考虑刚-柔-热耦合的板结构多体系统的动力学建模

对热载荷作用下中心刚体与大变形薄板多体系统的动力学建模问题进行研究.基于Kirchhoff假设,从格林应变和曲率与绝对位移的非线性关系式出发,推导了非线性广义弹性力阵,用绝对节点坐标法建立了大变形矩形薄板的有限元离散的动力学变分方程.为了考虑刚体姿态运动、弹性变形和温度变化的相互耦合作用,推导了热流密度与绝对节点坐标之间的关系式.引入系统的运动学约束方程,建立了中心刚体-矩形板多体系统的考虑刚-柔-热耦合的热传导方程和带拉格朗日乘子的第一类拉格朗日动力学方程.为了有效地提高计算效率,将改进的中心差分法和广义-α法相结合,求解热传导方程和动力学方程,差分后的方程通过牛顿迭代法耦合求解.对刚-柔耦合和刚-柔-热三者耦合两种模型的仿真结果进行比较表明,刚体运动对温度梯度和热变形的影响显著.此外,本文建模方法考虑了几何非线性项,因此也考虑了热膨胀引起的轴向变形对横向变形的影响.     

考虑几何非线性和热效应的刚柔耦合系统的频域特性研究

研究温度场中旋转刚体-梁系统的刚-柔耦合动力学特性.考虑几何非线性和热效应,从精确的应变-位移关系式出发,用虚功原理和有限单元法建立了旋转刚体-梁系统的刚-柔耦合动力学方程.由于非线性刚度阵与变形的高次项有关,将非线性刚度阵的各元素表示为广义坐标阵和常值阵的乘积.数值计算表明,该方法可避免重复积分,提高计算效率.在此基础上研究了在温度递增的情况下几何非线性对系统的刚-柔耦合动力学特性的影响,用频谱分析方法研究了系统的固有频率随中心刚体转动惯量和温度的变化.     

中心刚体-柔性梁刚柔耦合动力学模型降阶研究

有限单元法被广泛的采用来描述柔性体的弹性变形,然而有限元节点坐标数目庞大,将会给动力学方程求解带来巨大的计算负担.如何降低柔性体的自由度,是当前柔性多体系统动力学研究的一个重要命题.本文以中心刚体-柔性梁系统为例,采用Krylov方法和模态方法进行降价.然后分别采用有限元全模型、Krylov降阶模型和模态降阶模型,对中心刚体-柔性梁进行刚-柔耦合动力学仿真.仿真结果表明,与采用模态降阶方法相比,采用Krylov模型降阶方法只需要较低的自由度,就可以得到与采用有限元方法完全一致的结果.说明Krylov模型降阶方法能够有效的用于柔性多体系统的模型降价研究.     

哑铃型航天器刚-柔耦合动力学建模与仿真分析

为满足深空探测的需求,需要构建一种全新的哑铃型航天器.由于构型和质量分布的差异,传统"中心刚体+柔性附件"动力学模型将不再适用,因此必须针对该构型建立一种高效准确的动力学模型.本文基于小变形假设,利用浮动坐标法,采用多体系统动力学单向递推组集方法,建立了哑铃型航天器的刚-柔耦合动力学模型.该模型考虑了哑铃型航天器的轨道-姿态-变形之间的耦合效应,保留了全部变形高次耦合项.通过采用本文方法建立的"刚体-桁架-刚体"模型和已有的两种哑铃型航天器模型,对典型算例进行动力学仿真和比较.仿真结果表明,本文模型很好地反映了哑铃型航天器的刚-柔耦合动力学特性,末端物体的转动惯量将会影响系统的动力学响应,不能简单忽略.本研究将为哑铃型航天器的总体设计,特别是控制规律的设计,提供重要的技术支持.     

