热冲击下机械结构非线性热力耦合模型的建立

在热弹性耦合理论的基础上，考虑热冲击作用下弹塑性变形功的影响，建立了非线性热力耦合有限元模型。其中包括：基于能量守恒原理建立的非线性瞬态温度场模型；考虑几何非线性及材料非线性的位移场模型；求得改进应力场的最小二乘法模型。基于FEPG软件平台进行了实例求解，计算结果表明了此耦合模型的有效性。此模型的建立，拓展了热力耦合理论的应用范围，具有较高的工程实用价值。     

TEC结构的三维非线性瞬态温度场分析

热电制冷器(TEC)以其体积小、作用速度快及无噪音等机械制冷无法替代的优点在航空航天和电子工业等领域得到了越来越广泛的应用。本文根据TEC的导热特点,推导了TEC结构稳态温度场的解析解,建立了其瞬态非线性温度场分析的微分方程。利用伽辽金法导出TEC结构热分析的有限元方程,对非线性热分析的有限元方程进行了求解,得到了TEC的稳态温度场和瞬态响应温度场。算例结果表明,本文提出的TEC结构热分析有限元模型具有较高的精度,能够有效地分析TEC的非线性瞬态温度场。     

采用包络-准则法优化考虑瞬态传热的薄板结构

刚度和强度是薄板结构的两个主要性能。在瞬态传热过程中,考虑热-力耦合,随时间和空间变化的非均匀温度场在结构中会引起热变形和热应力,温度场随时间变化的规律和空间分布依赖于板的厚度变化,进而影响板的刚度和强度。因此,考虑瞬态传热的薄板优化问题具有更强的非线性,更加难以求解。本文给出一种包络-准则方法处理这类结构优化问题。首先,针对外力荷载,进行一个结构柔顺性的优化设计;以这一设计为基础,通过瞬态热-力耦合分析及优化准则,计算多个时刻的优化设计变量并取其包络,对上述优化结果进行迭代修正,以消除瞬态温度场作用下较高的局部应力。优化算例表明,该方法对于考虑瞬态传热薄板优化问题有效。     

耦合热弹性接触问题的有限元分析

对于受热的互相接触的弹性体的热负荷分析,需要在接触边界上同时考虑复杂接触传热条件及弹性接触条件,并计及耦合影响.本文对此提出了一个有效的解法——有限元混合法.计算表明:对求解这类复杂的非线性边界条件问题,该法在计算速度和机器存贮上仅比求解一般线性连续体的热负荷问题的花费略有增加以致相当。     

辐射换热下瞬态热-结构分析的一种空间薄壁杆单元

发展了一种用于辐射换热条件下瞬态热-结构分析的空间薄壁杆单元,其截面形式可以是任意形状的闭口截面和单支开口截面。该单元温度场分解为平均温度和多谐摄动温度,沿杆轴方向采用两结点线性插值,沿杆截面周向用三角函数展开,每结点含多个解耦的自由度,其中结点平均温度方程同传统一维温度有限元方程为非线性,各谐摄动温度方程为线性,然后利用Wilson-θ法求解结构的瞬态温度场。本文选择了两节点Ber-noulli直梁单元得到准静态热弹性有限元方程并求解,针对非对称开口截面考虑了翘曲变形及弯扭耦合的影响。温度场引起的等效热载荷不仅包括常规的热轴力,还包括热弯矩以及热双力矩。本文针对不同截面形式的梁单元给出了瞬态温度场以及热变形的验证算例,并通过与商业程序中二维壳元计算结果的比较说明了本文所提出方法的正确性和高效性。     

一类带单侧约束力学问题的变分方法

力学中许多问题如弹塑性问题，弹塑性接触问题、塑性耦合问题，渗流问题等，其约束条件或者边界形态是无法预知的，只能用一组不等式表示，属于非线性问题，经典的变人原理在求解此类问题时只能采取繁琐的迭代过程。     

辐射换热下瞬态热一结构分析的一种空间薄壁杆单元

发展了一种用于辐射换热条件下瞬态热一结构分析的空间薄壁杆单元，其截面形式可以是任意形状的闭口截面和单支开口截面。该单元温度场分解为平均温度和多谐摄动温度，沿杆轴方向采用两结点线性插值，沿杆截面周向用三角函数展开，每结点含多个解耦的自由度，其中结点平均温度方程同传统一维温度有限元方程为非线性，各谐摄动温度方程为线性，然后利用Wilson-θ法求解结构的瞬态温度场。本文选择了两节点Bernoulli直梁单元得到准静态热弹性有限元方程并求解，针对非对称开口截面考虑了翘曲变形及弯扭耦合的影响。温度场引起的等效热载荷不仅包括常规的热轴力，还包括热弯矩以及热双力矩。本文针对不同截面形式的粱单元给出了瞬态温度场以及热变形的验证算例，并通过与商业程序中二维壳元计算结果的比较说明了本文所提出方法的正确性和高效性。     

