虑拉压弹性模量差异的可压缩泡沫模型的夹芯板三点弯曲模拟结果进行了比较。研究表明,泡沫铝芯层的弹性模量对夹芯板的三点弯曲行为模拟有较大影响。若不考虑泡沫铝拉压弹性模量的差异,得到的夹芯板三点弯曲情况下的加载刚度和屈服荷载明显偏低。     

碳纤维增强聚合物复合材料方形蜂窝夹层结构水下爆炸动态响应数值模拟

基于ABAQUS有限元仿真软件,建立了不同夹芯相对密度的碳纤维增强聚合物（Carbon Fiber Reinforced Polymer,CFRP）复合材料方形蜂窝夹层结构在水中爆炸冲击波载荷作用下的仿真模型,分析了结构的变形过程、夹芯的压缩特性及结构的失效及破坏情况。数值模拟结果表明,CFRP复合材料蜂窝夹芯压缩量在前面板速度降至与后面板相同时达到最大; CFRP复合材料蜂窝夹芯的最大压缩量随着初始压力的增大呈先缓慢增大后快速增大的趋势,其增大趋势在夹芯接近完全压缩时又趋于缓慢; CFRP复合材料夹层结构失效随夹芯相对密度和初始压力的变化呈现不同的模式,且其防护性能优于等重的层合结构。研究结果可以为复合材料夹层结构在水中冲击波载荷防护中的应用提供参考。