Finite-rotation theories for composite laminates

Summary For the finite-element analysis of arbitrary composite laminates various finite-rotation theories are presented in a single formulation. First a refined theory is derived which allows a quadratic shear deformation distribution across the thickness. The so-called difference vector appearing in the kinematic relations is expressed in terms of rotational degrees of freedom permitting a clear determination of the deformed normal vector in every nonlinear range. The constitutive relations derived are applicable to orthotropic material properties varying arbitrarily across the thickness and to curvilinear laminate coordinates as well. This refined theory is then transformed into simplified theories of Kirchhoff-Love and Mindlin-Reissner types. Finally, the last formulation is used to formulate a layer-wise theory able to grasp the shear deformations very accurately. Kinematic relations and the corresponding constraints are presented in two alternative forms suitable for the application of isoparametric and classical finite-element formulations.     

Bondline strength evaluation of cocure/precured honeycomb sandwich structures under aircraft hygro and repair environments

Effects of moisture accumulated into the adhesively bonded composite structures on their bondline mechanical strengths are investigated through a series of comparative experiments. Those composite structures include a honeycomb sandwich structures fabricated by the cocure and the precure processes. Mass of moisture accumulated into the closed cells of the honeycomb sandwich panel specimens has been calculated. A pressure due to the vapor expansion in each cell of the sandwich panel has also been obtained for the minimum repair pressure to be applied to the laminate patched area by vapor pressure–temperature relations from the thermodynamic steam table, the ideal gas state equation and two vapor pressure equations. The bondline strengths of the laminated skins on the flat surface of honeycomb have been compared by the flatwise tension test and climbing drum peel test for dry, wet and repair-after-wet specimens, respectively.     

不同老化状态粘弹夹层结构的模态分析

Viscoelastic sandwich structure is widely used in sealing, vibration damping and noise reduction of mechanical equipment. However, viscoelastic material may appear aging phenomena in the process of long time storage, transportation and usage. The aging of viscoelastic material will result in the service performance degradation of viscoelastic sandwich structure, thus affect the performance and safe for use of whole mechanical equipment. Therefore, it is greatly required of the engineering practice to research the aging state recognition method of viscoelastic sandwich structure. In this paper, the experimental device of typical viscoelastic sandwich structure is designed. The hot oxygen accelerated aging experiment of viscoelastic material is accomplished, and the specimens with different aging degrees are obtained. The mechanical property test of viscoelastic material is implemented, and the performance indexes under different aging degrees are obtained. By the 3D modeling-importing-preprocessing method, the finite element model of viscoelastic sandwich structure is established. By importing the different parameters of viscoelastic material, the purpose of equivalent models with different aging states is reached. The finite element analysis of viscoelastic sandwich structure under different aging states is carried out, and the corresponding relations between aging state changes and natural frequency changes are built. Through impulse excitation experiment, the effectiveness of finite element model is verified. The research results show that the established finite element model of viscoelastic sandwich structure can reflect the structural aging state characteristics and its change, and can provide theoretical foundation and prior knowledge for the structural aging recognition.     

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.     

复合材料夹层板振动分析的精化锯齿理论和三角形板单元

基于精化锯齿理论,构造了六节点三角形协调板单元并推导了夹层板自由振动问题有限元列式。不同于已有锯齿理论,精化锯齿理论特点是面内位移不含有横向位移一阶导数,构造有限元时仅需要C0 插值函数。为验证单元性能,分析了软核夹层板自由振动问题。结果表明,该文构造的单元能准确计算软核夹层板固有频率,然而基于已有锯齿理论建立的不协调元计算结果精度较低。     

A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches

A critical review of literature pertinent to the subject matter of this paper was carried out under the following two broad headings: free vibration and transient dynamics. Each of these groups describes the various theoretical developments in fiber reinforced laminated composite and sandwich plates. The theoretical developments are further classified according to the refinement/accuracy of the theories developed, such as the classical theory, the first-order shear deformation theory, and the three-dimensional elasticity/higher-order shear deformation theories. The present literature review is limited to linear free vibration and transient dynamic analyses, and geometric nonlinear transient response of multilayer sandwich/fiber-reinforced composite plates. A comparative study of recently developed refined theories in conjunction with the C° isoparametric finite element formulation has been made and the conclusions were drawn based on the literature review and the refined theories results. In order to compare the present results with the available results and to provide an easy means for future comparisons by other investigators, the numerical results are presented in tabular form.     

