基于敏度分析的拉压不同模量桁架问题的数值分析

利用光滑函数技术,提出光滑化的拉压不同弹性模量问题的应力应变关系,与有限元方法相结合,建立了拉压不同模量一维连续体与桁架结构的数值求解模型,推导了敏度计算公式,采用Newton-Raphson算法进行求解.数值结果表明,本文算法具有较高的计算精度和收敛速度.     

共轭梯度法求解非线性多宗量稳态传热反问题

应用共轭梯度法求解非线性多宗量稳态热传导反问题。采用八节点的等参单元在空间上进行离散,建立了便于敏度分析的非线性正演和反演的有限元模型,可直接求导进行敏度分析。给出了相关的数值验证,对测量误差及测点数目的影响作了初步探讨,结果表明,采用的算法能够对非线性稳态热传导中导热系数和边界条件联合反问题进行有效的求解,并具有较高精度。     

基于同伦技术的偶应力反问题求解

引入Bregman距离构造同伦函数,建立偶应力反问题的一种求解模式,可以对偶应力理论相关参数进行识别.利用有限元技术,建立了偶应力正/反问题数值求解模型,该模型不仅考虑了非均质的影响,而且也便于反问题的敏度分析.文中给出了相关的数值算例,并对信息误差和不同的函数形式计算结果做了初步探讨,得到满意的结果.数值算例表明该模...     

应力和位移约束下桁架拓扑优化的有无复合体方法

按照独立连续拓扑变量的思想,将有无复合体模型由构造应力约束问题发展为应力与位移约束问题,用于桁架结构拓扑优化．基于该文提出的位移约束与拓扑变量关系的近似显式,建立了具有应力、位移约束下桁架结构拓扑优化的有无复合体模型,用序列二次规划算法求解．数值结果令人满意．这一工作表明独立连续拓扑变量的提出对于结构拓扑优化的研究是有价值的。     

基于响应面方法的桁架截面敏度分析和优化

把响应面方法引入桁架截面优化中,将应力和位移约束近似表达为桁架截面倒变量的线性函数。为拟合响应面,基于中心复合和单纯形试验设计方法开发了中心对称和拟单纯形试验设计两种方法,既可保证约束近似精度,又降低了结构分析计算量。对于桁架结构重量目标函数,直接推出倒变量的二阶形式,以桁架重量最小为目标的优化问题构造为标准的二次规划模型。将响应面方法计算的位移对设计变量的敏度与莫尔积分方法的近似显式进行了对比。以MSC.Patran为平台的数值算例表明:结合响应面方法,应用序列二次规划对问题进行寻优,其收敛精度及稳定性都可获得保障。     

高斯牛顿技术求解偶应力反问题

建立了便于敏度分析的偶应力反问题数值求解模型,给出了直接法和伴随法两种敏度计算格式.在反演计算中采用了高斯牛顿技术对未知本构参数进行识别,探讨了测点数目、初值选取和数据噪音对反演结果的影响,数值算例给出了令人满意的结果.     

时域自适应算法求解移动荷载下梁的多宗量反问题

通过一种时域自适应算法,建立了求解变速移动荷载下梁的多宗量反问题的数值模型,可同时识别移动荷载和梁的物性参数.正问题采用时域自适应算法和FEM建模,并可由此方便地推导敏度公式;在反问题求解中采用Levenberg-Marquardt法,计算表明该方法具有较好的抗不适定性.通过两个算例,对所提算法进行了数值验证,并探讨了噪声和测点的变化对反演结果的影响,结果令人满意.     

多宗量瞬态热传导反演识别

引入Bregman距离加权函数,建立了多宗量瞬态热传导反演的一种求解模式.时域上采用精细算法,分别建立了便于敏度分析的有限元正/反演模型,应用同伦算法进行反问题求解,对导热系数和边界条件等宗量进行有效的组合识别.对信息误差和计算效率作了探讨,并给出了相应的数值验证.     

