纤维增强复合材料靶板抗钢球贯穿的工程分析方法研究

介绍了钢球贯穿纤维增强复合材料靶板的一维工程近似分析方法.钢球被假定为刚体,复合材料靶被近似为横观各向同性弹埋性材料.通过将球腔膨胀模型和柱腔贯穿相结合的方法,提出了一种改进的复合材料靶抗贯穿的工程近似分析方法.利用该方法,对三维芳纶纤维编织(3DKw)复合材料靶板开展了抗钢球贯穿的工程近似分析,计算结果与实验结果一致性较好;并进一步讨论了计算中材料主要参数对靶板抗贯穿规律的影响.     

弹性圆板在一侧受均载而四周固定的条件下不用Kirchhoff-Love假设的一级近似理论(Ⅰ)

根据一般形状的三维弹性板不用Kirchhoff-Love假设的近似理论[1],[2],作者导出了三维弹性圆板的广义变分泛函,从而得到了圆板四周固定和一侧受均布载荷下的一级近似理论的微分方程和有关边界条件,其解析解答留待另文处理.     

双模量复合材料正交迭层矩形厚板的热弯曲问题

本文给出了双模量复合材料迭层板热弯曲的加权残数解。各层都假定为弹性和热弹性的双模量各向异性材料。该模型是建立在Whitney-Pagano迭层板理论和热弹性模型基础上,考虑了沿板厚的剪切应变。所得挠度和中性面位置的结果和精确解非常吻合。     

Poisson 方程的一个降维算法

Lions 建立在变分形式中的渐近展开方法,用于解决 Stiff 问题是很有力的工具.Ciarlet 利用[1]的方法,研究弹性薄板问题,对薄板不做任何假设,仅用严格的数学推理,证明了简化的二维模型是三维薄板模型的一阶近似.利用算子和边界条件,同时进行ε幂级数的渐近展开,研究在定义域 D={(x,y)|(x,y)∈R~2,x∈(0,1),y∈(0,ε)}(即细杆)上的抛物型问题.本文第一部分,利用[1,3]的方法,考虑定义在     

插值矩阵法分析正交各向异性板切口应力奇异性

基于切口尖端附近区域位移场渐近展开,提出了分析正交各向异性复合材料板切口奇异性的新方法.将位移场的渐近展开式的典型项代入弹性板的基本方程,得到关于正交各向异性板切口奇异性指数的一组非线性常微分方程的特征值问题;再采用变量代换法,将非线性特征问题转化为线性特征问题,用插值矩阵法求解获得的正交各向异性板切口若干阶应力奇异性指数和相应特征函数.该法可由相应的特征角函数对板切口的平面应力和反平面奇异特征值加以区分,并将计算结果与现有结果对照,表明了该文方法的有效性.     

Hamilton体系下层合板弱粘接模型的应用

层合板的层间粘接模型对整个层合板的结构有重要影响．运用Hamilton正则方程对层合板层间的不同类型的粘接模型进行了分析．结合弹性材料修正后的Hellinger Reissner变分原理和插值函数,构建了直角坐标系下8节点层合板的每一层的线性方程;考虑到脱层板的连接界面处应力和位移的关系,改进了现有的常用弱粘接模型,建立不同粘接模型的控制方程;最后通过求解整个板的控制方程,得到层合板的层间应力和位移．数值算例验证了该模型的正确性,并研究了层间界面为线性和非线性时的问题．结果表明:应用改进后的弱粘接模型,能够更好地模拟层合板的弱界面失效过程．     

复合材料层合板的三维非线性分析

本文提出了一种研究复合材料层合板壳三维问题的解析方法．该方法采用摄动方法和变分原理来满足三维弹性理论基本微分方程及限制条件，分析了受横向载荷作用的复合材料各向异性单层圆板及层合圆板的三维非线性问题．得到了高精确度的摄动级数解答．大量结果表明横向剪应力和横向正应力在层合板的三维非线性分析中是很重要的．     

