A new analytical formula to compute the step length of Padé approximants in the ANM: Application to buckling structures

In this paper, we propose a new analytical formula to define the next branch in the Asymptotic Numerical Method (ANM) using the Padé approximants. The proposed formula is based on the computation of the relative error of two consecutive Padé approximants. This formula is obtained by developing the relative error with respect to the path parameter. An appropriate matrix formulation is adopted for the computation of this relative error. A comparison between the analytical formula proposed in this paper and the classical continuation Padé approximants using the step length computed numerically using dichotomy method is presented for examples of buckling structures.     

带弹簧支撑超静定结构位移的简化计算方法

针对带有弹性支撑的超静定结构的位移计算问题, 对利用虚功原理得到的位移计 算一般公式进行了进一步推导, 提出了该类结构位移的简化计算方法. 文中计算公式表达形 式简洁, 且与一般刚性支撑超静定结构的位移计算方法一致. 通过与有限元分析结果的对比, 证明了该公式的正确性.     

一般情况下小垂度索的刚度方程及其应用

索单元的刚度随变形而变化,索结构的力学分析是一个典型的几何非线性问题,因而在数值分析中单索的刚度方程显得尤为重要。由于许多文献不常见的单索刚度方程在推导时忽略了索单元元弦向倾的影响,用来进行结构计算尚存在一定的误差。本文因此考虑了影响单元刚度的弦倾角等因素,推导了一般情况下小垂度索的显式表达刚度方程,并运用该刚度方程进行结构数值分析,与采用近似刚度方程的分析结果进行了比较,给出了近似刚度方程与本文     

A New Formula for Evaluating Indentation Toughness in Ceramics

The Lawn-Evans-Marshall model for Vickers-induced crack driving force is widely applied for determining fracture toughness of ceramic materials, yet its simplification that the volumes of Vickers impression and equivalent expanding cavity merely depend on the half-diagonal length of residual impression will bring significant error. In this work, the model is modified by considering the influence of elastic recovery in depth after completely unloading on the volumes. As a result, a new expression for crack driving force is obtained and correspondingly a new fracture toughness formula is presented based on the modified model, which is expressed as the well-known Anstis formula with a different constant multiplied by the ratio of residual impression depth to the maximum indentation depth. Both finite element analysis and experimental results demonstrate the effectiveness of the proposed formula and, especially, that it works much better than Anstis formula on materials with large ratio of hardness to elastic modulus.     

预应力约束下混凝土梁端的边角受压极限承载力分析1）

根据摩尔库伦破坏准则,提出梁端混凝土在预应力钢筋约束下的边角受压极限承载力的计算方法,并得出极限承载力理论值。通过与有限元软件ABAQUS计算出梁端混凝土在预应力钢筋约束下的边角受压极限承载力结果进行比较,发现摩尔库伦破坏准则所得的理论公式与数值分析结果相近,验证了本文推导的理论公式的正确性。该理论公式表明,预应力能较好地改善梁端混凝土的受力状态,提升梁端的极限承载力。     

ANALYSIS OF ULTIMATE BEARING CAPACITY OF PRESTRESSING CONCRETE BEAM END UNDER CORNER PRESSURE

根据摩尔库伦破坏准则，提出梁端混凝土在预应力钢筋约束下的边角受压极限承载力的计算方法，并得出极限承载力理论值.通过与有限元软件ABAQUS计算出梁端混凝土在预应力钢筋约束下的边角受压极限承载力结果进行比较，发现摩尔库伦破坏准则所得的理论公式与数值分析结果相近，验证了本文推导的理论公式的正确性.该理论公式表明，预应力能较好地改善梁端混凝土的受力状态，提升梁端的极限承载力.     

圆外Stokes问题的边界积分公式

针对圆外区域的Stokes问题,利用Fourier展开法,通过自然边界归化得到了一个只与边界速度有关的Stokes问题的边界积分公式.根据此公式及边界速度值,求得区域内速度及压力分布的解析表达式,并通过数值积分的方法进行求解,计算量小,所得速度及压力分布图曲线光滑.最后借助流体软件进行数值计算,结果验证了边界积分公式的正确性、可行性.     

