【作者】 刘建涛；

【导师】 杜平安； Gea HaeChang；

【作者基本信息】 电子科技大学 ， 机械电子工程， 2012， 博士

【摘要】 薄壁结构由于质量轻、承载性能优良,被广泛用于航空航天、船舶、汽车、压力容器等领域。此类结构的应力和应变受几何形状、边界条件等因素影响较大,除特殊情况外难以获得解析解,因此薄壁结构的基础理论和模拟方法一直是研究的热点。本文针对薄壁结构响应特性数值模拟、稳定性分析和疲劳寿命预测研究中存在的问题,进行了如下内容的研究:1.薄壁结构响应特性有限元模拟及误差修正方法研究基于薄壁结构的控制方程和有限元离散原理,系统研究了包含倒角、凸台、孔洞等特征的曲面薄壁结构的有限元离散特点和建模方法。同时基于离散过程的理论推导,研究了有限尺寸曲面薄壁结构的离散误差产生机理和计算应力的修正方法。以探针为对象,分析了曲面薄壁结构的屈曲载荷随几何尺寸和外形的变化规律,为结构稳定性分析和优化奠定了基础。2.薄壁结构基础振动数值计算方法研究基于连续体基础振动原理和有限元实现过程,建立了求解薄壁结构简谐基础振动和冲击问题的静力等效载荷法。通过施加静力等效节点载荷将简谐基础振动问题转化为基础固定的简谐响应问题,进而获得结构响应的幅值和时间历程,克服了现有方法的不足。3.薄壁结构疲劳裂纹形成寿命预测及结果显示方法研究基于疲劳累积损伤理论,建立了准静态和动态载荷作用下薄壁结构疲劳裂纹形成寿命的预测方法和有限元模拟及显示流程。同时以探针为对象,基于四点雨流计数法和双线性累积损伤准则,通过自编程序实现了薄壁结构疲劳寿命的自动预测和结果的图形化显示。4.薄壁结构疲劳裂纹扩展寿命理论模型和预测方法研究通过现有疲劳裂纹扩展速率影响因素特点和试验数据规律的研究,提出了描述试样厚度、循环应力比和材料参数等对疲劳裂纹扩展速率影响的综合影响系数模型。通过与Newman、Huang和Codrington模型对裂纹张开应力和有效应力强度因子范围比预测结果的对比,验证了模型的有效性。基于综合影响系数模型和钝化复锐理论开发了常幅和变幅载荷下疲劳裂纹扩展的通用模型,并通过试验数据和现有模型的预测结果验证了通用模型的有效性。5.薄壁结构疲劳裂纹扩展过程数值模拟方法研究基于第4部分的理论模型,采用扩展有限元和水平集法建立了常幅和变幅载荷下疲劳裂纹扩展过程的扩展有限元模拟流程和矩阵更新算法,并通过现有试验数据验证了理论模型、扩展有限元模拟流程和求解算法的有效性。6.基于ANSYS的薄壁结构数值仿真和疲劳寿命预测专用软件开发基于第1~5部分的研究成果,并以探针应用需求出发,开发了薄壁结构响应特性专用仿真和疲劳寿命预测软件。本论文取得的主要创新成果如下:1.提出了求解连续体简谐基础振动和冲击问题的静力等效载荷法该方法避免了瞬态计算方法中存在刚体位移、算法稳定性、模型规模等限制,以及反映谱法存在振形峰值组合规则的限制,可用于求解单点和多点非正弦(余弦)基础振动、冲击和瞬态响应等问题。2.建立了反映材料特性、试样尺寸、载荷特征等参数对疲劳裂纹扩展速率影响的综合影响系数模型该模型显式反映了材料特性、试样尺寸、循环应力比等因素对裂纹张开比和有效应力强度因子范围比及疲劳裂纹扩展速率的影响。通过代入试样参数、试验条件和材料参数可预估结构和试样的疲劳特性,可为试验设计、试样选型和实际应用提供指导。3.提出了常幅和变幅载荷下结构疲劳裂纹扩展过程的通用模型该模型能有效且定量描述单峰过载、单峰低载、序列加载和谱载荷等产生的延迟和加速效应,具有明确的断裂力学的物理含义,适用于描述各种韧性材料、不同加载条件和不同试样类型的疲劳裂纹扩展过程。4.建立了结构疲劳裂纹扩展过程的扩展有限元模拟流程和平衡方程更新算法该流程能有效模拟实际结构的疲劳裂纹扩展过程,同时通过水平集函数将模型分割为更新和非更新区域,疲劳裂纹扩展过程中仅需对更新区域的数据进行计算和集成,大大提高了求解效率。更多还原

