Nonlinear dynamic analysis of tapered sandwich plates with multi-layered faces subjected to air blast loading

The nonlinear dynamic behavior of simply supported tapered sandwich plates subjected to air blast loading is investigated theoretically and numerically. The plate is supposed to have both tapered core and tapered laminated face sheets and be subjected to uniform air blast load. The theory is based on a sandwich plate theory, which includes von Kármán large deformation effects, in-plane stiffnesses, inertias and shear deformations. The sandwich plate theory for plates with constant thickness which have one-layered face sheets found in the literature is developed to analyze the tapered sandwich plates with multi-layered face sheets. The equations of motion are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations. The Galerkin method is used to obtain the nonlinear differential equations in the time domain. The finite difference method is applied to solve the system of coupled nonlinear equations. The tapered sandwich plate subjected to air blast load is also modelled by using the finite element method. The displacement–time and strain–time histories are obtained. The theoretical results are compared with finite element results and are found to be in an agreement.     

Bending response of web-core sandwich beams

This paper presents a new analytical solution for the bending response of a web-core sandwich beam. The beam is a transverse cut from the sandwich plate. The method is based on the plane frame analysis, where the response of the beam is divided into local and global components. The Clebsch’s method is used to calculate the deflection of the face plates. The validation of the plane frame method is carried out with FE-analyses based on the shell element formulation. Also a comparison is made with the method based on homogenized beam. Periodic stress distributions in the face plates are revealed with the plane frame analysis and are supported by the FE-analysis. The existing methods based on homogenized beam are not able to predict these stresses. The plane frame analysis can benefit the development of the theory related to web-core sandwich plate.     

Mode shapes and frequencies of radially symmetric vibrations of annular sandwich plates of variable thickness

An analysis and numerical results of radially symmetric vibrations of annular sandwich plates with core of linearly varying thickness are presented. The face sheets are treated as membranes of constant thickness, and the core is assumed to be solid as well as moderately thick. Due to linear thickness variation in the core, the face sheets take the shape of a truncated conical shell and because of this the face sheets membrane forces contribute to the bending and transverse shear of the core of the sandwich plate. Keeping this in view, the equations of motion for such a plate are developed by Hamilton’s energy principle. The frequency equations for three different combinations of boundary conditions, namely clamped at the inner edge and clamped or simply supported or free at the outer edge, are obtained by employing the differential quadrature method. The lowest three roots of these frequency equations have been reported as the frequencies for the first three modes of vibration. The effect of various plate parameters such as taper parameter, thickness of the core at the center, face thickness, and radii ratio on the natural frequencies has been analyzed. Three-dimensional mode shapes for a specified plate for all the three boundary conditions are illustrated. A comparison of results is presented.     

方孔蜂窝夹层板在爆炸载荷下的吸能特性

通过有限元数值模拟方法,对方孔蜂窝夹层板在爆炸冲击载荷下的变形机理和吸能特性进行了分析。在单位面积质量以及夹层板芯层薄壁间距、高度给定的情况下,通过对不同夹芯层相对密度下夹层板的吸能率以及上、下面板最大变形的比较,得出了最优的夹芯层相对密度。在此相对密度下,夹芯层吸能率最高,下面板变形最小,夹层板的抗冲击性能最优。同时还讨论了夹层板芯层薄壁间距、厚度、高度以及面板厚度对其各部分吸能率的影响,以得到最优化的夹层板结构。     

The derivation of the equations of moderately thick plates by the method of successive approximations

In this article the equations of a moderately thick plate are derived by the method of successive approximations. The derived equations exactly satisfy all the elastostatic equations, the plate equilibrium equations and traction free face boundary conditions.     

利用平板炉校准辐射热流计时角系数影响的分析

平板炉用于校准辐射热流计。标准辐射热流计和被校辐射热流计分别放置在石墨平板两侧,且角系数保持一致。辐射热流计受热感应面对平板的角系数,可认为是圆盘对与它平行的矩形的角系数,并以此进行计算。本文分析了辐射热流计至平板的距离、受热感应面面积对角系数的影响。     

Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets

This paper studied the large amplitude vibration and the nonlinear bending of a sandwich plate with carbon nanotube-reinforced composite (CNTRC) face sheets resting on an elastic foundation in thermal environments. The material properties of CNTRC face sheets are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equation of the plate that includes plate-foundation interaction is solved by a two-step perturbation technique. The thermal effects are also included and the material properties of both CNTRC face sheets and homogeneous core layer are assumed to be temperature-dependent. A detailed parametric study is conducted to study the effects of nanotube volume fraction, core-to-face sheet thickness ratio, temperature change, foundation stiffness and in-plane boundary conditions on the nonlinear vibration characteristics and nonlinear bending behaviors of sandwich plates with functionally graded CNTRC face sheets. The results for the same plate with uniformly distributed CNTRC face sheets are also provided for comparison.     