BOUNDARY INTEGRAL FORMULA OF ELASTIC PROBLEMS IN CIRCLE PLANE

IntroductionConcerningtheelasticplaneprobleminaunitcircle ,ZhengShenzhouandZhengXueliangdevelopedaboundaryintegralformulaofthestressfunction[1]:Φ(r,θ) =-( 1 -r2 ) 24π ∫2π0ν( φ)1 -2rcos(θ-φ) r2 dφ　　 12π∫2π011 -2rcos(θ-ω) r2 dω∫2π0μ( φ)1 -cos(ω-φ) dφ　　 1 -r22π∫2π0μ( φ)1 -2rcos(θ -φ) r2 dφ　　 ( 0 ≤r <1 ) ,( 1 )whereμ(θ) =Φ(r,θ) ｜r=1,ν(θ) = Φ n r=1= Φ r r=1.Intheformula ( 1 )theseconditemisastrongsingularintegral,itshouldbeunderstoodasanintegra…     

On the Rayleigh Wave Speed in Orthotropic Elastic Solids

Recently, a formula for the Rayleigh wave speed in an isotropic elastic half-space has been given by Malischewsky and a detailed derivation given by the present authors. This study deals with the generalization of this formula to orthotropic elastic materials and Malischewsky’s formula is recovered as a special case. The formula is obtained using the theory of cubic equations and is expressed as a continuous function of three dimensionless material parameters.     

蜂窝芯层的等效弹性参数

反映蜂窝材料等效弹性参数的Gibson公式结果简单，便于应用然而由于对应于蜂窝壁板伸缩变形的刚度被忽略，导致蜂窝夹层结构数值分析时，芯层材料的弹性矩阵表现出不确定性本文重新考虑了蜂窝壁板的伸缩变形对面内刚度的影响，对Gibson公式进行了修正本本文结果不但克服了Gibson公式的缺陷，同时提出了考虑蜂窝芯层面内刚度的一种简化方案,该方案可以方便地应用于蜂窝夹层结构的计算。     

圆锥积分算法在划船效应补偿算法中的应用

介绍了捷联惯导系统中圆锥补偿算法与划船误差补偿算法之间的相似性；根据它们之间的相似性得出了一简单的公式，该公式能够将一种圆锥补偿算法转换成相应的划船误差补偿算法；此外还给出了该公式的推导过程及几种高精度补偿算法；最后进行了仿真。     

熔喷双槽形喷嘴气体射流流场初探

在熔喷非织造布加工中,气体射流作为工作介质使聚合物熔体实现拉伸,气体射流流场的研究对熔喷气流拉抻数学模型研究非常重要。熔喷双槽形喷嘴形成的流场可以看作两股平面射流的合成。从单个点涡的性质出发,研究了涡偶的性质和涡偶代替射流的可行性。研究表明,在喷丝孔轴线附近,涡偶和射流的速度分布趋势相同,且有比较相近的速度分布,从而说明以涡偶代替射流是可行的。在此基础上,用两个涡偶分别代替两股射流,然后进行合成,推导出两股射流合成后速度分布的理论公式,该公式的计算结果与实验结果吻合较好。将该公式引入熔喷气流拉伸数学模型,预测出的纤维直径与采用经验公式时的预测结果几乎完全相同。结果表明,应用涡偶代替射流推导出的气流速度分布公式能够较好地描述熔喷双槽形喷嘴气体射流流场,可以用于完善熔喷气流拉伸数学模型。     

