Reissner型板表面裂纹应力强度因子的线弹簧-不连续位移边界积分方程解法

本文由Reissner型板的不连续位移基本解，根据Betti互换定理，导出了Reissuer型板的不连续位移边界积分方程；结合平面问题的不连续位移边界积分方程─—边界元方法和线弹簧模型，给出了Rrissner型板表面裂纹应力强度因子的线弹簧-不连续位移边界积分方程解法。     

Reissner裂板表面裂纹应力强度因子的线弹簧—不连续位移…

本文由Ｒｅｉｓｓｎｅｒ型板的不连续位移基本解，根据Ｂｅｔｔｉ互换定理，导出了Ｒｅｉｓｓｎｅｒ型板的不连续位移边界积分方程，结合平面问题的不连续位移边界积分方程－－边界元方法和线弹簧模型，给出了Ｒｅｉｓｓｎｅｒ型板表面裂纹应力强度因子的线弹簧－不连续位移边界积分方程解法。     

弹性理论几类导数边界积分方程之间的变换关系

导数场边界积分方程通常难以应用，因为存在着超奇异主值积分的计算障碍。弹性理论中有几类不同的位移导数边界积分方程，本文采用算子δij和∈ij(排列张量)作用于这些导数边界积分方程，做一系列变换，原有的超奇异积分被正则化为强奇异积分获解。从而建立了这些位移导数边界积分方程之间的转换关系，它们均可以归结为自然边界积分方程。自然边界积分方程仅存在容易计算的Cauchy主值积分。自然边界积分方程分析可直接获得边界应力和位移导数。     

薄板稳定问题的边界元法

本文基于小挠度薄板弯曲问题的基本解,建立了求解薄板稳定问题的边界积分方程,并计算了若干算例,结果表明用边界元法求解薄板的稳定问题是行之有效的.     

按位移求解弹性力学平面问题的解析构造解研究

针对弹性力学平面问题偏微分方程组的位移法,引入多指数函数,提出了含未知参量的指数函数、三角函数和线性函数组合形式的位移函数解析构造解。建立了任意边界条件与未知参量之间所满足的非线性代数方程组,确定了边界节点条件和未知参量的数量关系。推导了具有对称位移边界的位移函数解析构造解。构建了位移函数构造解的精度判定方法。求解了具有对称位移边界条件的矩形板算例的位移解与误差分析。研究结果可为位移法理论和实际工程应用提供参考。     

扁球壳的边界元几何非线性分析

本文从壳体位移的三个微分方程出发，采用付立叶积分变换的基本解，利用加权残值法推导了几何非线性边界积分方程。这种基本解的壳体边界元法类似于板的非线性边界元法，各种变量物理意义明确，能方便地处理各种复杂边界条件及有开口情况。文末算例说明本文方法的可行性、收敛性和精确性，并与二变量边界单元法或有限元结果相比较，吻合较好。     

扁球壳的边界元几何非线性分析

本文从壳体位移的三个微分方程出发，采用付立叶积分变换的基本解，利用加权残值法推导了几何非线性边界积分方程。这种基本解的壳体边界元法类似于板的非线性边界元法，各种变量物理意义明确，能方便地处理各种复杂边界条件及有开口情况。文末算例说明本文方法的可行性、收敛性和精确性，并与二变量边界单元法或有限元结果相比较，吻合较好。     

计入横向剪切变形时层合板位移差分解法

在考虑横向剪切变形对层合板弹性解的影响时，本文提出一种数值计算方法。由边界条件给出边界结点位移的表达式，根据薄板的经典理论和一阶横向剪切变形理论导出位移增量所满足的平衡微分方程，引用经典理论计算的横向剪力修正了荷载列阵。致使在较粗的网格划分时、宽广的层合板长厚比范围内，仍能得到与解析解颇为一致的数值解。     