Theoretical and experimental investigation of bending of sandwich beams

We present the results of theoretical and experimental investigation of problems on bending of composite inhomogeneous sandwich beams. The theoretical results obtained by using the basic equations of the stress-strain state deduced within the framework of classical and refined nonclassical theories of bending of composite beams were compared with the experimental data. The nonclassical theory is based on a hypothesis taking into account the effect of deplanation of cross sections of the beam caused by transversal shear deformations. As experimental data, we use the results of experimental investigation of the process of bending of sandwich beams. Translated from Problemy Prochnosti, No. 3, pp. 76–85, May–June, 2000.     

The contact behavior between a foam core sandwich plate and a rigid indentor

The purpose of this paper is to determine the indentation produced by a rigid indentor falling on a sandwich plate with a height–density closed cellular foam core. Two different indentor shapes are considered: a rigid sphere and a cylindrical rigid punch. By assuming that the time of complete indentation of the indentors is much larger than the time required by the elastic waves to propagate from the point of first contact to the boundary of the plate, a static analysis is performed. A distribution of surface pressures reproducing the contact law of the rigid indentor on an elastic half-space is introduced and the sandwich plate theory proposed by Dundrová, Kovarı́k and Slapák (1970) is adopted; the explicit solutions with pre-assigned surface pressures are obtained and the contact force–indentation relations, before the sandwich plate is damaged, are found. The contact laws are obtained for both a simply supported and a clamped circular sandwich plate and the relevant influence of boundary conditions on the elastic response of the sandwich plate is shown.     

High-order free vibration analysis of sandwich plates with both functionally graded face sheets and functionally graded flexible core

Free vibration analysis of functionally graded material sandwich plates is studied using a refined higher order sandwich panel theory. A new type of FGM sandwich plates, namely, both functionally graded face sheets and functionally graded flexible core are considered. The functionally graded material properties follow a power-law function. The first order shear deformation theory is used for the face sheets and a 3D-elasticity solution of weak core is employed for the core. On the basis of continuities of the displacements and transverse stresses at the interfaces of the face sheets and the core, equations of motion are obtained by using Hamilton’s principle. The accuracy of the present approach is validated by comparing the analytical results obtained for a degradation model (functionally graded face sheets and homogeneous flexible core) with ones published in the literatures, as well as the numerical results obtained by finite element method and good agreements are reached. Then, parametric study is conducted to investigate the effect of distribution of functionally graded material properties, thickness to side ratio on the vibration frequencies.     

Local effects in the vicinity of inserts in sandwich panels

The paper considers local bending effects induced in the vicinity of inserts in sandwich panels. Such local bending effects are associated with an increase of bending stresses in the sandwich faces and normal and shear stresses in the sandwich core. An earlier developed analytic model [Proceedings of the Sixth International Conference on Sandwich Structures (ICSS-6) (2002) 551] is adapted for the case of a sandwich panel with circular insert, with elastic properties differing from those of the core. The locally induced stresses in the faces and core due to presence of the insert are expressed via simple analytic relations (and charts) enabling an estimation of these local stresses. Finite element analysis is employed to demonstrate the applicability of the analytic model, and a good correspondence between the numerical and the analytical data is found. A study case related to marine applications, namely a circular insert in a sandwich deck panel used for mounting of a rigging fixture, is considered, and optimization of an existing design is carried out.     

