弹塑性位移反分析的遗传算法研究

弹塑性位移反分析问题的目标函数具有多个极小值, 用常规的数学优化方法求解该优化问题时,时常出现陷入局部极小而无法继续寻优的状态。为了克服这一缺陷,应用遗传算法原理建立了弹塑性位移反分析的遗传算法,并应用其对所设定的弹塑性问题进行了反演,反演结果的精度达90%以上。     

基于多变量小波有限元的一维结构分析

基于区间B样条小波(B-Spline Wavelet on the Interval, BSWI)和多变量广义势能函数,该文构造了二类变量小波有限单元,并用于一维结构的弯曲与振动分析。基于广义变分原理,从多变量广义势能函数出发,推导得到多变量有限元列式,并以区间B样条小波尺度函数作为插值函数对两类广义场变量进行离散。此单元的优势在于可以提高广义力的求解精度,因为在传统有限元中,只有一类广义位移场函数,所以广义力通常是通过对位移的求导得到,而多变量单元中,广义位移和广义力都是作为独立变量处理的,避免了求导运算。此外,区间B样条小波是现有小波中数值逼近性能非常好的小波函数,以它作为插值函数可进一步保证求解精度。转换矩阵的应用,可以将无任何明确物理意义的小波系数转换到相应的物理空间,方便了问题的处理。最后,通过数值算例对Euler梁和平面刚架的分析,验证了此单元的正确性和有效性。     

基于遗传算法的混凝土一维瞬态导热反问题

基于Laplace积分变换法和遗传算法,提出了一种混凝土一维瞬态导热反问题求解的新方法。运用Laplace变换将温度的求解表示为只与空间坐标及浇筑时间有关的函数,使得反问题的求解具有测点布置灵活的特点。运用遗传算法寻求非线性反演问题全局最优解,只需要若干点温度实测值便可实现多个热学参数的同时反演,算例对反演方法的反演精度及数值稳定性给出了满意的证明。     

位移测量反演分析的正、逆定式化方法及其算法程序实现

位移测量反演分析已应用于岩石工程、结构检测、生物力学诊断等领域。介绍了位移反演分析的逆定式化方法与正定式化方法,以及基于这两种方法的初始地应力与岩层介质模量识别的两个算法程序,对比分析了两者在地应力模型、目标参数、反演算法等几个方面区别,重点说明了约束变尺度法优化算法能较好地解决非线性规划问题。并应用于岩石力学施工预报,获得了不同合理性和精度的反分析结果,以及区间最优的反演参数。     

基于遗传算法的混凝土-维瞬态导热反问题

基于Laplace积分变换法和遗传算法，提出了一种混凝土-维瞬态导热反问题求解的新方法。运用Laplace变换将温度的求解表示为只与空间坐标及浇筑时间有关的函数，使得反问题的求解具有测点布置灵活的特点。运用遗传算法寻求非线性反演问题全局最优解，只需要若干点温度实测值便可实现多个热学参数的同时反演，算例对反演方法的反演精度及数值稳定性给出了满意的证明。     

基于实验的钛合金优化动态本构模型与有限元模拟

为确定钛合金材料的Johnson-Cook模型中5个待定本构参数,克服传统单因素分析法的弊端并提高参数识别效率和精度,采用拉丁超立方抽样、Spearman秩相关分析的参数敏感度整体分析方法,并在参数敏感度分析结果和基本遗传算法的基础上,建立了一种基于改进小生境算法、可疑峰值点判断策略和局域精确搜索技术的改进遗传算法,基于实验数据建立了精细的钛合金Johnson-Cook本构模型。采用隐式应力积分法将该模型嵌入到ABAQUS用户材料子程序UMAT中,并通过隐函数求导方法推导出一致切线刚度矩阵。通过ABAQUS有限元软件对钛合金材料的动态响应进行数值模拟分析,计算结果与已有的实验数据吻合良好,UMAT子程序的准确性得到验证,可用于钛合金材料的动态响应预测分析中。     

建筑围护材料热导率反演模拟研究

本文建立了建筑围护墙体导热反问题求解模型.采用控制容积法求解一维非稳态导热方程,得到墙体各节点的温度值;应用遗传算法编制建筑围护材料热导率的反演程序.确定了墙体的热导率,结果具有较高的计算精度,该方法可为确定广阔地理位置所对应气候条件下的建筑维护墙体热导率提供准确参照.     