梯度材料中矩形裂纹的对偶边界元方法分析

采用对偶边界元方法分析了梯度材料中的矩形裂纹. 该方法基于层状材料基本解,以非裂纹边界的位移和面力以及裂纹面的间断位移作为未知量. 位移边界积分方程的源点配置在非裂纹边界上,面力边界积分方程的源点配置在裂纹面上. 发展了边界积分方程中不同类型奇异积分的数值方法. 借助层状材料基本解,采用分层方法逼近梯度材料夹层沿厚度方向力学参数的变化. 与均匀介质中矩形裂纹的数值解对比,建议方法可以获得高精度的计算结果. 最后,分析了梯度材料中均匀张应力作用下矩形裂纹的应力强度因子,讨论了梯度材料非均匀参数、夹层厚度和裂纹与夹层之间相对位置对应力强度因子的影响.      

弹性力学位移构造解待定参数的优化算法研究

从弹性力学平面问题位移解析构造通解的基本原理出发,针对含未知参量的位移函数确定问题,分析了应力边界、位移边界、混合边界的离散节点需要满足的函数关系,构建了以位移解析构造解中未知参量为设计变量,以边界离散节点满足的代数关系为目标函数的优化问题,提出了获得任意边界平面问题的位移构造解中未知参量的优化求解算法,编制了任意节点边界条件的未知参量通用求解程序,给定误差计算的判定方法。求解了平面应力问题的具体实例,通过本文算法与有限元计算结果的误差对比,表明所研究算法的正确性,为任意边界的复杂工程问题求解提供依据。     

The solution of elastostatic problems and the principles of minimum potential energy,minimum complementary work,under fuzzy boundary conditions

A Solution of elastostatic problem is defined on the basis of set theory and extended to the cases with fuzzy boundary conditions. Extension is also given for the principles of minimum potential energy and minimum complementary work with fuzzy boundary conditions. A quasisolution of an elastostatic problem is defined as an approximate solution with boundary conditions most close to the original. And the existance of quasisolution of an elastostatic problem can be proved on the basis of certain assumptions and the theorem of minimum elementary potential energy.     

考虑最小尺寸精确控制的SIMP和MMC混合拓扑优化方法

拓扑优化作为一种先进设计方法, 已被成功用于多个学科领域优化问题求解, 但从拓扑优化结果到其工程应用之间仍存在诸多阻碍, 如在结构设计中存在难以制造的小孔或边界裂缝和单铰链连接等. 在拓扑优化设计阶段考虑结构最小尺寸控制是解决上述问题的一种有效手段. 在最小尺寸控制的结构拓扑优化方法中, 通用性较强的固体各向同性材料惩罚法SIMP优化结果边界模糊不光滑, 包含精确几何信息的移动变形组件法MMC对初始布局具有较强依赖性. 本文提出一种考虑最小尺寸精确控制的SIMP和MMC混合拓扑优化方法. 所提方法继承了二者优势, 避免了各自缺点. 在该方法中, 首先采用活跃轮廓算法ACWE获取SIMP输出的拓扑结构边界轮廓数据, 提出了SIMP优化结果到MMC组件初始布局的映射方法. 其次, 通过引入组件的3个长度变量, 建立了半圆形末端的多变形组件拓扑描述函数模型. 最后, 以组件厚度变量为约束, 构建了考虑结构最小尺寸控制的拓扑优化模型. 采用最小柔度问题和柔性机构问题验证了所提方法的有效性. 数值结果表明, 所提方法在无需额外约束的条件下, 仅通过组件厚度变量下限设置, 可实现整体结构的最小尺寸精确控制, 并获得了具有全局光滑的拓扑结构边界.      

A note on the minimum complementary energy theorem

In this paper we propose a very simple and clear method whichcan prove that the minimum complementary energy theorem isequivalent to the condition of single-valued displacementsand displacement boundary condition of the deformable body.     

