参数拟二次规划法及其在复合材料失效过程分析中的应用

本文介绍关于不连续线弹性静力学问题的多变量变分原理与相应的参数拟二次规划算法在复合材料层压板强度分析及纤维增强脆性基体材料单元细观失效过程分析中的应用。     

理想粘塑性流体润滑问题的参变量变分原理

本文给出了理想粘塑性流体润滑问题的参变量变分原理.在膜厚方向压力为常数的假设下,塑性剪切滑移面将发生在固液交界面上,因而可以选择边界速度滑移量为参变量(控制变量).文中讨论了采用有限元求解时的实施过程,原问题最后可化为求解带约束条件的参数二次规划问题.该方法简单可靠,具有良好的工程应用前景.     

复合材料厚板双轴非线性渐进失效分析

为计算复合材料厚板在三维应力状态下的极限承载,综合考虑复合材料厚板的三维应力特性和厚板的本构理论,基于非线性本构关系与增量步迭代法,以Hashin 3D失效准则为单层板失效判据;当层压板中有一层或多层被检测到失效时,对失效层进行刚度折减,并在增量过程中不断更新刚度矩阵。同时,对航空结构件中使用的复合材料厚层压板进行了双轴载荷下的渐进失效过程模拟,分别计算了两种碳纤维环氧复合材料单向带在两种铺层形式以及三种载荷工况下的初始失效和极限承载包线;并给出了不同的铺层和材料组合下层压板的初始失效与最终失效强度包线及每一段所代表的失效模式,展示了层压板的渐进失效过程。本文研究方法解决了对复合材料厚层压板失效过程状态的跟踪与判定问题,同时又不必去建立复杂的三维有限元模型,减小了计算量。     

一类铁电模型的参变量变分原理及其应用

将参变量变分原理引入铁电问题。对一类借用了经典弹塑性理论中的概念和方法的多轴铁电模型建立基于Helmholtz自由能的参变量变分原理,可以有效处理传统变分原理中由非关联流动法则或屈服面不考虑材料系数变化所引起的切线模量非对称困难。相应于参变量变分原理,引入参数二次规划算法,可获得具有可靠数值稳定性的一套铁电算法。将该算法应用于一个具体的铁电模型,数值计算结果表明本文方法的有效性。     

含缺口复合材料层合板的三维有限元失效分析

本文研究了复合材料层合板最终强度计算的有限元理论,讨论了修正的Newton-Raphson迭代方法在层合板失效过程中应力场计算的迭代过程.同时本文建立了带缺口的复合材料层合板三维有限元模型,充分考虑层合板的纤维断裂、基体开裂和分层三种失效模式,采用修正的三维Hashin准则作为失效判断的依据,计算了三种不同铺层的层合板最终失效载荷值,与试验值吻合得很好.鉴于层压板材料常数ν23的数值难于测定的特点,讨论其对最终失效载荷的影响.在三维有限元模型的基础上,实现了失效扩展仿真分析.     

参变量变分原理的提出、发展与应用

参变量变分原理及其参数二次规划算法是由钟万勰院士1985年针对弹性接触边界非线性问题首次提出来的,经过将近40年的不断发展,目前参变量变分原理已经成功应用于各个领域,其中包括弹塑性分析、接触问题、润滑力学、岩土力学、变刚度杆系结构、先进材料性能分析、材料的蠕变与损伤、柔性结构力学和LQ最优控制等各个工程领域。本文首先回顾了参变量变分原理的起源,介绍了参变量变分原理的基本概念,然后以弹塑性分析问题为例,阐明建立参变量变分原理的理论模型以及实现数值参数二次规划求解原理,最后详细回顾了参变量变分原理的基本理论与相应数值算法在各个领域的发展及其工程应用,展示了参变量变分原理在求解各类非线性问题的特色与优势。     

飞机复合材料层压板结构中的广义强度准则

通过对经典复合材料结构强度理论和准则在层压板上的适用性计算和试验对比研究，指出了在层压板上采用经典强度理论所得计算结果与试验结果的差异。并分析了产生这种差异的原因，主要是经典强度准则表达武中采用的无拉剪耦合假设和层与层之间理想粘接假设，只适用于单层板或正交各向异性板。本文提出了一种广义强度准则的思想，其核心是放松正交各向异性约束条件和通过试验测定强度参数，而在实际飞机结构中的准正交各向异性层压板结构设计上仍可使用经典层压板强度准则。     

