Non-linear panel flutter for temperature-dependent functionally graded material panels

The non-linear flutter and thermal buckling of an FGM panel under the combined effect of elevated temperature conditions and aerodynamic loading is investigated using a finite element model based on the thin plate theory and von Karman strain-displacement relations to account for moderately large deflection. The aerodynamic pressure is modeled using the quasi-steady first order piston theory. The governing non-linear equations are obtained using the principal of virtual work adopting an approach based on the thermal strain being a cumulative physical quantity to account for temperature dependent material properties. This system of non-linear equations is solved by Newton–Raphson numerical technique. It is found that the temperature increase has an adverse effect on the FGM panel flutter characteristics through decreasing the critical dynamic pressure. Decreasing the volume fraction enhances flutter characteristics but this is limited by structural integrity aspect. The presence of aerodynamic flow results in postponing the buckling temperature and in suppressing the post buckling deflection while the temperature increase gives way for higher limit cycle amplitude.     

Thermo-mechanical load interactions in foam cored axi-symmetric sandwich circular plates – High-order and FE models

This work presents analytical and finite element analysis (FEA) results of the thermo-mechanical non-linear response of an axi-symmetric circular sandwich plates with a compliant foam core. The study investigates the load–thermal interaction response of a sandwich panel where the properties of the core are temperature dependent and degrade as the temperatures are raised. It presents briefly the governing equations for a sandwich plate based on the principles of the high-order sandwich panel theory (HSAPT) which incorporates the effects of the vertical flexibility of the core material as well as the effects of temperature independent/dependent mechanical properties of the foam core. The effects of the thermal degradation of core material on the thermo-mechanical non-linear response of a simply supported circular sandwich plate are studied through the analytical and FE models. The difficulties involved in non-linear geometrical FE modeling of sandwich panels with a compliant “soft” core with temperature-dependent mechanical properties are discussed. The HSAPT model predictions are compared very well with FE result. An important conclusion of the study is that the interaction between mechanical loads, temperature induced deformations, and degradation of the mechanical properties due to elevated temperatures, may seriously affect the structural integrity of foam cored sandwich plates.     

Assessment of models for analysis of singly-curved sandwich panels

Overall behaviour of a simply-supported singly-curved shallow sandwich panel under lateral loading is considered. Three types of linear models — general shell, shallow shell and curved plate theories — are employed to describe a static overall behaviour of such a panel. The shallow panel with a constant curvature loaded by a uniform pressure is used as a trial case to assess the accuracy of the models. A nonlinear model for a panel of arbitrary shape under an arbitrary loading is developed on the basis of the curved plate theory. A closed-form nonlinear analytic solution for the panel of constant curvature under a uniform lateral pressure is obtained, and its accuracy is estimated. An experimental investigation of a sandwich beam under a uniform lateral loading is carried out, and the data obtained are compared with the theoretical calculations.     

Effects of in-plane constraints on the free vibration of a symmetrically laminated doubly curved panel

Summary. For a symmetrically laminated curved panel, although the stretching-bending anisotropic coupling stiffnesses are zero, but due to presence of the curvature, the in-plane and out-of-plane behaviors of the panel are still coupled, and hence the in-plane constraints at the boundaries have influences on the transverse behavior of the panel. Such effects of in-plane constraints on the free vibration of the symmetrically laminated curved panel are investigated using a modified Galerkin method in this study. Transverse shear deformation of the panel is considered by using first-order shear deformation theory. Numerical results of the symmetric angle-ply and cross-ply laminated panel with simply supported boundary conditions (SS2 and SS3) are presented. Results show that the in-plane boundary constraints have significant effects on the vibration behavior of the symmetrically laminated curved panel, and the effects strongly depend on the radius of curvature, thickness and lamination schemes, etc. Effects of bending-twisting anisotropic coupling of symmetric angle-ply laminate on the vibration behavior are also discussed.     

Geometrically nonlinear flexural analysis of hygro-thermo-elastic laminated composite doubly curved shell panel

In this article, nonlinear flexural behaviour of laminated composite doubly curved shell panel is investigated under hygro-thermo-mechanical loading by considering the degraded composite material properties through a micromechanical model. The laminated panel is modelled using higher order shear deformation mid-plane kinematics and Green–Lagrange geometric nonlinear strain displacement relations. In the present case, all the nonlinear higher order terms are included in the mathematical model to obtain the exact flexure of the structural panel. The nonlinear system governing equations are derived using variational method and discretised using the nonlinear finite element steps. Numerical results are computed through direct iterative method and validated by comparing with those published results available in open literature. Finally, wide variety of numerical examples are computed using the proposed model to address the effect of hygrothermal conditions, geometrical and material parameters and support conditions on the flexural behaviour of laminated composite doubly curved shell panel.     