白铜弹簧丝两级载荷下累积疲劳损伤预测模型

通过对文献中白铜弹簧丝疲劳寿命试验数据的分析,给出了具带存活率的疲劳寿命曲线表达式。在此基础上,建立了两级载荷下累积疲劳损伤及概率分布的预测模型。     

考虑时变效应的面板堆石坝三维湿化变形研究1）

针对堆石料浸水后的湿化变形并不是瞬时产生,而是一个渐进发展过程这一现象,建议将湿化变形进行时变计算。首先采用Prandtl-Reuss流动法则推导了湿化剪切应变分量,然后叠加湿化体积应变分量,获得三维湿化应变分量;通过分析三维湿化应变分量和单轴应力状态下的湿化应变的关系,指出有关文献推导的三维湿化应变分量计算公式不严谨;然后类比于堆石料流变变形计算公式,推导了湿化变形时变计算公式。实例分析表明,湿化引起坝顶沉降随时间逐渐增大,变形稳定的时间与湿化变形速率呈反比关系。     

闭式柴油喷嘴阀体座面的冲击应力计算

介绍按应力波理论推导出的无推杆式低惯量喷油嘴的针问座面冲击应力的计算公式,该式不仅为此类喷油嘴的设计和启喷压力的选择提出了一个可靠的理论依据,也解决了长期以来此类喷油嘴用传统计算公式计算得到的允许启喷压力值与其实际应用的启喷压力值不一致的矛盾．     

The Stress Intensity Factor for an Elliptic Crack Under a Piecewise-Constant Load

A closed approximate solution is given for the stress intensity factor (SIF) at the front of an elliptic crack under uniform loading on the elliptic ring. The solution is constructed by modifying Rice's variational formula that integrally relates the SIFs for two different states on the crack faces. The first state is a combination of the second and principal states such that the total SIF is zero. In this case, Rice's formula reduces to the virtual-displacement principle for a combined loading on the crack faces.     

THREE-DIMENSIONAL WETTING DEFORMATION FOR CONCRETE FACED ROCKFILL DAM CONSIDERING TIME-EFFECT

针对堆石料浸水后的湿化变形并不是瞬时产生,而是一个渐进发展过程这一现象,建议将湿化变形进行时变计算. 首先采用Prandtl-Reuss 流动法则推导了湿化剪切应变分量,然后叠加湿化体积应变分量,获得三维湿化应变分量;通过分析三维湿化应变分量和单轴应力状态下的湿化应变的关系,指出有关文献推导的三维湿化应变分量计算公式不严谨;然后类比于堆石料流变变形计算公式,推导了湿化变形时变计算公式. 实例分析表明,湿化引起坝顶沉降随时间逐渐增大,变形稳定的时间与湿化变形速率呈反比关系.     

多层复合壁构筑物水压爆破药量计算及应用

根据水中爆炸荷载的特点,应用能量准则和声学近似公式,计算出水压爆破作用于构筑物每层壁的等效静载。以声波在各层介质中传播时波速的加权平均值作为构筑物的平均声波波速,计算出结构自振频率。再考虑构筑物的强度和动力特性,以及预期的破坏程度,把每层介质假设为一独立的构筑物,提出了多层复合壁构筑物水压爆破药量计算的模型,并列举了工程实例。     

An upper bound solution for the force of combined backward-torward extrusion

A rigid-triangle velocity field for combined backward-forward extrusion based on the experiments and the slip-line field is proposed in this paper. The flow separation point in the rigid-triangle velocity field is defined in accordance with the slip-line theory. A formula of minimum upper bound solution for the punch pressure of the combined extrusion is derived. The values from this formula are compared with those from the slip-line solution and with experimental results. The formula of upper bound solution can be used in practice.     

Constitutive potential for ductile damaged material and void growth rate

In this paper a general formula for plastic potential including isotropic ductile damage has been presented on the basis of the thermodynamics for irreversible process and intemal variable theory. With this formula the mass conservation law is satisfied and it also contains a series of unknow coefficients which are the function of macro equivalent stress and the average micro equivalent stress and an unknown function which is the function of two generalized forces. The approximate yield surface equation for isotropically damaged materials is developed. Using this equation the void growth rate is calculated for nonlinear material containing voids. The present results are in good agreement with the numerical results given by the cell model.