轴向可伸缩悬臂复合材料层合板横向振动的解析研究

通过解析和数值方法对可伸缩悬臂复合材料层合板的时变动力学特性进行研究.根据经典层合板理论和Hamilton原理对面内激励和横向载荷共同作用下的可伸缩悬臂复合材料层合板进行线性动力学建模,选取符合可伸缩悬臂板位移边界条件的时变模态函数,利用Galerkin方法对所得的偏微分方程进行离散,得到复合材料层合板的时变常微分线性动力学方程.研究轴向移动速度对可伸缩悬臂板动力学特性的影响,并通过改进的多尺度法得到了一阶时变线性系统的解析解和数值解比较.结果表明,轴向移动速度对可伸缩悬臂板的动力学特性影响很大;相比文献［12］,本文采取的改进的多尺度法对一阶线性时变系统更高效.     

复合材料层合板低频声辐射优化

为使复合材料层合板低频声辐射性能最优,根据无限域声场的特点,介绍将有限元与无限元耦合进行声辐射性能分析的理论和方法,采用2个算例验证该方法的有效性.将有限元软件Abaqus与数值优化软件Isight相结合完成复合材料铺层角的优化,并提出逐层优化的思路.以含有8层单层板和1层阻尼芯层的复合材料层合板为研究对象,以铺层角为设计变量,采用逐层优化方法(layer-wise optimization method,LOM)优化层合板的声学性能,并分析阻尼芯层对层合板声辐射的影响.结果表明:合理的铺层角可以提高复合材料层合板的1阶固有频率,达到减少声辐射谱峰数量和降低辐射声功率的效果;增加阻尼芯层可以抑制声辐射谱峰,有利于提高层合板的低频声辐射性能.     

柔性航天器动力学建模及模型降阶研究

针对柔性航天器振动影响飞行器姿态稳定性和精度.为了解决上述问题,提出了多柔体航天器的动力学建模.首先,根据工程实现的假设振型法,采用拟坐标拉格朗日方程,推导出带有刚体模态的二阶系统刚柔耦合动力学模型,其中,为了减少模型计算量,通过坐标变换将刚体模态和柔性模态解耦,利用一种刚体模态解耦的二阶不稳定系统的模型降阶方法,并对航天器多柔体系统动力学方程进行了仿真分析,结果飞行姿态稳定,满足了精度要求,表明了动力学建模与模型降阶法的有效性和正确性.     

基于刚-柔混合模型的300T铁水车动力学仿真

为保证300t铁水车的安全运输,采用刚-柔混合动力学模型研究了该车的动力学性能.以I-DEAS软件为柔性体仿真平台,ADAMS/Rail软件为多刚体系统仿真平台,给出了创建刚-柔混合动力学模型的技术路线,采用在系统外将所关心的对象柔性化的建模方法建立了某公司研制的特种车辆-300t铁水运输车的刚-柔混合动力学模型.基于刚-柔混合模型的动力学仿真结果表明:弹性轨道对该车运行平稳性和曲线通过性能的影响大于柔性转向架对运行平稳性和曲线通过性能的影响.因此,对这类特种车辆进行动力学仿真应采用弹性轨道.当计算规模很大无法考虑转向架的柔性效应时,仅使用弹性轨道所获得的结果也能达到相当的精度.     

振动破碎系统的建模与动力学分析

对振动破碎机的多刚体-散体(物料层)耦合动力学问题进行了深入研究．首先通过实验识别出物料层的非线性滞回力的数学模型和参数,然后根据拉格朗日方程建立了振动破碎机的动力学方程,并用数值方法分析了该系统中刚散耦合的动力学特性,初步揭示了物料层对四动颚的相对运动轨迹的影响规律,并通过动力学试验验证了数值分析结果的正确性．为实际振动破碎机的动力学设计和产品开发奠定了基础．     

基于Lagrange法的刚体与柔体动力学对比研究

对于机器人、航天器和车辆悬架部件等一些多体系统来说,其中一些部件的大尺寸、轻型化趋势使得传统的刚性体建模已经难以准确地模拟实际的工况,将部件所具有的柔性特性加入到多体系统模型中进行柔体动力学仿真,由于考虑了部件弹性变形与大范围刚性运动之间的耦合,故可以得到部件更为真实的动力学行为.文中通过与基于Lagrange法的刚体动力学基本方程进行对比研究,详细说明了柔体动力学方程中上述的耦合作用.以某大型雷达可展开天线为例,分别在刚体和柔体的假设下对其展开运动进行动力学仿真,结果表明采用柔性体仿真更能真实反映其动力学特性.     