空间薄壁管结构瞬态温度场、热变形有限元分析

对于辐射换热的薄壁杆件航天结构，为分析其在太空中不同时刻的姿态下的温度场和热变形，构造了一种相对自由度矩形管单元。其基本思想是从2维非线性瞬态热传导方程出发，假设沿矩形管横截面上每边的温度为线性分布，用4个角点的平均温度和温差来表示矩形管横截面上的温度分布，构造了一种1维2结点温度杆单元，该单元每个结点包含平均温度，上下面温差，左右面温差3个自由度；在计算热变形时，此三个广义温度参数分别对应热轴力和2个热弯矩载荷。经与三维有限元计算结果的比较，证明用该单元计算的矩形管温度场和位移场是可靠的。利用这种新型的薄壁矩形管单元和本文作者在其他文章中提出的薄壁圆管单元，可以对非线性换热条件下的复杂空间结构进行比较准确的温度场和热变形有限元分析，最后本文计算了考虑遮挡的太阳能帆板的瞬态温度场和热变形以说明其应用价值。     

点焊瞬态热过程的有限元分析

基于ANSYS有限元分析系统,建立了用于点焊瞬态热过程分析的电热耦合有限元模型．分析中考虑了随温度变化的材料特性参数、相变问题以及对流边界条件等,对点焊过程中的接触问题进行了适当简化,以避免耗时的迭代算法．通过对低碳钢薄板的分析,得到了整个焊接过程的热历程以及焊件各部位的温度分布,并且可以求得焊核及热影响区的形状和尺寸,同时本模型也可用于其它材料的点焊过程分析．     

盘式制动器摩擦界面接触压力分布研究

在考虑具有可变效应的移动热源影响、制动盘与片的弹性影响以及界面摩擦热流影响等的耦合作用下,建立了一个三维瞬态盘式制动器热-结构耦合模型,利用大型有限元软件ANSYS的非线性多场耦合分析方法,分别数值模拟了不同状态下的制动器摩擦接触界面上的压力场分布情况.发现制动接触压力并非均匀分布,而是与制动盘和片的变形、摩擦力以及摩擦热-结构耦合有关.     

接触问题应力分析的混合解法

接触问题是一个极其复杂的非线性问题，单独使用数值方法或实验方法求解应力都有一定的困难．有限元计算与平面光弹性实验相结合的混合法是对接触问题进行应力分析简单而有效的途径．     

A nonlinear,transient finite element method for coupled solvent diffusion and large deformation of hydrogels

Hydrogels are capable of coupled mass transport and large deformation in response to external stimuli. In this paper, a nonlinear, transient finite element formulation is presented for initial boundary value problems associated with swelling and deformation of hydrogels, based on a nonlinear continuum theory that is consistent with classical theory of linear poroelasticity. A mixed finite element method is implemented with implicit time integration. The incompressible or nearly incompressible behavior at the initial stage imposes a constraint to the finite element discretization in order to satisfy the Ladyzhenskaya–Babuska–Brezzi (LBB) condition for stability of the mixed method, similar to linear poroelasticity as well as incompressible elasticity and Stokes flow; failure to choose an appropriate discretization would result in locking and numerical oscillations in transient analysis. To demonstrate the numerical method, two problems of practical interests are considered: constrained swelling and flat-punch indentation of hydrogel layers. Constrained swelling may lead to instantaneous surface instability for a soft hydrogel in a good solvent, which can be regulated by assuming a stiff surface layer. Indentation relaxation of hydrogels is simulated beyond the linear regime under plane strain conditions, in comparison with two elastic limits for the instantaneous and equilibrium states. The effects of Poisson’s ratio and loading rate are discussed. It is concluded that the present finite element method is robust and can be extended to study other transient phenomena in hydrogels.     