单侧接触约束下桁架拓扑优化的若干结果

对考虑应力和无摩擦单侧接触位移约束的桁架拓扑优化问题进行了研究,采用解析方法,通过对典型算例不同初始接触间隙下的拓扑优化解的讨论,发现这一优化问题中存在解不唯一现象,研究也表明,接触状态对结构拓扑有一定影响,不同初始接触间隙可能导致不同的拓扑结构,对利用数值方法该问题进行了研究,为克服结构拓扑优化中奇异最优解问题,采用ε松弛方法建立桁架拓扑优化模型列式,并利用双层优化方法求解本拓扑优化问题,第一层,通过求解与原接触问题等价的二次规划问题来进行结构接触分析;第二层,利用第一层得到的位移及应力,采用ε-松弛方法进行结构拓扑优化。     

平面膜结构拓扑优化的有无复合体方法

将作者对桁架在应力约束下结构拓扑优化的有无复合体模型发展到平面膜结构在应力、位移约束下结构拓扑优化的建模与求解。同时提出了该模型的有效解法,获得了令人满意的数值结果。本文工作表明独立连续拓扑变量的提出对于结构拓扑优化的研究是有意义的。     

结构优化半解析灵敏度分析的改进算法

提出了结构半解析灵敏度分析的改进算法,该算法实现简便,对于设计变量摄动步长具有极佳的数值稳定特性。首先,从总体角度推导静力问题半解析法灵敏度分析新算法,提出了位移与应力灵敏度列式,并给出了算法实施途径;然后,将此思路推广于自振频率、屈曲临界荷载和瞬态响应等多种问题,提出了相应的计算步骤。以梁单元与壳单元等典型结构为例,开展了多个算例测试。测试表明,改进算法计算精度和效率均有提升,特别是设计变量步长有更大的数值稳定区域,为复杂工程结构形状优化的灵敏度分析提供了新途径。     

Design sensitivity analysis for parameters affecting geometry,elastic–viscoplastic material constant and boundary condition by consistent tangent operator-based boundary element method

This paper presents a design sensitivity analysis method by the consistent tangent operator concept-based boundary element implicit algorithm. The design variables for sensitivity analysis include geometry parameters, elastic–viscoplastic material parameters and boundary condition parameters. Based on small strain theory, Perzyna’s elastic–viscoplastic material constitutive relation with a mixed hardening model and two flow functions is considered in the sensitivity analysis. The related elastic–viscoplastic radial return algorithm and the formula of elastic–viscoplastic consistent tangent operator are derived and discussed. Based on the direct differentiation approach, the incremental boundary integral equations and related algorithms for both geometric and elastic–viscoplastic sensitivity analysis are developed. A 2D boundary element program for geometry sensitivity, elastic–viscoplastic material constant sensitivity and boundary condition sensitivity has been developed. Comparison and discussion with the results of this paper, analytical solution and finite element code ANSYS for four plane strain numerical examples are presented finally.     

基于拓扑优化的结构弹性成像方法

弹性模量是工程材料重要的性能参数, 可以衡量物体抵抗弹性变形的能力. 弹性成像是一种通过弹性模量表征生物体组织物理特性的医学成像方法. 为了将弹性成像应用于机械装备结构的缺陷识别, 提高弹性成像的局部表征和全局识别能力, 提出一种基于拓扑优化的结构弹性成像方法. 受拓扑优化理论启发, 采用结构离散单元的相对密度(弹性模量系数)作为弹性成像参数来表征损伤程度, 建立成像参数与弹性模量的插值模型, 基于有限元模型构建损伤表征、结构模型与物理响应的映射关系. 以损伤结构和无损结构位移响应的最小二乘为目标函数, 以成像参数上下限为约束, 建立结构弹性成像的优化模型. 以伴随法推导弹性成像问题的灵敏度, 并详细给出了弹性成像反演的数值实施方式. 二维悬臂梁和米歇尔梁算例表明, 本文提出的基于拓扑优化的弹性成像方法无需先验损伤信息, 可有效实现均质/非均质、单/多缺陷结构的弹性成像, 且弹性成像结果不依赖于特定的边界条件, 进一步将弹性成像方法扩展至三维悬臂梁问题验证了其通用性.      