具有边梁加固的板弯曲问题的变分-差分方法研究

具有边梁加固的板的弯曲问题,其平衡方程模型为四阶椭圆型偏微分方程的边值问题,其中的自然边界条件涉及到了沿板边的切线和法线方向的高阶导数,对于非均匀、变厚度的板,该问题还具有"变系数"的特点.由问题的变分模型入手,应用变分-差分方法构造了该边值问题的一个差分格式.由于该方法能够结合平衡方程模型中的边界条件以消除沿板边的高阶导数项,因而,所得差分算子仅仅依赖于板面网格结点,并且保持了差分算子的对称、正定性质.同时,将已得算法在计算机上进行了数值模拟,并与现有文献进行了对比计算.结果显示本文所给出的算法具有较高的精确度,该算法将可用于定量地揭示板与边梁之间相互作用的规律,为工程设计提供参考依据.     

复合材料层合板三维线性理论的完整性

本文针对文献[1]所述复合材料层合板三维模型,在三维线性弹性理论基本方程和经典变分原理的基础上,通过分块矩阵运算和线性Lagrange乘子法,推导出比文献[1]更全面更系统的基本方程和变分原理,使复合材料层合板三维线性理论臻于完整。     

杂交能变分原理及层合板三维理论的基础——分析复合材料层间应力的新方法

本文讨论了复合材料层合板层间界面处应力和应变的间断性问题,并提出了复合材料层合板的三维理论.本文还以在层合板中全局连续的变量为基础,提出了与传统的势能和余能不同的一种新的弹性能.并得到与复合材料三维理论相应的变分原理.本文得到的三维层合板理论和杂交能变分原理,可以作为校核层合板二维经典理论和确定自由边界附近层间应力的理论基础.     

功能梯度板中Griffith裂纹尖端应力场的三维解析研究

基于推广后的England-Spencer板理论,研究了横观各向同性功能梯度板中Griffith裂纹尖端的三维应力场.假定材料参数沿板厚方向可以任意连续变化,利用复变函数解法和保角变换技术分别给出了受无穷远处荷载作用和受均匀内压时裂纹尖端应力的三维解析解.当材料退化为各向同性均匀材料时,将该解答与经典二维解进行了比较,...     

Stress and fracture analysis in delaminated orthotropic composite plates using third-order shear deformation theory

The third-order shear deformable plate theory is applied in this work to calculate the stresses and energy release rates in delaminated orthotropic composite plates with straight crack front. The delaminated parts are modeled by the general third-order plate theory, while a double-plate model with interface constraint is developed for the uncracked portion of the plate. The governing equations of the uncracked part are formulated by considering the equilibrium and the displacement continuity along the interface. As an example, a simply-supported delaminated orthotropic plate subjected to a point force is solved adopting Lévy plate formulation and the state-space approach. The mode-II and mode-III energy release rate distributions along the crack front were calculated by the J-integral. To verify the analytical results the 3D finite element model of the plate was constructed and the energy release rates were calculated by the virtual crack-closure technique. A previous second-order plate theory solution was also utilized in the course of the comparison. The results indicate a good agreement between analysis and numerical computation and that third-order theory is better in some cases than the second-order approximation.     

弹性约束边界条件下矩形蜂窝夹芯板的自由振动分析

蜂窝夹芯板在飞行器、高速列车等领域有广泛的用途，对其开展振动分析具有明确的科学价值及工程意义.为区别于诸简支等传统约束边界，提出了弹性约束边界下蜂窝夹芯板结构的自由振动特性分析方法.具体来说，首先通过将蜂窝夹芯层等效为各向异性板，将夹芯板问题转变为三层板结构.进一步地，将板结构的位移场函数由改进的二维Fourier级数表示，并基于能量原理的Rayleigh Ritz法得到结构的固有频率和固有振型，理论预测结果与数值模拟分析吻合较好.提出的理论模型可用于系统讨论约束边界对蜂窝夹芯结构自由振动特性的影响，为此类结构的约束方案设计提供理论依据.     