The influence of core height and face plate thickness on the response of honeycomb sandwich panels subjected to blast loading

This paper reports on an investigation into the behaviour of circular sandwich panels with aluminium honeycomb cores subjected to air blast loading. Explosive tests were performed on sandwich panels consisting of mild steel face plates and aluminium honeycomb cores. The loading was generated by detonating plastic explosives at a pre-determined stand-off distance. Core height and face plate thickness were varied and the results are compared with previous experiments. It was observed that the panels exhibited permanent face plate deflection and tearing, and the honeycomb core exhibited crushing and densification. It was found that increasing the core thickness delayed the onset of core densification and decreased back plate deflection. Increasing the plate thickness was also found to decrease back plate deflection, although the panels then had a substantially higher overall mass.     

基于NX平台的船舶板区域识别算法研究

目的基于NX11.0平台,开发一种船舶板区域识别算法,准确、高效地识别船舶板区域。方法介绍了计算机图形学中面、环、边的关系,采用面和边的拓扑关系,描述板架区域面和区域边界的关系。以板架上最小面的集合作为板架区域,最短边的集合作为板架区域边界,将围成板架区域面的一组边赋予特殊属性,以区分板架区域边界与板架普通边。在此基础上,通过搜索一组板架区域边界围成的所有板架最小面,进而识别出一个板架区域。在NX11.0平台上,使用C++语言实现该算法,并使用实船模型进行测试,结论该算法对能够准确、高效地实现船舶板区域识别。     

Vibration analysis of variable stiffness laminated composite sandwich plates

Abstract

This paper presents the free vibration analysis of a variable stiffness laminated composite sandwich plates. The fiber orientation angle of the face sheets (Skin) is assumed to vary linearly with the x-axis. The problem formulation is based on the higher-order shear deformation plate theory HDST C⁰ coupled with p-version of finite element method. The elements of the stiffness and mass matrices are calculated analytically. The sandwich plate is presented with a uniform mesh of four p-elements and the convergence properties are achieved by increasing the degree p of the hierarchical shape functions. A calculation program is developed to determine the fundamental frequencies for different physical and mechanical parameters such as plate thickness, core to face sheets thickness ratio, orientation angle of curvilinear fibers and boundary conditions. The results obtained show a good agreement with the available solutions in the literature. New comparison study of vibration response of laminated sandwich plate between the straight and curvilinear fibers is presented.     

粘贴片材加固混凝土梁的粘结剪应力分析

在受拉区表面粘贴加强片是加固混凝土梁的一种有效方法。本文在弹性理论的基础上,推导了受任意线性分布荷载作用下的混凝土梁采用粘贴加强片加固时,加强片端部粘结剪应力和最大粘结剪应力的计算公式。本文方法和有限元方法基本吻合。结果表明,最大锚固剪应力不但和粘胶层厚度、弹性模量有关,还和加强片厚度、弹性模量及长度有关。采用本文方法可以对加强片端部最大锚固剪应力进行验算,防止混凝土梁出现局部受拉破坏。本文研究结果将为进一步完善我国有关规范提供重要的参考资料。     

Nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations

Nonlinear vibration, nonlinear bending and postbuckling analyses are presented for a sandwich plate with FGM face sheets resting on an elastic foundation in thermal environments. The material properties of FGM face sheets are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equation of the plate that includes plate-foundation interaction is solved by a two-step perturbation technique. The thermal effects are also included and the material properties of both FGM face sheets and homogeneous core layer are assumed to be temperature-dependent. The numerical results reveal that the foundation stiffness and temperature rise have a significant effect on the natural frequency, buckling load, postbuckling and nonlinear bending behaviors of sandwich plates. The results also reveal that the core-to-face sheet thickness ratio and the volume fraction distribution of FGM face sheets have a significant effect on the natural frequency, buckling load and postbuckling behavior of the sandwich plate, whereas this effect is less pronounced for the nonlinear bending, and is marginal for the nonlinear to linear frequency ratios of the same sandwich plate.     

面内压缩超轻质点阵夹芯板的优化、 试验与仿真

为揭示点阵材料在航空航天工程中的应用潜力,对承受面内压缩载荷点阵夹芯板的力学行为进行了研究。基于夹芯板整体欧拉失稳、剪切失稳、格间局部失稳、跨格局部失稳和应力破坏多种理论失效模式,引入面板厚度、厚度方向的点阵层数、点阵杆件长度、截面尺寸、倾斜度、胞元长细比等优化变量,推导了点阵夹芯板的最小质量优化设计方法。同时利用激光选取熔融（SLM）增材制造工艺生产了点阵夹芯板试验件。随后,采用有限元方法对试验结果进行了仿真分析,两者误差在10%以内,证实了数值方法的准确性。最终对初始设计和优化设计方案进行了数值分析,发现优化方案在保持相同承载力的条件下,实现结构减重16.6%,验证了优化设计方法的有效性。同时,试验与仿真的一致性有力地证明了增材制造工艺在点阵夹芯结构制造方面的可行性。      