Response of composite sandwich panels with transversely flexible core to low-velocity transverse impact: A new dynamic model

A new computational procedure based on improved higher order sandwich plate theory (IHSAPT) and two models representing contact behavior between the impactor and the panel are adopted to study the low velocity impact phenomenon of sandwich panels comprising of a transversely flexible core and laminated composite face-sheets. The interaction between the impactor and the panel is modeled with the help of a new system having three-degrees-of-freedom, consisting of spring–mass–damper–dashpot (SMDD) or spring–mass–damper (SMD). The effects of transverse flexibility of the core, and structural damping are considered. The present analysis yields analytic functions describing the history of contact force as well as the deflections of the impactor and the panel in the transverse direction. In order to determine all components of the displacements, stresses and strains in the face-sheets and the core, a numerical procedure based on improved higher order sandwich plate theory (IHSAPT) and Galerkin's method is employed for modeling the layered sandwich panel (without the impactor), while the analytic force function developed on the basis of SMDD or SMD model, can be used for the contact force between the impactor and the panel. The contact force is considered to be distributed uniformly over a contact patch whose size depends on the magnitude of the impact load as well as the elastic properties and geometry of the impactor. Various boundary conditions for the sandwich panel have also been considered. Finally, the numerical results of the analysis have been compared either with the available experimental results or with some theoretical results.     

Structural health monitoring based on sensitivity vector fields and attractor morphing

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.     

Non-linear analysis of fiber-reinforced open conical shell panels considering variation of thickness and fiber orientation under thermo-mechanical loadings

Non-linear bending analysis of moderately thick laminated conical panels under various thermo-mechanical loadings and boundary conditions is presented using the generalized differential quadrature (GDQ) method together with the Newton–Raphson iterative scheme. The stiffness coefficients are assumed to be functions of the meridional and circumferential coordinates in panels for the realistic applications. In the first case of orthotropic open conical shell panels, the orientation of fibers are assumed to be in the meridional and circumferential directions. The stiffness coefficients of this type of fiber-reinforced panel are usually assumed to be constant. It is shown that due to the geometry of the conical surface, thickness of laminate will be changed along the meridional direction. The effect of stiffness variation on the non-linear response of panel is considered for the first time. In the second type, open conical shell panel can be made by cutting from a filament wound circular conical shell. In this case, thickness and ply orientation are functions of the shell coordinates. In this paper, different path definitions for variable stiffness filament wound shells are considered. The inclusion of this geometric complicating effect in large deformation analysis will add considerably to the complication and cost of a solution scheme. Paper presents some results to show when these assumptions have a significant effect on the end result. Assuming the effects of shear deformation and initial curvature, based on the first-order shear deformation theory (FSDT) and von Kármán-type of geometric non-linearity, the governing system of equations is obtained. Comparisons of the predictions with those available in the literature and finite element analyses show very good agreement. More results for panels with particular boundary conditions and thermo-mechanical load are presented for future references. For the sake of brevity, numerical results which presented in this paper are limited to deflection responses only.     

Postbuckling analysis of composite panels with imperfection damage

In order to promote the efficient use of composite materials in civil engineering infrastructure, effort is being directed at the development of design criteria for composite structures. Insofar as design with regard to buckling of composite shells is concerned, it is well known that a key step is to investigate the influence of initial geometric imperfection. At present, imperfection sensitivity study of composite shells has not been explored in detail. Thus, the objective of this paper is to present the formulation used in developing a composite shell element and to validate the element from the composite curved panel. The non-linear formulation of the shell element is based on the updated Lagrangian method. The shell element is capable of small strain and large displacement analysis with finite rotations. In order to remove the rigid body rotation, a co-rotational method is used. Subsequently the postbuckling analyses from the modeling of the curved panel with initial imperfection damage are performed to investigate the effect of initial geometric imperfection shape and amplitude. The results are used to estimate imperfection sensitivity for such panels.     