基于多分辨率-多边形单元建模策略的多材料结构动刚度拓扑优化方法

利用多边形有限单元的高精度求解优势,融合多分辨率拓扑优化方法,实现粗糙位移网格条件下的高分辨率构型设计,由此提出多材料结构动刚度问题的拓扑优化方法。将多边形单元(位移场求解单元)劈分为精细的小单元,构造设计变量与密度变量的重叠网格,形成多分辨率-多边形单元的优化建模策略;以平均动柔度最小化为目标和多材料的体积占比为约束,建立多材料结构的动力学拓扑优化模型,通过HHT-α方法求解结构动响应,采用伴随变量法推导目标函数和约束的灵敏度表达式,利用基于敏度分离技术的ZPR设计变量更新方案构建多区域体积约束问题的优化迭代格式;通过典型数值算例分析优化方法的可行性和动态载荷作用时间对优化结果的影响机制。     

基于Hoek-Brown准则的岩体弹塑性损伤模型及其应力回映算法研究

为了克服一般弹塑性损伤模型不能反映岩体结构、岩块强度、应力状态的影响以及非线性破坏特征等问题,该文基于广义的Hoek-Brown（HB）屈服准则,考虑损伤引起的刚度退化和塑性导致的流动两种破坏机制的耦合作用,同时引入修正有效应力原理来考虑孔隙水压力的作用,建立了岩体弹塑性损伤本构模型,给出了损伤变量定义及演化方程。针对该模型在数值求解过程中存在的奇异点问题,从主应力空间推导了弹塑性损伤模型的完全隐式返回映射求解算法,包括弹性预测、塑性修正和损伤修正三个步骤。通过ABAQUS软件的用户子程序接口Umat,实现了弹塑性损伤模型的数值求解过程。采用单轴、三轴压缩试验和隧道算例对模型算法进行验证和分析,结果表明,所建立的HB损伤本构模型能够很好地描述岩体材料的力学特性,在实际岩体工程的损伤模拟中效果令人满意,计算结果对工程有指导意义。     

模拟退火算法在线热源反问题数值求解中的应用

提出采用模拟退火算法(simulated annealing,SA)来数值求解线热源反问题.探讨了如何设计算法使之适合反问题求解,并给出了算法求解的伪代码;通过线源正问题的模拟数据,使用设计的SA算法进行反问题求解,以此来验证算法求解的准确性和可靠性,并对一组实测数据进行了计算.结果表明,该算法不但可以实现两个参数同时、快速反演,而且具有求解精度高,对初始条件依赖少,编制容易等优点.     

Finite element analysis of elastoplastic modeling: application to one-dimensional loading of as-received and pre-strained materials

A constitutive modeling is proposed to describe the elastoplastic behavior of materials. The model response for uniaxial loading of as-received and pre-strained materials is investigated. The most important characteristic of the model for as-received material is the consideration of a von Mises yield criterion that is valid from onset of loading. The same concept as the one for as-received material is followed to deal with the elastoplastic behavior of pre-strained material. However, a proportionality concept is also introduced in this case to calculate the plastic deformation. After the implementation of the model in ABAQUS procedure by creation of an appropriate user material subroutine, the results of finite element analysis are studied and validated by some experimental results obtained from uniaxial test.     

考虑剪切和扭转变形的有限质点法纤维梁单元研究

为提高有限质点法分析结构弹塑性问题的精度,该文将纤维梁模型融入有限质点法的计算求解框架中,推导了考虑剪切变形和扭转变形的有限质点法纤维梁单元的质点内力求解公式。该单元采用Timoshenko梁理论描述梁截面变形状态,以单元纯变形分量表示截面上任一点的位移,并结合纤维材料的三维本构关系以考虑弯曲、剪切和扭转变形之间的耦合作用。数值算例的分析结果表明,该纤维梁单元能够有效地模拟结构弹塑性行为,相较于塑性铰法具有更高的精度。     

An efficient algorithm to estimate material parameters of biphasic mixtures

The paper describes an inverse numerical experimental method to determine material parameters for biological tissues. Measured field quantities are compared to calculated field quantities. The field equations are solved with the finite element method, using an assumed constitutive model and estimations of the material parameters. The parameter estimates are improved iteratively by means of an algorithm that calls the finite element program as a subroutine. The paper is focused on biological materials that can be described as biphasic mixtures. An efficient recursive algorithm is presented. All parameters are determined on the basis of displacements and pressures measured at different positions within the material at subsequent points in time. A pseudo‐analytical approach is used to determine the sensitivity matrix. The algorithm has been tested in a simulation of an experiment on a mixture of a solid and a fluid. It appears that for this example an iterative loop to determine the material parameters requires no more than 30 per cent more CPU‐time than one straightforward analysis of the problem. Copyright © 1999 John Wiley & Sons, Ltd.     

A new inverse analysis approach for multi-region heat conduction BEM using complex-variable-differentiation method

This paper presents a new inverse analysis approach for identifying material properties and unknown geometries for multi-region problems using the Boundary Element Method (BEM). In this approach, the material properties and coordinates of an unknown region boundary are taken as the optimization variables, and the sensitivity coefficients are computed by the Complex-Variable-Differentiation Method (CVDM). Due to the use of CVDM, the sensitivity coefficients can be accurately determined in a way that is as simple to use as the Finite Difference Method (FDM) and an inverse analysis for a complex composite structure can be easily performed through a similar procedure to the direct computation. Although basic integral equations are presented for heat conduction problems, the application of the proposed algorithm to other problems, such as elastic problems, is straightforward. Two numerical examples are given to demonstrate the potential of the proposed approach.     