Bending analysis of composite laminated plates using a partially hybrid stress element with interlaminar continuity

A partially hybrid stress element for modelling composite laminated plates is developed based on the state space in which only the displacement components and the transverse stress components are assumed to be independent. This formulation satisfies exactly the interlaminar continuity requirements and the surface traction free conditions. It also combines the advantages of both the conventional displacement elements and the fully hybrid stress elements. Numerical examples are illustrated to investigate the accuracy, convergence and shear locking sensitivity of the present method. The nonlinear distributions of the normal and transverse stresses along the thickness direction are also especially studied.     

A partial hybrid stress solid-shell element for the analysis of laminated composites

In this paper we introduce a low order partial hybrid stress solid-shell element based on the composite energy functional for the analysis of laminated composite structures. This solid-shell element has eight nodes with only displacement degrees of freedoms, and three-dimensional constitutive models can be directly employed in the present formulation without any additional treatment. The assumed interlaminar stress field provides very accurate interlaminar stress calculation through the element thickness. These elements can be stacked on top of each other to model multilayer structures, fulfilling the interlaminar stress continuity at the interlayer surfaces and zero traction conditions on the top and bottom surfaces of the laminate. The present solid-shell does not show the transverse shear, trapezoidal and thickness locking phenomenon, and passes both the membrane and the bending patch tests. To assess the present formulation’s accuracy, a variety of popular numerical benchmark examples related to element convergence, mesh distortion, shell and laminated composite analyses are investigated and the results are compared with those available in the literature. The numerical results show the accuracy of the presented solid-shell element for the analysis of laminated composites.     

Laminated composite structures by continuum-based shell elements with transverse deformation

In this paper a first-order shear/fourth-order transverse deformation theory of laminated composite shells is presented. A nonlinear continuum-based (degenerated 3D) finite element model with a strain/stress enhancement technique is developed in such a way that the nonzero surface traction boundary conditions and the interlaminar shear stress continuity conditions are all satisfied identically. Analytical integration through the shell thickness is performed. The resultants of the stress integrations are expressed in terms of the laminate stacking sequence. Consequently, the shell laminate characteristics in the normal direction can be evaluated precisely and the computational cost of the overall analysis is reduced. The numerical results are compared with analytical solutions and other finite element solutions to demonstrate the effectiveness of the theory and the computational procedure developed herein.     

Accurate computation of critical local quantities in composite laminated plates under transverse loading

The design of laminated composite based components requires a detailed analysis of the response of the structure when subjected to external loads. For the analysis of laminated composite plates, several plate theories have been proposed in the literature. Generally, these plate theories are used to obtain certain global response quantities like the buckling load. However, the use of these theories to obtain local response quantities, i.e. point-wise stresses; interlaminar stresses and strains, can lead to significant errors.In this paper, a detailed study of the quality of the point-wise stresses obtained using higher-order shear deformable, hierarchic and layerwise theories is done for a plate under transverse loading. The effect of equilibrium based post-processing on the transverse stress quantities is also studied. From the detailed study it is observed that the layerwise theory is very accurate. However, for all the models proper mesh design is required to capture boundary layer effects, discretization error, etc. Using focussed adaptivity, and post-processed state of stress, accurate representation of the local state of stress can be obtained, even with the higher-order shear deformable theories. Using this approach, the first-ply failure load is obtained with the Tsai–Wu criterion. It is observed that use of an adaptive procedure leads to significantly lower failure loads as compared to those given in the literature.     

