节理岩体脆弹性断裂损伤模型及其工程应用

根据Ｂｅｔｔｉ能量互易定理并考虑节理裂纹扩展过程中的能量转换和节理裂纹扩展过程中的相互作用建立了裂隙岩体的损伤演化方程和三维脆弹性断裂损伤本构模型,并将该本构模型应用于三峡船闸高边坡,进行了边坡裂隙岩体开挖卸荷稳定三维非线性有限元计算,获得了比较理想的结果。     

弹性地基上自由层合圆板弯曲问题的解析解

从三维弹性力学基本方程出发 ,建立了弹性地基上周边自由的横观各向同性层合圆板轴对称弯曲问题的状态方程 ,并将板面的法向载荷展成傅里叶 -贝塞尔级数 ,从而给出问题的解析解。此解满足弹性力学全部方程 ,计及了所有独立的弹性常数 ,并满足层间连续性条件。     

层理页岩水力裂缝扩展规律的相场法研究

准确预测层理页岩水力裂缝扩展路径对于页岩压裂方案优化与压裂效果评价至关重要.基于多孔弹性理论和能量最小化原理建立水力耦合的相场模型,采用交错策略的分离式耦合方法进行求解.通过压裂试验数据对比验证模型的可靠性,同时基于页岩三维水力压裂模拟分析,验证该方法对于模拟不同地应力条件下的水力裂纹扩展问题的适用性.基于该模型,利用...     

一种改进的Pasternak地基模型及层合地基板的解析解

从三维弹性力学基本方程出发,建立了正交异性材料层合板的状态方程,并提出一种改进的Pasternak弹性地基模型,给出了四边简支层合地基板的解析解。此解满足层合板的基本方程和层间连续条件,适合任意厚跨比,计及了所有材料常数,考虑了基底切向接触应力的影响。算例讨论了地基参数对几种地基模型的影响。计算结果表明,随着地基刚度的增大,剪应力的影响是不可忽略的。     

多裂隙岩体三维加锚损伤断裂模型及其数值模拟与工程应用研究

 博士学位论文摘要　利用断裂力学理论、损伤力学理论和三维非线性有限元数值分析方法系统研究了断续多裂隙岩体的力学变形特性、强度特性和空间损伤岩锚支护效应。(1) 根据断续节理面几何特征的概率统计模型, 推导出了节理面主要几何特征参数的数学计算表达式, 为正确分析裂隙岩体的力学变形特性提供了重要的节理面几何特征参数保证。(2) 根据节理裂纹压剪应力场中的扩展变化过程和扩展过程中的能量转换与能量变化, 建立了多裂隙岩体的能量损伤演化方程。(3) 根据脆性岩体的损伤变形机制, 建立了脆性岩体在初始损伤和损伤演化状态下的三维脆弹性损伤断裂本构关系。(4) 考虑多裂隙岩体的损伤变形机制, 通过引入有效应力反映损伤与塑性变形的耦合效应, 并根据能量损伤演化方程、不可逆热力学定律、广义正交法则和塑性损伤一致性条件建立了多裂隙岩体在初始损伤、损伤演化和塑性损伤变形状态下的三维弹塑性损伤本构关系。(5) 根据锚杆、锚索对裂隙岩体的支护、加固作用机理, 建立了多裂隙岩体锚杆支护的空间损伤岩锚单元支护模型和锚索加固的空间加索损伤岩体联合作用模型。(6) 根据脆性岩体的断裂破坏机制, 建立了脆性裂隙岩体的起裂准则和初裂强度计算公式, 并推导出了成组有序分布的平面裂隙岩体和三维币状裂隙岩体的脆性断裂破坏强度计算公式。(7) 将上述损伤断裂本构模型和岩锚支护、加固作用模型编制成三维非线性有限元计算程序, 应用于三峡船闸高边坡开挖卸荷稳定分析, 获得了较为满意的计算结果, 验证了模型的有效性和正确性。     

多源输入条件下的黏弹性人工边界研究

应用弹性波动理论,推导多源输入条件下的二维时域人工边界条件。首先基于二维波动方程建立两个波源时二维黏弹性人工边界的法向和切向方程,提出相应的数值模拟方法,并通过简单模型的波动问题进行验证。最后将多源输入条件下的二维黏弹性边界扩展至三维条件,模型验算结果表明多源输入条件下的黏弹性边界亦适用于三维模型。     

复合材料本构模拟的三维均匀化方法

将小参数渐近展开和摄动方法的均匀化理论与三维有限元方法结合起来应用于复合材料的弹性本构数值模拟.通过对二维和三维结构有效模量数值计算,结果表明,该方法可得到较为准确的复合材料有效模量,并较其他解法大大降低了计算量,因而是一种可靠、高效的方法.     