An exact element method

This paper presents a new element based method through a treatment of a one dimensional model problem. The case solved in this work is of a rod with variable cross-sectional area, supported along its length by variable stiffness elastic foundation, and loaded with variable axial load. The variations of all the quantities are taken as general polynomials. Using this method the exact terms in the stiffness matrix are found using the solution for the differential equation (up to any desired accuracy). The exact solution is obtained using one element for each segment with continuously varying properties, and the displacements and stresses are exact all along the rod.     

A shear-flexible triangular finite element model for laminated composite plates

Formulation and numerical evaluation of a shear-flexible triangular laminated composite plate finite element is presented in this paper. The element has three nodes at its vertices, and displacements and rotations along with their first derivatives have been chosen as nodal degrees-of-freedom. Computation of element matrices is highly simplified by employing a shape function subroutine, and an optimal numerical integration scheme has been used to improve the performance. The element has satisfactory rate of convergence and acceptable accuracy with mesh refinement for thick as well as thin plates of both homogeneous isotropic and laminated anisotropic materials. The numerical studies also suggest that reliable prediction of the behaviour of laminated composite plates necessitates the use of higher order shear-flexible finite element models, and the proposed finite element appears to have some advantages over available elements.     

Low-impulse blast behaviour of fibre-metal laminates

This paper presents three dimensional (3D) finite element (FE) models of the low-impulse localised blast loading response of fibre-metal laminates (FMLs) based on an 2024-O aluminium alloy and a woven glass-fibre/polypropylene composite (GFPP). A vectorized user material subroutine (VUMAT) is developed to define the mechanical constitutive behaviour and Hashin’s 3D failure criteria incorporating strain-rate effects in the GFPP. In order to apply localised blast loading, a user subroutine VDLOAD is used to model the pressure distribution over the exposed area of the plate. These subroutines are implemented into the commercial finite element code ABAQUS/Explicit to model the deformation and failure mechanisms in FMLs. The FE models consider FMLs based on various stacking configurations. Both the transient and permanent displacements of the laminates are investigated. Good correlation is obtained between the measured experimental and numerical displacements, the panel deformations and failure modes. By using the validated models, parametric studies can be carried out to optimise the blast resistance of FMLs based on a range of stacking sequences and layer thicknesses.     

A globally convergent algorithm for transportation continuous network design problem

The continuous network design problem (CNDP) is characterized by a bilevel programming model, in which the upper level problem is generally to minimize the total system cost under limited expenditure, while at the lower level the network users make choices with regard to route conditions following the user equilibrium principle. In this paper, the bilevel programming model for CNDP is transformed into a single level convex programming problem by virtue of an optimal-value function tool and the relationship between System Optimum (SO) and User Equilibrium (UE). By exploring the inherent nature of the CNDP, the optimal-value function for the lower level user equilibrium problem is proved to be continuously differentiable and its derivative in link capacity enhancement can be obtained efficiently by implementing user equilibrium assignment subroutine. However, the reaction (or response) function between the upper and lower level problem is implicit and its gradient is difficult to obtain. Although, here we approximately express the gradient with the difference concept at each iteration, based on the method of successive averages (MSA), we propose a globally convergent algorithm to solve the single level convex programming problem. Comparing with widely used heuristic algorithms, such as sensitivity analysis based (SAB) method, the proposed algorithm needs not strong hypothesis conditions and complex computation for the inverse matrix. Finally, a numerical example is presented to compare the proposed method with some existing algorithms.     

基于灵敏度分析的复合材料组分参数识别方法

为了获取准确的复合材料细观模型,提出了一种复合材料组分参数识别方法。在细观单向碳纤维增强树脂基复合材料（CFRP）有限元模型基础上,构造静态位移场对复合材料组分弹性参数的灵敏度矩阵,以测量位移和有限元计算位移差的二范数为目标函数,针对待识别参数量纲差异较大的问题,利用相对灵敏度提高材料组分弹性参数识别的精度和效率。以纤维均匀分布的复合材料平面模型和纤维随机分布的复合材料实体模型为研究对象,验证所提出组分参数识别方法的有效性和准确性。此外,研究了测点数目及测量误差对识别结果的影响。结果表明：本文提出的复合材料组分参数识别方法在测点数目变化和测量误差影响下仍然稳定。     

An inverse method for determining elastic material properties and a material interface

A numerical procedure which integrates optimization, finite element analysis and automatic finite element mesh generation is developed for solving a two-dimensional inverse/parameter estimation problem in solid mechanics. The problem consists of determining the location and size of a circular inclusion in a finite matrix and the elastic material properties of the inclusion and the matrix. Traction and displacement boundary conditions sufficient for solving a direct problem are applied to the boundary of the domain. In addition, displacements are measured at discrete points on the part of the boundary where the tractions are prescribed. The inverse problem is solved using a modified Levenberg-Marquardt method to match the measured displacements to a finite element model solution which depends on the unknown parameters. Numerical experiments are presented to show how different factors in the problem and the solution procedure influence the accuracy of the estimated parameters.