Active damping of geometrically nonlinear vibrations of laminated composite shallow shells using vertically/obliquely reinforced 1-3 piezoelectric composites

This paper addresses the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated thin composite cylindrical shallow shells using vertically reinforced 1-3 piezoelectric composite (PZC). The constraining layer of the ACLD treatment is considered to be made of this 1-3 PZC material. The Golla–Hughes–McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The Von Kármán type non-linear strain displacement relations and the first-order shear deformation theory (FSDT) are used for deriving this electromechanical coupled problem. A three dimensional finite element (FE) model of smart composite shallow shells integrated with a patch of such ACLD treatment has been developed to demonstrate the performance of the patch on enhancing the damping characteristics of thin laminated cylindrical shells, in controlling the geometrically nonlinear transient vibrations. The numerical results indicate that the ACLD patch significantly improves the damping characteristics of the shells for suppressing the geometrically nonlinear transient vibrations of the shells. The effect of variation of fiber orientation in the PZC material on the control authority of the ACLD patch has also been investigated.     

KOITER'S ANALYSIS OF THIN-WALLED STRUCTURES BY A FINITE ELEMENT APPROACH

This paper refers to the analysis of the postbuckling behaviour of thin-walled structures by means of an asymptotic approach based on a finite element implementation of Koiter's non-linear theory of instability. The analysis has been accomplished by using the following assumptions: (i) the structure is described as an assemblage of flat slender rectangular panels; (ii) a non-linear Kirchhoff-type plate theory is used to model each panel; (iii) HC finite elements discretization is used; (iv) linear and quadratic extrapolations are assumed for the fundamental and the postbuckling paths, respectively; (v) multimodal buckling is considered; and (vi) imperfection sensitivity analysis is performed in both multimodal and monomodal form based on the steepest– descent path criterion. Several numerical results are presented and discussed. Comparisons with numerical solution obtained by standard incremental codes are given, which show the accuracy and reliability of the proposed approach.     

高速客车蛇行运动Hopf分叉的研究

建立了高速客车非线性系统数学模型,模型中考虑了轨道的整体弹性和阻尼。基于常微分方程的一次近似理论和Hopf分叉理论,研究了高速客车在直线和大半径曲线轨道上蛇行运动的Hopf分叉情况。借助于DEPAR延续算法解决了圆曲线上车辆系统平衡位置难以确定的难题,分析了轨道整体刚度和阻尼、圆曲线半径和外轨超高及转向架悬挂参数等因素对高速客车Hopf分叉速度的影响。研究表明,高速客车在大半径曲线上也有可能出现Hopf分叉现象,并且曲线半径越大、外轨超高越大,车辆的Hopf分叉速度越高,但最大值不会超过车辆系统在直线上运行时的Hopf分叉速度。车辆系统在弹性轨道条件下的Hopf分叉速度高于刚性轨道条件下车辆系统对应的Hopf分叉速度。不论是刚性轨道还是弹性轨道,转向架悬挂参数对车辆系统Hopf分叉速度的影响趋势是一致的。     

Shell–tensionless foundation interaction and nonlinear thermoelastic stability analysis of laminated composite cylindrical panels

In this paper, the thermal buckling behavior of composite laminated curved panels on one-sided foundation is addressed. Governing equations of shell stability are derived based on classical shell theory (CST) and minimum total potential energy. They are solved by a hierarchical Rayleigh–Ritz technique. A part of the contribution is formulating effects of curvature and composite materials in nonlinear analysis of stability for cylindrical panels surrounded by one-sided foundations subjected to thermal loading. The other part is related to the results from parametric studies. In this work, the effects of parameters such as panel aspect ratio thickness, central angle, degree of material orthotropy, and foundation stiffness are investigated. It is observed that with an increase in panel aspect ratio the influence of one-sided constraint on the critical temperature is reduced for a flat panel, while it is magnified for a curved panel. The effect of nonlinear foundation on one-sided buckling of curved panels is highly dependent on parameters such as central angle, aspect ratio, thickness, and degree of foundation stiffness, such that any change in each parameter might have direct influence and severe change on the penetration of the panel into the foundation. The results for simpler case studies are compared and validated with those available in the literature.     

Application of the cohesive model for predicting the residual strength of a large scale fuselage structure with a two-bay crack

The residual strength of a curved and stiffened panel containing a two-bay crack was assessed using the cohesive model. This panel represents a section of a wide-body aeroplane fuselage. The tests were conducted at IMA GmbH Dresden in cooperation with Airbus Industries Germany. The structural panel was modelled using 3D finite elements and a layer of cohesive elements ahead of each crack tip allowing for 70 mm crack extension. Identification of the cohesive parameters was done on small laboratory test pieces. Special effort was made for the transfer of these parameters to the structure. Reasonably conservative predictions of the residual strength of the panel were achieved. The boundary conditions of the loading devices of the test rig are shown to have substantial influence on the predictions.     