FRP拉挤复合材料本构关系模型研究

为了更加精确的描述厚型拉挤复合材料的力学性能和力学响应特征,文中以厚型E玻璃纤维/环氧树脂拉挤型复合材料系统为例,运用三维细观力学模型描述材料的非线性本构关系。模型从纤维和基质成分的角度对由粗纱层和玻纤双轴布构成的层合材料进行材料响应描述,最终建立了相应的有限元模型并通过试验进行校准。试验和数值分析结果表明:三维细观力学模型能够准确的描述E玻璃纤维/环氧拉挤型复合材料的力学响应,其精确度可以通过横向试样拉伸试验结果进行校准提高。     

三维离散元模型的滑坡能量守恒模拟研究

岩土体的破坏涉及复杂的断裂、摩擦作用、弹性波和能量转换过程。本文给出了离散元模型中各类机械能,以及断裂热、阻尼热和摩擦热的计算理论。同时,考虑外力做功,建立了离散元能量转化和能量守恒计算法则。基于此理论改进Mat DEM软件,实现了31.2万单元三维滑坡的滑动过程和能量转化模拟。模拟中,各类机械能相互转化,并在阻尼、断裂和摩擦作用下转化为热量,但是总能量始终保持不变,有效地实现了离散元能量守恒模拟。模拟中发现滑坡滑带产生大量摩擦热,并提高滑带的温度。能量转化和热量生成曲线反映了滑坡在滑动各阶段的运动特征。此模型可广泛应用于岩土体破坏和多场耦合数值模拟研究。     

能量法求解有侧移框架的弹性屈曲荷载

运用层模型能量法研究了有侧移框架弹性屈曲,根据框架失稳模式和边界条件,选择合适的位移函数,采用Timoshenko梁理论,建立结构总势能方程,利用势能驻值条件求解结构弹性失稳临界荷载,能量法简单实用,精度很高。     

Accurate dynamic response of laminated composites and sandwich shells using higher order zigzag theory

Forced vibration response of laminated composite and sandwich shell is studied by using a 2D FE (finite element) model based on higher order zigzag theory (HOZT). This is the first finite element implementation of the HOZT to solve the forced vibration problem of shells incorporating all three radii of curvatures including the effect of cross curvature in the formulation using Sanders' approximations. The proposed finite element model satisfies the inter-laminar shear stress continuity at each layer interface in addition to higher order theory features, hence most suitable to model sandwich shells along with composite shells. The C₀ finite element formulation has been done to overcome the problem of C₁ continuity associated with the HOZT. The present model can also analyze shells with cross curvature like hypar shells besides normal curvature shells like cylindrical, spherical shells etc. The numerical studies show that the present 2D FE model is more accurate than existing FE models based on first and higher order theories for predicting results close to those obtained by 3D elasticity solutions for laminated composite and sandwich shallow shells. Many new results are presented by varying different parameters which should be useful for future research.     

Asymptotic solutions of axisymmetric laminated conical shells

The three-dimensional (3D) solution of laminated conical shells subjected to axisymmetric loads is presented using the method of perturbation. The formulation begins with the basic 3D elasticity equations without making any static or kinematic assumptions in advance. After introducing a set of proper dimensionless variables, asymptotically expanding the field variables and then successively integrating the resulting equations through the thickness direction, we obtain the recursive sets of governing equations for various orders. The edge boundary conditions at each order level are derived as the resultant forms by following the variational approach. The method of differential quadrature (DQ) is used to determine the present asymptotic solution for various orders. For illustration purposes, the simply supported laminated conical shells under uniformly and sinusoidally distributed lateral pressure and the clamped laminated conical shells under edge torsion, are studied. It is shown that the present asymptotic DQ solution can be obtained order-by-order in a hierarchic and consistent manner and asymptotically approaches to the 3D elasticity solution.     

Stability analysis of cross-ply laminated shells of revolution using a curved axisymmetric shell finite element

A curved axisymmetric shell finite element based on a consistent first-order shear deformable shell theory is developed for the linear stability analysis of cross-ply laminated shells of revolution under compressive loads. Finite element analysis results are presented for isotropic, orthotropic and cross-ply laminated shells of revolution in comparison with the analytical and numerical results found in the literature. These comparisons demonstrate the applicability and the high performance of the element in stability analysis of thin and moderately thick cross-ply laminated composite shells of revolution under compressive loads.     

Instability of cracked CFRP composite cylindrical shells under combined loading

Numerical analysis of cracked composite cylindrical shells under combined loading is carried out to study the effect of crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, torsion, internal pressure and external pressure are obtained, using the finite element method. In general, the internal pressure increases the critical buckling load of the CFRP cylindrical shells while torsion and external pressure decrease it. Numerical analyses show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell while for cylindrical shells under combined external pressure and axial load, the global buckling shape is insensitive to the crack length and crack orientation.     