C0 FE model based on HOZT for the analysis of laminated soft core skew sandwich plates: Bending and vibration

Bending and free vibration behaviour of laminated soft core skew sandwich plate with stiff laminate face sheets is investigated using a recently developed C₀ finite element (FE) model based on higher order zigzag theory (HOZT) in this paper. The in-plane displacement fields are assumed as a combination of a linear zigzag function with different slopes at each layer and a cubically varying function over the entire thickness. The out of plane displacement is considered to be quadratic within the core and constant in the face sheets. The plate theory ensures a shear stress-free condition at the top and bottom surfaces of the plate. Thus, the plate theory has all of the features required for accurate modelling of laminated skew sandwich plates. As very few element model based on this plate theory (HOZT) exist and they possess certain disadvantages, an attempt has been made to check the applicability of the refined element model. The nodal field variables are chosen in such a manner that there is no need to impose any penalty stiffness in the formulation. Refined C₀ finite element model has been utilized to study some interesting problems on static and free vibration analysis of laminated skew sandwich plates.     

Free vibration analysis of piezoelectric coupled annular plates with variable thickness

This paper presents the free vibration analysis of piezoelectric coupled annular plates with variable thickness on the basis of the Mindlin plate theory. No work has yet been done on piezoelectric laminated plates while the thickness is variable. Two piezoelectric layers are embedded on the upper and lower surfaces of the host plate. The host plate thickness is linearly increased in the radial direction while the piezoelectric layers thicknesses remain constant along the radial direction. Different combinations of three types of boundary conditions i.e. clamped, simply supported, and free end conditions are considered at the inner and outer edges of plate. The Maxwell static electricity equation in piezoelectric layers is satisfied using a quadratic distribution of electric potential along the thickness. The natural frequencies are obtained utilizing a Rayleigh–Ritz energy approach and are validated by comparing with those obtained by finite element analysis. A good compliance is observed between numerical solution and finite element analysis. Convergence study is performed in order to verify the numerical stability of the present method. The effects of different geometrical parameters such as the thickness of piezoelectric layers and the angle of host plate on the natural frequencies of the assembly are investigated.     

A homogeneous limit methodology and refinements of computationally efficient zigzag theory for homogeneous,laminated composite,and sandwich plates

The Refined Zigzag Theory (RZT) for homogeneous, laminated composite, and sandwich plates is revisited to offer a fresh insight into its fundamental assumptions and practical possibilities. The theory is introduced from a multiscale formalism starting with the inplane displacement field expressed as a superposition of coarse and fine contributions. The coarse displacement field is that of first‐order shear‐deformation theory, whereas the fine displacement field has a piecewise‐linear zigzag distribution through the thickness. The resulting kinematic field provides a more realistic representation of the deformation states of transverse‐shear‐flexible plates than other similar theories. The condition of limiting homogeneity of transverse‐shear properties is proposed and yields four distinct variants of zigzag functions. Analytic solutions for highly heterogeneous sandwich plates undergoing elastostatic deformations are used to identify the best‐performing zigzag functions. Unlike previously used methods, which often result in anomalous conditions and nonphysical solutions, the present theory does not rely on transverse‐shear‐stress equilibrium constraints. For all material systems, there are no requirements for use of transverse‐shear correction factors to yield accurate results. To model homogeneous plates with the full power of zigzag kinematics, infinitesimally small perturbations in the transverse shear properties are derived, thus enabling highly accurate predictions of homogeneous‐plate behavior without the use of shear correction factors. The RZT predictive capabilities to model highly heterogeneous sandwich plates are critically assessed, demonstrating its superior efficiency, accuracy, and a wide range of applicability. This theory, which is derived from the virtual work principle, is well‐suited for developing computationally efficient, C⁰ a continuous function of (x₁,x₂) coordinates whose first‐order derivatives are discontinuous along finite element interfaces and is thus appropriate for the analysis and design of high‐performance load‐bearing aerospace structures. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Assessment of an edge type settlement of above ground liquid storage tanks using a simple beam model