复合材料层合夹芯板局部变形行为研究

在局部荷载作用下,带软夹芯层的夹芯板结构将产生一定的局部变形现象。本文采用双参数基础模型模拟软夹芯材料与受载层合面板间的相互作用,基于经典层合板理论,推导并给出了夹芯板结构局部变形问题的半解析分析方法,并通过算例讨论了边界条件、荷载作用方式、夹芯层厚度与弹性模量等因素对该类结构局部弯曲和局部屈曲行为的影响。     

泡沫铝夹心板的制备及其界面结合机理的研究

由泡沫铝芯材与金属面板构成的夹心结构具有轻质、高强度、良好的减震性等优点.现存的泡沫铝夹心板的制备方法很多,但均为先制备芯材再进行连接的方法.本研究提出一种新的工艺方法即采用粉末与面板直接轧制然后发泡的方法制备了Fe/Al/Fe泡沫铝夹心结构.研究了泡沫铝芯的发泡不均的问题,分析了发泡前和发泡后面板与泡沫铝芯的冶金结合过程,提出了扩散微观结合机理.最终面板与泡沫芯材通过扩散反应形成了牢固的冶金结合.     

Transverse shear and pressurization effects in the bending of plates with reinforced cracks

The authors develop an eigth-order model for bending of transversally isotropic plates and use integral transforms and a collocation method to form a line-spring model for a cracked plate. The eigth-order model allows satisfaction of the three standard plate bending boundary conditions; the normal moment, twisting moment, and transverse shear force, and an additional shear stress resultant that allows analysis of transverse normal stresses near the crack tip. The line-spring model is used to develop geometry correction factors for bending of finite-thickness plates, accounting for transverse shear deformation and pressurization of the plate near the crack tip. The line-spring model is then applied to the problem of a plate with a reinforced crack, and the results are used to validate an interpolation solution based on an energy method. While not explicitly analysed, the models are applicable to many problems, including bending of bonded repairs, fracture and fatigue of composite and layered materials, surface cracks, crack tip plasticity and crack closure or crack face interaction.     

Numerical and experimental studies on aluminum sandwich plates of variable thickness

Abstract

The elastic flexural behavior of static deformation and free vibration of sandwich plates of variable thickness is investigated numerically and experimentally. In the analysis, the face plates are treated as Marguerre shells, and the core is assumed to be an antiplane core and to provide resistance to transverse shear and normal stresses only. Displacement continuity conditions are used at the interfaces between face plates and the core to derive the displacement field. Energy formulations are obtained and solved by the isoparametric finite element method. The numerical results are obtained to compare with the results in the existing literature and to show the effects of taper constant and face plate thickness on deflections and natural frequencies. Finally, experimental works based on the method of holographic interferometry are conducted to confirm the theoretical findings. Experimental and numerical data agree quite well in this work.     

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.     

Effects of face plates on surface displacement profile in 2-2piezoelectric composites

A simple model is developed to describe the inhomogeneous surface deformation profile of face plated 2-2 type piezocomposites. The contribution of face plate to the equilibrium condition is approximated by simple elastic bending of the plate. Analytical solutions were obtained for the inhomogeneous surface displacement profile. From these solutions one can predict the variation of the nonuniform surface displacement in a 2-2 composite with respect to material and geometry parameters. It is shown that the surface displacement uniformity depends on several factors: the ceramic aspect ratio, the spacing between ceramic plates, the thickness of face plate, the Young's modulus of the polymer and of the face plate. The calculated results indicate that stiffer face plates, softer polymer resin, and closer ceramic spacing could make the piezocomposite transducers have more uniform surface displacement     

高温与脱粘对复合材料蜂窝板模态特性影响的试验

复合材料蜂窝板是目前航空航天领域中一类非常重要的结构,但此类结构在热环境下的模态特性研究鲜有公开报道。本文针对由碳纤维增强环氧树脂基复合材料层合板和Nomex蜂窝芯层复合而成的夹层板进行了不同温度下的模态试验,在加热过程中结构面板与芯层脱离,向外凸出。损伤发生前,结构固有频率随温度升高而下降,在识别出的前7阶模态中,弯曲振型的下降幅度较大,而扭转振型的降幅较小。对损伤后的结构再次进行常温模态试验,其模态特征发生显著变化,除了固有频率的变化外,模态阻尼比明显提高,而且其中两阶模态振型的顺序发生对调。此外,本文还对该损伤形式的成因进行了分析,所得结论对用于热环境的复合材料蜂窝结构设计具有一定的指导意义。