基于Excel的强大功能在Solid Edge中实现曲线零件的精确建模

研究了复杂曲线零件的精确建模，在研究非圆曲线插值算法理论的基础上，利用Excel的数据处理功能，对函数进行误差处理插值计算，在Solid Edge环境中使用Excel创建点曲线的方法进行曲线零件的精确建模，探索出了一种Excel与Solid Edge的完美结合方法，通过凸轮零件精确建模的实际案例，示出了曲线零件建模的整个过程，给出了这种方法在分段曲线中的具体应用。     

大扁平比胎侧解析刚度建模及轮胎动力学分析EI北大核心CSCD

针对重载轮胎大扁平比结构建模问题,从动力学建模、实验模态分析、结构参数辨识等方面,基于解析弹性基础的欧拉梁模型,对重载轮胎的柔性胎体和大扁平比胎侧曲梁的低频动力学特性开展研究,建立了考虑充气预紧力的欧拉梁胎体模型,利用实验模态方法,探究了不同充气压力下的柔性胎体振动特性;考虑胎侧曲梁预紧力弦效应和结构弯曲效应,建立了大扁平比胎侧曲梁解析刚度模型;基于模态测试结果,进行柔性胎体与解析胎侧结构参数辨识。研究结果表明:在0~180 Hz频率范围内,重载轮胎以结构周向弯曲振动为主,可利用基于弹性基础的柔性梁模型表征;大扁平比胎侧曲梁的解析刚度与胎侧的几何、结构和充气压力参数直接相关;轮胎充气压力影响柔性胎体梁的轴向预紧力和胎侧的弦刚度,进而影响轮胎弯曲振动特性。     

Performance of composite structural insulated panel with metal skin subjected to blast loading

Structural insulated panel (SIP) is a lightweight composite panel widely used in commercial, industrial and residential building industry. It consists of insulating polymer foam sandwiched by two layers of structural skins. The composite structural insulated panel is considered as a sustainable, economical, thermal insulated, moisture resistant, acoustic insulated and flame retardant panel, which has been more and more commonly used in building industry, and also in petrochemical industry for construction of office buildings, control rooms, store rooms and residential structures. These structures might be subjected to far field explosion loads caused by accidental gas explosion in residential areas and vapor cloud explosion (VCE) in petroleum and chemical processing industries. The performance of composite structural insulated panel against accidental explosions has yet been investigated. In this study, the blast resistant performance of the composite panel is numerically investigated by using software LS-DYNA with the calibrated numerical model. Its blast resistance capacity and energy absorption capacity are quantitatively examined. Parametric studies are also carried out to investigate the effect of panel configurations on its blast resistance capacity.     

Non-linear free vibrations of symmetrically laminated, slightly compressible cylindrical shell panels

A geometrically non-linear dynamic shell theory presented by the authors in an earlier work is used to study the non-linear free vibrations of symmetrically laminated cylindrical shell panels. The theory accounts for arbitrary lamination constructions, anisotropy, and slight compression across the thickness. In this paper, this theory is used to derive the equation of motion of the panel with quadratic and cubic non-linearities and symmetric lamination schemes. The symbolic manipulator Mathematica™ is used to perform the Rayleigh-Ritz procedure and derive a single-mode approximation to the vibration of the panel. The Lindstedt-Poincare perturbation technique is used to analyze the resulting non-linear differential equation of motion and study the effects of non-linearities on the dynamics of free vibrations of the panel. A numerical example of a symmetrically laminated graphite/epoxy shell panel is used to demonstrate the procedure. The numerical example shows that non-linearities are of the hardening type and are more pronounced for smaller opening angles. Moreover, it shows that the larger-amplitude motions are dominated by the lower modes.     

Dimensional analysis for concrete in fracture

A structural element of high strength in compression and extremely low strength in tension, such as concrete, is considered. Based on linear-elastic fracture mechanics a simple model law for ultimate load was derived by the author in 1986. This model law is shown also to be consistent with the non-linear fracture mechanical theory called the fictious crack model.     

斜拉桥有限元建模与模型修正

以圆弧桥面、单偏置斜塔的Safti斜拉桥为对象，研究了斜拉桥的有限元建模技术和基于敏感度分析的有限元模型修正技术及其对该桥的应用。基于该桥现场测量的模态数据，修正后的有限元模型获得了较好的改善。