Analysis of deformation and bending moment distributions along sections of the bottom plate of a large unanchored cylindrical liquid storage tank with appreciable out-of-plane localized differential edge settlement is considered. The analysis uses approximate simple slender beam bending theory to model localized edge settlements of the plate and takes into account the effects of foundation compliance, initial settlement shape, shell and hydrostatic loadings and the shell-bottom plate junction stiffness. The obtained model is solved, in the elastic range, using a combined analytical–numerical procedure for the deflection and bending moment distributions along the beam. The obtained approximate solutions were displayed graphically for selected values of system parameters: edge settlement amplitude, plate thickness, foundation stiffness, and hydrostatic load. The maximum allowable edge displacement amplitudes based on the plate yielding stress predicted by the present study are compared for the selected values of system parameters with those recommended in the API standard 653.     

Multi-displacement continuum modelling of the metamaterial plate with periodical arranged resonators

Multi-displacement continuum modelling of a two-dimensional (2D) elastic metamaterials plate with periodically arranged local resonator over the surface of the plate is studied in this paper. The additional displacement fields are introduced to model the response of the local resonators. The continuous conditions between the adjacent unit-cells are used to reflect the periodicity of the microstructured continuum and resultantly turned into the constraint conditions between the additional displacement field and the other continuous field. The dispersion features of the multiple-displacement coupled wave propagating along the high symmetrical direction and any oblique direction are both studied numerically. It is found that the multi-displacement coupled waves can be divided into the coupled longitudinal wave and the coupled transversal wave when propagating along the highly symmetric direction but cannot be divided into the coupled longitudinal wave and the coupled transversal wave when propagating along any oblique direction. The effects of boundary conditions on the dispersion of acoustic and optical branches of coupled waves are discussed in detail. At last, the influences of the parameters of resonator on the dispersion feature of the multi-displacement coupled waves are investigated numerically.     

面内功能梯度三角形板等几何面内振动分析

基于平面应变理论,利用等几何有限元方法分析了弹性边界条件下面内功能梯度三角形板的面内振动特性.板的材料属性沿厚度方向呈均匀分布,而在面内方向呈任意指数梯度变化.采用非均匀有理B样条(NURBS)基函数对三角形结构进行等几何建模和位移描述,实现了三角形板几何设计和振动分析的无缝衔接.在三角形板边界上引入虚拟弹簧约束并通过调节虚拟弹簧刚度,实现任意边界条件的施加.通过不同的单元细化方案和对比算例,验证了等几何方法的灵活性、准确性和快速收敛性.系统研究了边界条件、材料属性和几何参数对三角形板振动特性的影响.同时给出了弹性边界条件下面内功能梯度三角形板的振动特性解,具有重要参考价值.     

Thermal Buckling Analysis of FGM Sandwich Circular Plates Under Transverse Nonuniform Temperature Field Actions北大核心CSCD

Based on the von Kármán geometric nonlinear plate theory, the displacement⁃type geometric nonlinear governing equations for FGM sandwich circular plates under transverse nonlinear temperature field actions were derived. With the immovable clamped boundary condition, the analytical formula for dimensional critical buckling temperature differences of the system was obtained from the solution of the linear eigenvalue problem. Moreover, the 2⁃point boundary value problem of ordinary differential equations was solved with the shooting method. The effects of geometric parameters, constituent material properties, gradient indexes, temperature field parameters and layer⁃thickness ratios on the critical buckling temperature differences, the thermal postbuckling equilibrium paths, and the buckling equilibrium configurations of FGM sandwich circular plates, were investigated. The results show that, with the increases of the thickness⁃radius ratio, the relative thickness of the FGM layer and the gradient index, the FGM sandwich circular plate's critical buckling temperature difference will increase monotonically. Given a fixed radius and a fixed total thickness, the postbuckling deformation of the FGM sandwich circular plate will decrease significantly with the relative thickness of the FGM layer. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.