【Abstract】 Thin-walled structures are widely used in aeronautics, watercrafts, automobiles, vessels and so on because of its light weight and good load-carring property. But the theoretical stress and strain results of these structures can be hardly derived due to the influence of geometrical shape, boundary conditions and so on. Hence, the basic theory and numcerical simulation methods of these structures have been the research focus for decades. In the dissertation, the following topics are studied based on the problems existing in numerical simulation, stability analysis and fatigue life prediction:1. Research on the finite element modeling method and error correction method of the response characteristics of thin-walled structuresThe modeling method and discrete characteristics of curved thin-walled structures with chamfers, bosses, holes and so on are studied systematically based on its governing equations and the discrete principles of finite element method (FEM) at first. Then, the error mechanism of discrete preocess and the correction method of the calculated stress results are studied by theoretical deduction and a display method of the corrected stress results is proposed. Finally, a probe inside the turboprop is taken as an example to analyze the variation of buckling load and structure geometric features thoroughly, which lays a foundation for structure stability analysis and optimization.2. Research on the finite element method for analyzing thin-walled structures under foundation vibrationThe dissertation proposes a new method named static inertia method to calculate the structural response under foundation vibration with FEM by theoretical deduction. The original problem is transformed into an ordinary vibration problem with fixed base by applying the equivalent nodal loads from the new method and the response results can be calculated accordingly. The new method overcomes the restrictions of existing methods and provides a new thought to handle the problems under flush and anharmonic vibration from the base.3. Research on the fatigue life prediction of thin-walled structures and display method of fatigue livesBased on the cumulative fative damage theory, the dissertation estabilishes a procedure for fatigue life prediction of thin-walled structures under quasi-static and dynamic loads as well as a display method of fatigue lives with FEM package. Moreover, A program is developed accordingly and a probe is taken as an example to verify the procedure and the display method. The results indicate that the procedure above is effective and the display method is feasible.4.Research on the fatigue crack growth (FCG) model and prediction method of thin-walled structuresThe dissertation presents a new model named integrative influence factor model (IIF) to account for the intergrative influence of specimen thickness, cyclic stress ratio, material property and so forth on FCG rates by analyzing the characteristics of existing models and experimental results. Furthermore, predictions of the crack opening ratioγand effective stress intensity factor range ratio U by Newman, Huang and Codrington models are used to validate the IIF model, which indicates that the IIF model predicts the results more accurately and describes the influence of Poisson’s ratio, specimen thickness, R ratio and so on explicitly. In addition, a general model of fatigue crack growth in ductile alloys under variable amplitude loading is developed based on the IIF model and Passivation-Lancet theory. Several sets of test data are used to validate the general model and the predictions are in good agreement with the test data.5.Research on the numerical simulation method of FCG processIn the dissertation, a new procedure of numerical simulation of FCG process under constant and variable amplitude loading is established via extended finite element method (XFEM), level set method and the general model in part 4. In addition, a matrix update algorithm based on LDU decomposition is introduced. After that, the validity of the procedure and the matrix updata algorithm are verified with several sets of test data from academic publications, which shows great consistency.6. Research on the redevelopment of ANSYS package for numerical simulation and fatigue life prediction of thin-walled structuresThe dissertation proposes a method for secondary development of ANSYS package based on the conclusions in part 1~5 and a special software for numerical simulation and fatigue life prediction of probes is developed accordingly. The originalities of this dissertation are summarized as follows:1. Estabilishment of the static inertia method for simulation of the continua responses under foundation vibrationThis method overcomes the restrictions of existing models and can be extended to the problems under single- and multi-points anharmonic vibration from the base, flush, transient loading and so on.2. Development of the IIF model to account for the influence of Poisson’s ratio, specimen thickness, R ratio and so forth on FCG rates The IIF model describes the influece of material property, specimen dimensions, cyclic stress ratio and so forth onγ, U and FCG rates explicitly. Furthermore, the fatigue property of real structures and specimens can be estimated by substituting the geometric parameter, experimental conditions and material parameter into IIF model. It is very helpful for fatigue tests, specimen selection and real application.3. Estabilishment of the general model for FCG rates under constant and variable amplitude loadingThe model describes the retardation and acceleration effect of single overloading, single underloading, sequential loading and spetrum loading effectively and quantitatively, owns explicit physical meaning and is suitable for modeling the FCG process of structures with various ductile materials under different loading conditions.4. Development of a numerical simulation procedure of FCG process with XFEM and a new matrix update algorithm for equilibrium equationThe procedure inherits the advantages of level set method and XFEM, and describes the FCG process of real structures effectively. In addition, the whole continua domain is divided into two parts by the level set functions in the procedure, only the nodal data in updating region needs to be calculated and integrated, which improves the computational efficiency significantly.更多还原