Transverse shear effect on vibration of laminated plate using higher-order plate element

An approach using a higher-order plate element to include the effect of transverse shear deformation on free vibration of laminated plate is presented. The total displacement of the element is expressed as the sum of the displacement due to bending and that due to shear deformation. The double-sized stiffness and mass matrices due to the separation of bending and shear displacements are then reduced to the size as if only the total deflection was considered. Numerical results for natural frequencies for a range of different isotropic and anisotropic plates with various thickness-to-length ratios are obtained and compared with solutions available in the literature. The effect of transverse shear deformation on natural frequencies of higher modes of laminated plates is also discussed.     

三阶剪切变形板的振动特性研究

对于中厚板或层合板而言,横向剪切变形的影响是显著的,采用三阶剪切变形理论比采用经典薄板理论和一阶剪切变形理论能更好的满足精度的要求,而且能更好地描述板的剪切变形和剪应力沿厚度方向的分布情况.本文用解析的方法研究了简支、自由和固定三种边界条件的任意组合下三阶剪切变形板的自由振动问题.首先应用哈密顿原理建立自由振动方程,再通过引入中间变量使得原来耦合的自由振动方程得到解耦和简化,基于分离变量法,利用边界条件得到基函数的表达式,利用Rayleigh-Ritz法,求得三阶剪切变形板在任意边界条件下的固有频率和振型.本文得到的结果可以为厚板在工程中的应用提供理论依据,具有较高的工程实际应用价值.     

Three-dimensional finite element analysis of thick laminated plates

A displacement-based, three-dimensional finite element scheme is proposed for analyzing thick laminated plates. In the present formulation, a thick laminated plate is treated as a three-dimensional inhomogeneous anisotropic elastic body. Particular attention is focused on the prediction of transverse shear stresses. The plane of a laminated plate is first discretized into conventional eight-node elements. Various through-thickness interpolation is then denned for different regions of the plate; layerwise local shape functions are used in the regions where transverse shear stresses are of interest, while an ad hoc global-local interpolation is used in the region where only the general deformation pattern is concerned. For satisfying the displacement compatibility between these two regions, a transition zone is introduced. The model incorporates the advantages of the layerwise plate theory and the single-layer plate theory. Details of formulation will be presented together with several numerical examples for demonstrating the proposed scheme.     

A class of C finite elements for the static and dynamic analysis of laminated plates

A general higher-order deformation theory is developed to analyse the behaviour of an arbitrary laminated fibre-reinforced composite plate. Three-dimensional effects such as the warping of sections and the presence of interlaminar stress field components are taken into account assuming a power series expansion of displacements along the thickness. A class of C⁰ finite element models based on this theory is then developed for mono- and bi-dimensional elements. Applications of the models to bending and vibration of laminated plates are then discussed. The present solutions are compared with those obtained using the three-dimensional elasticity theory, classical laminate theory and other higher-order theories.     

A new unconstrained third-order plate theory for Navier solutions of symmetrically laminated plates

Among the many higher order plate theories, the third-order shear deformation plate theory (TSDT) of Reddy is, perhaps, the most widely adopted model in the study of laminated plates. It, however, imposes a restriction that transverse shear stress vanishes on the top and bottom surfaces of the plate. Such requirement, although reasonable in many engineering applications, is not valid when the plate is subject to shear traction parallel to the surface. To account for such problems, the present plate model releases the constraints of vanishing transverse shear stress on the top and bottom plate surfaces. This unconstrained third-order shear deformation plate theory (UTSDT) is particularly useful for the study of a plate with contact friction or present in a flow field where the boundary layer shear stress is significant. The governing differential equations of UTSDT are of similar complexity as that of TSDT but it yields more accurate solutions. In addition, it is more flexible as it can be degenerated to the first-order shear deformation plate theory (FSDT) of Reissner and Mindlin if the higher-order rotation coefficients are neglected and a shear correction factor is considered, or to the TSDT if the relevant rotation coefficients are constrained. The present study further develops the unconstrained theory in composite laminates. Navier solutions for bending and stress analysis of multilayered and symmetrically laminated composite plates are presented. It is concluded that the present plate model provides more accurate solutions than that of TSDT, with similar level of analytical complexity, when compared with the 3D elasticity exact solutions.