Dynamics of Articulated Structures. Part I. Theory

ABSTRACT

A finite element based method is developed for geometrically nonlinear dynamic analysis of spatial articulated structures; i.e., structures in which kinematic connections permit large relative displacement between components that undergo small elastic deformation. Vibration and static correction modes are used to account for linear elastic deformation of components. Kinematic constraints between components are used to define boundary conditions for vibration analysis and loads for static correction mode analysis. Constraint equations between flexible bodies are derived in a systematic way and a Lagrange multiplier formulation is used to generate the coupled large displacement-small deformation equations of motion. A lumped mass finite element structural analysis formulation is used to generate deformation modes. An intermediate-processor is used to calculate time-independent terms in the equations of motion and to generate input data for a large-scale dynamic analysis code that includes coupled effects of geometric nonlinearity and elastic deformation. Examples are presented and the effects of deformation mode selection on dynamic prediction are analyzed in Part II of the paper.     

A FE‐based algorithm for the inverse natural convection problem

Several numerical algorithms for solving inverse natural convection problems are revisited and studied. Our aim is to identify the unknown strength of a time‐varying heat source via a set of coupled nonlinear partial differential equations obtained by the so‐called finite element consistent splitting scheme (CSS) in order to get a good approximation of the unknown heat source from both the measured data and model results, by minimizing a functional that measures discrepancies between model and measured data. Viewed as an optimization problem, the solutions are obtained by means of the conjugate gradient method. A second‐order CSS in time involving the direct problem, the adjoint problem, the sensitivity problem and a system of sensitivity functions is used in order to enhance the numerical accuracy obtained for the unknown heat source function. A spatial discretization of all field equations is implemented using equal‐order and mixed finite element methods. Numerical experiments validate the proposed optimization algorithms that are in good agreement with the existing results. Copyright © 2010 John Wiley & Sons, Ltd.     

Stabilized Crouzeix-Raviart element for the coupled Stokes and Darcy problem

This paper introduces a new stabilized finite element method for the coupled Stokes and Darcy problem based on the nonconforming Crouzeix-Raviart element. Optimal error estimates for the fluid velocity and pressure are derived. A numerical example is presented to verify the theoretical predictions.     

弹性接触问题的形状优化设计方法

设计模型复杂和结构的高度非线性等问题使得目前结构优化技术中很少涉及接触问题。面向对象的有限元法利用了面向对象编程的优点，有效地提高了编程的效率，并便于程序的扩充。在Visual C 软件平台上，开发编制了面向对象的有限元法程序，并对含接触问题的结构进行形状优化设计，重点推导并给出了含接触问题有限元法的灵敏度全解析分析的表达式，包括位移和应力的灵敏度分析、接触条件的灵敏度分析及相应的边界支配方程等。最后通过算例，验证了所提出的优化方法的正确性。     

解三维摩擦接触问题的一个二阶锥线性互补法

针对三维摩擦接触问题的求解,给出了一种基于参变量变分原理的二阶锥线性互补法. 首先,基于三维Coulomb摩擦锥在数学表述上属于二阶锥的事实,利用二阶锥规划对偶理论,建立了三维Coulomb摩擦接触条件的参变量二阶锥线性互补模型,它是二维Coulomb摩擦接触条件参变量线性互补模型在三维情形下的自然推广;随后,利用参变量变分原理与有限元方法,建立了求解三维摩擦接触问题的二阶锥线性互补法. 较之于将三维Coulomb摩擦锥进行显式线性化的线性互补法,该方法无需对三维Coulomb摩擦锥进行线性化,因而在保证精度的前提下所解问题的规模要小很多. 最后通过算例展示了该方法的特点.      

UZAWA TYPE ALGORITHM BASED ON DUAL MIXED VARIATIONAL FORMULATION

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复合材料结构的内部分层及其扩展

本文用接触观点分析了复合材料壳体结构的内部分层问题，建立了求解摩擦接触问题的有限元迭代格式，并采用释放率判据分析分层裂纹的扩展。分层裂纹前缘采用轴对称奇异单元，并了结构的大变形特性。计算表明，层间裂纹呈Ⅱ型扩展趋势。本文同时还分析了层间摩擦系数的影响，并指出分层将导致壳体结构承载能力显著下降。     

Canonical dual finite element method for solving post-buckling problems of a large deformation elastic beam

This paper presents a canonical dual mixed finite element method for the post-buckling analysis of planar beams with large elastic deformations. The mathematical beam model employed in the present work was introduced by Gao in 1996, and is governed by a fourth-order non-linear differential equation. The total potential energy associated with this model is a non-convex functional and can be used to study both the pre- and the post-buckling responses of the beams. Using the so-called canonical duality theory, this non-convex primal variational problem is transformed into a dual problem. In a proper feasible space, the dual variational problem corresponds to a globally concave maximization problem. A mixed finite element method involving both the transverse displacement field and the stress field as approximate element functions is derived from the dual variational problem and used to compute global optimal solutions. Numerical applications are illustrated by several problems with different boundary conditions.