索网天线的参变量变分及非线性有限元方法

针对大型周边桁架式索网天线由拉索拉压模量不同引起的本构非线性和结构大变形引起的几何非线性问题,给出了基于参变量变分原理的几何非线性有限元方法. 首先针对含预应力索单元拉压模量不同分段描述的本构关系,通过引入参变量,导出了基于参变量及其互补方程的统一描述形式,避免了传统算法需要根据当前变形对索单元张紧/松弛状态的预测,提高了算法收敛性. 然后利用拉格朗日应变描述索网天线结构大变形问题,结合几何非线性有限元法,建立了基于参变量的非线性平衡方程和线性互补方程;并给出了牛顿-拉斐逊迭代法与莱姆算法相结合的求解算法. 数值算例验证了本文提出的算法比传统算法具有更稳定的收敛性和更高的求解精度,特别适合于大型索网天线结构的高精度变形分析和预测.      

弹性接触问题的变分原理及参数二次规划求解

本文给出了平面与空间接触问题的带参变量的变分极值原理。接触是考虑库伦摩擦的。参变量二次规划可以用于精确求解,并且通过数例说明了计算方法。     

岩土中弹塑性渗透固结问题的参变量变分原理

本文给出渗透固结过程的参变量变分原理,可以用来处理岩土弹塑性渗透固结问题,并不受 Drucker 假设的限制,对于关连或非关连塑性流动情形皆可。     

High-rank nonlinear sequentially laminated composites and their possible tendency towards isotropic behavior

This work is concerned with the determination of the effective behavior of sequentially laminated composites with nonlinear behavior of the constituting phases. An exact expression for the effective stress energy potential of two-dimensional and incompressible composites is introduced. This allows to determine the stress energy potential of a rank-N sequentially laminated composite with arbitrary volume fractions and lamination directions of the core laminates in terms of an N-dimensional optimization problem.

Stress energy potentials for sequentially laminated composites with pure power-law behavior of the phases are determined. It is demonstrated that as the rank of the lamination becomes large the behaviors of certain families of sequentially laminated composite tend to be isotropic. Particulate composites with both, stiffer and softer inclusions are considered. The behaviors of these almost isotropic composites are, respectively, softer and stiffer than the corresponding second-order estimates recently introduced by Ponte Castañeda (1996).     

A continuum damage model for delaminations in laminated composites

Delamination, a typical mode of interfacial damage in laminated composites, has been considered in the context of continuum damage mechanics in this paper. Interfaces where delaminations could occur are introduced between the constituent layers. A simple but appropriate continuum damage representation is proposed. A single scalar damage parameter is employed and the degradation of the interface stiffness is established. Use has been made of the concept of a damage surface to derive the damage evolution law. The damage surface is constructed so that it combines the conventional stress-based and fracture-mechanics-based failure criteria which take account of mode interaction in mixed-mode delamination problems. The damage surface shrinks as damage develops and leads to a softening interfacial constitutive law. By adjusting the shrinkage rate of the damage surface, various interfacial constitutive laws found in the literature can be reproduced. An incremental interfacial constitutive law is also derived for use in damage analysis of laminated composites, which is a non-linear problem in nature. Numerical predictions for problems involving a DCB specimen under pure mode I delamination and mixed-mode delamination in a split beam are in good agreement with available experimental data or analytical solutions. The model has also been applied to the prediction of the failure strength of overlap ply-blocking specimens. The results have been compared with available experimental and alternative theoretical ones and discussed fully.     

A LOWER BOUND LIMIT ANALYSIS OF DUCTILE COMPOSITE MATERIALS

The plastic load-bearing capacity of ductile composites such as metal matrix composites is studied with an insight into the microstructures. The macroscopic strength of a composite is obtained by combining the homogenization theory with static limit analysis, where the temperature parameter method is used to construct the self-equilibrium stress field. An interface failure model is proposed to account for the effects of the interface on the failure of composites. The static limit analysis with the finite-element method is then formulated as a constrained nonlinear programming problem, which is solved by the Sequential Quadratic Programming （SQP） method. Finally, the macroscopic transverse strength of perforated materials, the macroscopic transverse and off-axis strength of fiber-reinforced composites are obtained through numerical calculation. The computational results are in good agreement with the experimental data.     