Free vibration analysis of a sandwich nano-plate including FG core and piezoelectric face-sheets by considering neutral surface

In this article, two-variable sinusoidal shear deformation theory, nonlocal piezoelasticity relations incorporating with concept of neutral surface are employed for free vibration analysis of a sandwich nano-plate. Due to using the functionally graded materials, the concept of neutral surface must be employed through formulation of the problem. A parametric study is performed to show how natural frequencies of sandwich nano-plate are changed in terms of nonlocal parameter, non-dimensional geometric parameters and in-homogeneous index. Before presentation of full numerical results, a comparison with a valid reference is performed to confirm our formulations and corresponding numerical results.     

Strength of an oil pipeline with surface defects

A determination is made of the load-carrying capacity of an oil pipeline with defects with allowance for the changes in the radius, thickness, and ductility properties of the constituent steels and the biaxial nature of the loading. The use of a fracture criterion connected with loss of plastic stability by the pipe is substantiated. This criterion is refined with consideration of the biaxial character of the load and the parameters of a longitudinal crack in the pipe. New analytical relations are derived for engineering calculations of the ultimate strength of thin-walled cylindrical pressure vessels, and a coefficient expressing the effect of the dimensions of the surface crack is refined for these formulas, Examples are presented to illustrate the calculation of the force exerted by a hydraulic expander in the last forming operation for large-diameter pipe. Also, practical recommendations are given on determining hydraulic testing regimes, load-carrying capacity, working pressure for oil pipelines. Translated from Problemy Prochnosti, No. 12, pp. 51–59, December, 1993.     

Longitudinal vibrations of a rod with a coating

A solution is obtained to the problem of the longitudinal vibration of a rod with a coating. The solution is obtained in a refined formulation. The same theoretical model is also used to find the solution for the case of static tension. An analysis is made of the way in which the properties of a deformable rod are affected by the stiffness of the shear constraints, which is regarded as a physicomechanical characteristic of the coating-substrate system. A method is proposed for experimental determination of stiffness for both static and cyclic loading conditions. All of the relations needed to analyze the stress-strain state are presented, including those required for fatigue tests in tension-compression.Translated from Problemy Prochnosti, No. 10, pp. 68–75, October, 1994.     

Investigation on the square cell honeycomb structures under axial loading

To investigate into the collapse of a sandwich panel or beam with a square cell honeycomb, the novel plate model and beam model are developed according to the cross-sectional symmetry of the cell. The treble series solution of buckling mode is presented, and the formulas of critical compressive stress on skins are derived. The honeycomb sandwich panels are classified as thin, medium and thick plates based on their failure forms. It is found that the different kinds of cells have different buckling modes and different parameter governing equations. A new iterative optimization design method for a square honeycomb sandwich panel is developed and the curves of critical compressive stresses with geometrical parameters are provided in details. Finally, the 3D finite element numeric simulations have validated the formulas presented by this paper. Our study reveals some mechanical characteristics of the square honeycomb sandwich structures.     

Transient response of composite sandwich plates

The transient response of orthotropic, layered composite sandwich plates is investigated by using two new C⁰ four and nine node finite element formulations of a refined form of Reddy's higher-order theory. This refined third order theory accounts for parabolic variation of the transverse shear stresses, and requires no shear correction factors. The assumed strain approach is employed to model both thin and thick plates without any major defects like shear locking and parasitic spurious zero energy modes. A consistent mass matrix formulation is adopted. The Newmark direct integration scheme is used to solve the governing equilibrium equations. The parametric effects of plate aspect ratio, length to thickness ratio, boundary conditions and lamination scheme on the transient response are investigated. The present results are in very close agreement with earlier published results in the literature and can serve as a benchmark for future investigators.     