Analysis and optimization of laminated composite circular cylindrical shell subjected to compressive axial and transverse transient dynamic loads

Optimization is one of the important stages in the design process. In this paper the genetic algorithms method is applied for weight and transient dynamic response and two constraints including critical buckling loads and principle strains optimization of laminated composite cylindrical shells. The multi-objective function seeks the minimum structural weight and transient dynamic response. Nine design variables including material properties (fibre and matrix), volume fraction of fibre, fibre orientation and thickness of each layer are considered. In analytical solution, vibration of composite circular cylindrical shells are investigated based on the first-order shear deformation shell theory. The boundary conditions are assumed to be fully simply support. The dynamic response of the composite shells is studied under transverse impulse and axial compressive loads. The modal technique is used to develop the analytical solution of the composite cylindrical shell. The solution for the shell under the given loading conditions can be found using the convolution integrals. An example of simply supported laminated composite cylindrical shells is given to demonstrate the optimality of the solution obtained by the genetic algorithms technique. Results are shown that the weight coefficient of multi-objective function and the type of the constraints have considerable effect on the optimum weight and dynamic response.     

Delamination buckling for composite laminated cylindrical shells in Hamilton system

In this article, a semi-analytical three-dimensional model based on the modified Hellinger–Reissner (H–R) variational principle and a nonlinear spring-layer model are presented for the buckling analysis of composite laminated cylindrical shells with a delamination. The method allows the effect of transverse shear deformation in the control equations of the composite laminated structures. In addition, it uses a two-dimensional mesh and can ensure that the number of variables is independent of the layer number. The nonlinear spring-layer model between the exterior and interior sub-laminates ensures the continuity of transverse stresses and displacements in the undelaminated region by specifying infinite values of springs and therefore avoids the possibility of material penetration phenomenon in the delaminated region. As an application of the present method, the influence of the delamination length on the critical buckling loads of delaminated composite laminated stiffened cylindrical shells is investigated.     

某单层柱面网壳的制作与安装

华能大厦的中庭屋盖为单层柱面网壳结构体系,屋面采用双层夹胶玻璃。该网壳的杆件为焊接箱形截面,截面尺寸小、板材厚,杆件相交节点多且角度小,制作难度大;因场地条件限制,在高空拼装,采用累积滑移进行安装,安装要求高。通过对该网壳进行深化设计,并对制作、拼装、滑移和安装等施工工艺进行分析和优化以及对支座等关键节点进行处理,使得该网壳顺利安装就位,并满足设计要求。     

Transient vibrations of laminated composite cylindrical shells exposed to underwater shock waves

The problem of the transient vibration of an elastic laminated composite cylindrical shell with infinite length exposed to an underwater shock wave is solved approximately. The linear acoustic plane wave assumption and Sanders thin shell theory are adopted. The reflected-afterflow virtual-source (RAVS) procedure is used to model the fluid–structure interaction involved during the underwater shock event. For the validity of the present analysis, the response of a laminated cylindrical shell under step plane wave is first analyzed and compared with the numerical solution available in the literature. Detailed numerical results for the transient responses of the shells under an exponentially decaying underwater shock wave are presented, and the influences of fiber angle, shell radius and thickness upon the dimensionless radial velocity, mid-surface strain, 0th mode radial displacement and 1st mode radial velocity of the shells, are investigated.     

网状扁壳与带肋扁壳组合结构的拟三层壳分析法

本文对网状扁壳与带肋扁壳共同工作的组合结构(可简称组合网状扁壳),采用连续化的拟三层壳的计算模型,按弹性小挠度薄壳理论进行分析计算,推导建立了混合法的基本方程式。由于这种构造上的拟三层壳在一般情况下不存在中面,因而壳体的薄膜内力、弯矩与薄膜应变,弯曲应变是耦合的,存在一个耦合矩阵,使得基本方程式比单层光面的符氏扁壳方程要复杂得多。对于周边简支的组合网状扁壳可求得基本方程式的解析解。文中对三向、四向组合网状扁壳进行了详细讨论,并指出了在特定条件下,可退化为一个当量的各向同性单层扁壳。对于一般网状扁壳的拟壳分析法及带肋扁壳的拟壳分析法分别属于本文的两种特殊情况。文中附有计算例题。     

Design and optimization of laminated conical shells for buckling

Optimum laminate configuration for the maximum buckling load of filament-wound laminated conical shells is investigated. In the case of a laminated conical shell, the thickness and the ply orientation (the design variables) are functions of the shell coordinates, influencing both the buckling load and the weight of the structure. Thus, optimization can be performed by maximization of the buckling load for a specific weight, or by minimization of the weight of the structure under the constraint of applied buckling load. Due to the complex nature of the problem a preliminary investigation is made into the characteristic behavior of the buckling load with respect to the volume as a function of the ply orientation.The exact buckling load is calculated by means of the computer code STAGS-A (Structural Analysis of General Shells [Almroth BO, Brogan FA, Meller E, Zele F, Petersen HT. Collapse analysis for shells of general shape, user's manual for STAGS-A computer code. Technical report AFFDL TR-71-8; 1973]) by adding a user written subroutine WALL, see Ref. [Goldfeld Y, Arbocz J. Buckling of laminated conical shells taking into account the variations of the stiffness coefficients. AIAA J 2004; 42(3):642–649]. The optimization problem is solved using response surface methodology.