Limit analysis of composite materials based on an ellipsoid yield criterion

Employing repeating unit cell (RUC) to represent the microstructure of periodic composite materials, this paper develops a numerical technique to calculate the plastic limit loads and failure modes of composites by means of homogenization technique and limit analysis in conjunction with the displacement-based finite element method. With the aid of homogenization theory, the classical kinematic limit theorem is generalized to incorporate the microstructure of composites. Using an associated flow rule, the plastic dissipation power for an ellipsoid yield criterion is expressed in terms of the kinematically admissible velocity. Based on nonlinear mathematical programming techniques, the finite element modelling of kinematic limit analysis is then developed as a nonlinear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the limit load of a composite is then obtained. The nonlinear formulation has a very small number of constraints and requires much less computational effort than a linear formulation. An effective, direct iterative algorithm is proposed to solve the resulting nonlinear programming problem. The effectiveness and efficiency of the proposed method have been validated by several numerical examples. The proposed method can provide theoretical foundation and serve as a powerful numerical tool for the engineering design of composite materials.     

Stability of rectangular plates made of a laminated composite with components subject to long-term damage

The problem of bifurcational instability of rectangular plates made of laminated composites with components subject to long-term damage is formulated and solved by the proposed method. Numerical results are presented     

Behavior of Pin-loaded Laminated Composites

In this study, an investigation was carried out to determine the effects of joint geometry and fiber orientation on the failure strength and failure mode in a pinned joint laminated composite plate. Behavior of pin-loaded laminated composites with different stacking sequence and different dimensions has been observed experimentally. E/glass–epoxy composites were manufactured to fabricate the specimens. Mechanical properties of the composites were characterized under tension, compression and in-plane shear in static loading conditions. Laminated composites were loaded through pins. Single-hole pin-loaded specimens were tested for their tensile response and width-to-hole diameter (W/D) and edge distance-to-hole diameter (E/D) ratios evaluated. A series of experiments was performed with six different material configurations ([0/±45]_s–[90/±45]_s, [0/90/0]_s–[90/0/90]_s and [90/0]_2s–[±45]_2s), in all, over 120 specimens. E/D ratios and W/D ratios of plates were changed from 1 to 5 and 2 to 5, respectively. Failure propagation and failure type were observed on the specimens. The influence of the joint geometry on the strength of the pin-loaded composites was assessed. When laminated composite plates were loaded to final failure, three basic failure modes consisting of net-tension, shear out and bearing failure were observed for the different geometric dimensions. All the connections tested showed that the fiber orientations have a definite influence on the position around hole circumference at which failure initiated. Net-tension failure occurred for specimens that had small width and large end distance. When the width was increased, the specimens which had small end distances failed in the shear-out modes. When the end distance was increased, bearing failure developed in addition to shear-out failure. The experimental results showed that the ultimate load capacities of E/glass–epoxy laminate plates with pin connection were increased by increasing W and E. However, increasing the E/D and W/D ratios beyond a critical value has an insignificant effect on the ultimate load capacity of the connection.     

Reliability analysis of FRP laminated plates with consideration of both initial imperfection and failure sequence

A probabilistic progressive failure analyzing method is applied to estimating the reliability of a simply supported laminated composite plate with an initial imperfection under bi-axial compression load. The initial imperfection and the strength parameters are considered as random variables. Ply-level failure probability is evaluated by the first order reliability method (FORM) together with the Tsai-Wu strength criterion and Tan criterion. Current stresses in the laminated structure are calculated by the classical lamination theory with the stiffness modified based on the last step ply failure. Probabilistically dominant ply-level failure sequences leading to overall system failure are identified, based on which the system failure probability is estimated. A numerical example is presented to demonstrate the methodology proposed. Through parameter studies it is shown that the deviation of the initial imperfection and some of the strength parameters largely influence the system reliability. Project supported by the Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry, and the Research Foundation of Huazhong University of Science and Technology.     

Surface Instability of Laminated Materials of Regular Structure Under Triaxial Compression

The surface instability of laminated composites of regular structure is analyzed in a three-dimensional linearized formulation. A case is considered where the material is compressed by a surface distributed dead or follower load. Numerical results are presented for a specific problem.     

复合材料层合板的可靠性和优化问题的研究进展

纤维增强复合材料是由高强度、低密度的纤维材料与基体组成, 具有很多其它材料所不具有的特性, 其应用范围越来越大. 复合材料的机械性能与加工制造等过程密切相关, 其材料性能的离散度较大, 因此考虑不确定性因素的结构可靠性分析非常必要. 可设计性是复合材料的另一个特点, 因此复合材料结构的优化设计也是研究的热点之一. 本文讨论了复合材料层合板结构的可靠性分析方法, 优化设计, 可靠性优化设计以及鲁棒优化等, 并对其发展趋势作出展望.