Optimization of Sandwich Composites Fuselages Under Flight Loads

The sandwich composites fuselages appear to be a promising choice for the future aircrafts because of their structural efficiency and functional integration advantages. However, the design of sandwich composites is more complex than other structures because of many involved variables. In this paper, the fuselage is designed as a sandwich composites cylinder, and its structural optimization using the finite element method (FEM) is outlined to obtain the minimum weight. The constraints include structural stability and the composites failure criteria. In order to get a verification baseline for the FEM analysis, the stability of sandwich structures is studied and the optimal design is performed based on the analytical formulae. Then, the predicted buckling loads and the optimization results obtained from a FEM model are compared with that from the analytical formulas, and a good agreement is achieved. A detailed parametric optimal design for the sandwich composites cylinder is conducted. The optimization method used here includes two steps: the minimization of the layer thickness followed by tailoring of the fiber orientation. The factors comprise layer number, fiber orientation, core thickness, frame dimension and spacing. Results show that the two-step optimization is an effective method for the sandwich composites and the foam sandwich cylinder with core thickness of 5 mm and frame pitch of 0.5 m exhibits the minimum weight.     

A four‐noded quadrilateral element for composite laminated plates/shells using the refined zigzag theory

A new bilinear four‐noded quadrilateral element (called quadrilateral linear refined zigzag) for the analysis of composite laminated and sandwich plates/shells based on the refined zigzag theory is presented. The element has seven kinematic variables per node. Shear locking is avoided by introducing an assumed linear shear strain field. The performance of the element is studied in several examples where the reference solution is the 3D finite element analysis using 20‐noded hexahedral elements. Copyright © 2013 John Wiley & Sons, Ltd.     

Refined global–local higher-order theory for angle-ply laminated plates under thermo-mechanical loads and finite element model

To analyze angle-ply laminated composite and sandwich plates coupled bending and extension under thermo-mechanical loading, a refined global–local higher-order theory considering transverse normal strain is presented in this work. Hitherto, present theory for angle-ply laminates has never been reported in the literature, and this theory can satisfy continuity of transverse shear stresses at interfaces. In addition, the number of unknowns in present model is independent of layer numbers of the laminate. Based on this theory as well as methodology of the refined triangular discrete Kirchhoff plate element, a triangular laminated plate element satisfying the requirement of C¹ continuity is presented. Numerical results show that the present refined theory can accurately analyze the bending problems of angle-ply composite and sandwich plates as well as thermal expansion problem of cross-ply plates, and the present refined theory is obviously superior to the existing global–local higher-order theory proposed by Li and Liu [Li XY, Liu D. Generalized laminate theories based on double superposition hypothesis. Int J Numer Meth Eng 1997;40:1197–212]. After ascertaining the accuracy of present model, the distributions of displacements and stresses for angle-ply laminated plates under temperature loads are also given in present work. These results can serve as a reference for future investigations.     

Behavior of laminated sandwich plates having interfacial imperfections by a new refined element

The static response of laminated sandwich plates having imperfections at the layer interfaces is investigated by a refined plate theory. The plate theory represents parabolic through thickness variation of transverse shear stresses, which are continuous at the layer interfaces and become zero at the plate top and bottom surfaces. In this plate model the interfacial imperfection is represented by a linear spring-layer. Moreover, with all these features of an accurate modeling, it involves unknowns only at the reference plane of the plate. To have generality in the analysis, finite element method is adopted. But any existing plate element cannot be used, as the plate theory demands certain inter-elemental continuity. Thus an attempt has also been made to develop a new triangular element. As there is no published result on imperfect sandwich plates, the problems of perfect sandwich plates and ordinary laminated plate with inter-laminar imperfection are used for validation.     

基于有限元法的蜂窝夹层结构稳定性研究

蜂窝夹层结构随面板厚度的逐渐变化会出现不同的屈曲现象。针对连续芯层有限元模型, 求出不同面板厚度时结构的屈曲因子, 并与经验失稳公式预测值进行对比, 两种方法的结果基本吻合。建立考虑芯层几何特征的有限元模型, 进行屈曲分析并研究芯层几何参数对结构稳定性的影响。介绍了一种局部屈曲现象——蜂窝壁屈曲, 提出了相应的失稳预测分析方法, 并与三维有限元分析结果进行比较, 验证该方法的正确性。对承受多轴惯性载荷的蜂窝夹层承力筒结构进行稳定性分析, 通过改变面板厚度和纵横惯性载荷比, 得到一系列有限元解, 给出了相关的多轴惯性载荷相关方程。