Loosening of elastic inclusions

A numerical method is presented for simulating the occurrence of localized slip and separation along the interfaces of multiple, randomly distributed, circular elastic inclusions in an infinite elastic plane. The method is an extension of a direct boundary integral approach previously described elsewhere for solving problems involving perfectly bonded circular inclusions. Here, we allow displacement discontinuities to develop along the inclusion/matrix interfaces in accordance with a linear Mohr–Coulomb yield condition combined with a tensile strength cut-off. The displacements, tractions, and displacement discontinuities on the inclusion boundaries are all represented by truncated Fourier series, and an explicit iterative algorithm is adopted to determine zones of slip and separation under the prevailing loading conditions. Several examples are given to demonstrate the accuracy and generality of the approach.     

Domain Decomposition Methods for Sensitivity Analysis of a Nonlinear Aeroelasticity Problem

Abstract

We consider the nonlinear aeroelasticity problem of the interaction between a viscous, incompressible fluid and Lin elastic solid undergoing large displacement. The non-linearities of the problem formulation include the solid and fluid governing equations. as well as thc dependence of the How geometry on the solid deformation. The resulting coupling is thus two-way. We develop domain-decomposition methods for solution and sensitivity analysis of the coupled problem. The domain decomposition is in the form of a block-Gauss-Seidel-like prcconditioncr that decomposes ihc coupled-domain problem into distinct nonovcrlapping fluid and solid subdotnain problems. The preconditioner thus enables exploitation or single-domain algorithms for solid and fluid mechanics discretization and solution. On the other hand, two-way fluid-solid coupling is retained within the residuals, which is essential for correct sensitivities. Sensitivities of field quantities can be found with little additional work beyond that required for solving the coupled fluid-solid system. The methodology developed here is illustrated by the solution of a problem of viscous incompressible flow about an infinite clastic cylinder. Sensitivities of the resulting velocity and displacement fields with respect to elastic modulus and fluid viscosity are computed.     

The elastic response of a cohesive aggregate—a discrete element model with coupled particle interaction

A model is presented for the deformation of a cohesive aggregate of elastic particles that incorporates two important effects of large-sized inter-particle junctions. A finite element model is used to derive a particle response rule, for both normal and tangential relative deformations between pairs of particles. This model agrees with the Hertzian contact theory for small junctions, and is valid for junctions as large as half the nominal particle size. Further, the aggregate model uses elastic superposition to account for the coupled force–displacement response due to the simultaneous displacement of all of the neighbors of each particle in the aggregate. A particle stiffness matrix is developed, relating the forces at each junction to the three displacement degrees of freedom at all of the neighboring-particle junctions. The particle response satisfies force and moment equilibrium, so that the model is properly posed to allow for rigid rotation of the particle without introducing rotational degrees of freedom. A computer-simulated sintering algorithm is used to generate a random particle packing, and the stiffness matrix is derived for each particle. The effective elastic response is then estimated using a mean field or affine displacement calculation, and is also found exactly by a discrete element model, solving for the equilibrium response of the aggregate to uniform-strain boundary conditions. Both the estimate and the exact solution compare favorably with experimental data for the bulk modulus of sintered alumina, whereas Hertzian contact-based models underestimate the modulus significantly. Poisson's ratio is, however, accurately determined only by the full equilibrium discrete element solution, and shown to depend significantly on whether or not rigid particle rotation is permitted in the model. Moreover, this discrete element model is sufficiently robust, so it can be applied to problems involving non-homogeneous deformations in such cohesive aggregates.     

计及表面能的应变梯度理论本构参数识别

本文提出利用静态位移信息对一种计及表面能的应变梯度理论本构参数进行识别的求解策略.基于Vardoulakis和Sulem的计及表面能的简单线性应变梯度理论,文献[13]给出了伯努力-欧拉梁弯曲问题的正演解析模型,本文将其反演归结为两个带有不等式约束的非线性规划问题.在此基础上,采用黄金分割一维搜索方法进行求解,给出了数值验证,讨论了信息误差对反演结果的影响.结果显示,这种方法可以用来对应变梯度理论本构参数进行识别,即使在体积和表面能常数非常小的情况下,仍然能够得到满意的结果.     

Analytic elasticity solution of bi-modulus beams under combined loads

A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ≤5. The error also varies with the distributed load patterns.