On the unilateral contact problem of structures with a non quadratic strain energy density

The analysis of structures with “unilateral contact” boundary conditions is considered. The stress-strain relations are nonlinear and they are derived from a non quadratic strain energy density by “subdifferentiation”. It is proved that for the inequality constrained boundary value problem the “principles” of virtual and of complementary virtual work hold in an inequality form constituting a variational inequality. The theorems of minimum potential and complementary energy are proved to be valid to account for this type of boundary conditions. These theorems are used to formulate the analysis as a nonlinear programming problem. A numerical example of a structure having the “unilateral contact” boundary condition illustrates the theory.     

任意有限个平行移动荷载作用下简支梁绝对最大挠度的解析算法研究

利用能量原理中的最小势能原理以及多元函数的极值原理，得到了简支梁在任意有限个平行移动荷载作用下的挠度方程与绝对最大挠度的解析算式。建立的可能位移函数既满足了位移几何边界条件，又满足了静力边界条件，故足可以保证简支梁的挠度计算精度。     

Determination of crack spacing and penetration due to shrinkage of a solidifying layer

A method based on energy minimisation is used to determine the spacing and penetration of a regular array of cracks in a layer of material whose thickness is increasing as it solidifies from a liquid. After solidification, the slab shrinks and subsequently cracks due to internal stresses. A simple Stefan solidification model is used to determine the thickness of the slab as time progresses as well as the temperature profile in the slab. The key feature of the results is that a minimum crack spacing occurs early in the solidification process and this minimum defines a basic spacing for the crack array. The minimum spacing occurs for a range of constraints (boundary conditions) and thermal profiles in the material, indicating the robustness of the phenomenon. Cracks propagating with the unique minimum spacing are subject to a period doubling instability that acts to coarsen the crack pattern, which brings the crack spacing close to the minimum energy state for later time. Good numerical comparison between the crack spacings predicted by energy minimisation and those observed in basalt columns is demonstrated.     

The interaction of a shock wave with the boundary layer in a reflected shock tunnel

The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature and the Mach number profiles in the boundary layer in reflected shock fixed coordinates has been obtained. To account for equilibrium real gas effects of nitrogen, the numerical results show that the minimum Mach number in the boundary layer has been moved from the wall into the boundary layer with the increasing of the incident shock Mach number. The minimum Mach number, the shock angle in the bifurcated foot and the jet velocity along the wall to the end plate are reduced owing to the increasing of the area of nozzle throat. The numerical results are in good agreement with measurements.     

一种岩石断裂韧度试样应力强度因子的三维边界元法标定

用三维边界元法(BEM)标定了一种岩石断裂韧度试样的柔度,求出了这种试样的平均无量纲应力强度因子(SIF),并得到了对应于最大载荷时的临界裂纹长度和平均无量纲SIF的最小值.     

A fast and reliable overset unstructured grids approach

A cell-centred overset unstructured grids approach is developed.In this approach,the intergrid boundary is initially established based on the wall distance from the cell centre,and is then optimized.To accelerate the intergrid-boundary definition much more,a neighbor-toneighbor donor search algorithm based on advancing-front method is modified with the help of minimum cuboid boxes.To simplify the communications between different grid cell types and to obtain second-order spatial accuracy,a new interpolation method is constructed based on linear reconstruction,which employs only one layer of fringe cells along the intergrid boundary.For unsteady flows with relative motion,the intergrid boundary can be redefined fast and automatically.Several numerical results show that the present dynamic overset unstructured grids approach is accurate and reliable.     

Remarks of some problems for rectangular thin plates with free edges on elastic foundations

For the bending,stability and vibrations of rectangular thin plates with free edges onelastic foundations,in this paper we give a flexural function which exactly satisfies not onlyall the boundary conditions on free edges but also the conditions at free corner points.Applying energy variation principle,we give equations defining parameters in flexuralfunction,stability equation,frequency equation,and general formulae of minimum criticalforce and minimum eigenfrequency as well.